Investigating the working and limitations of a DIY Spectrophotometer by designing and

testing a low cost prototype.

Raahish Kalaria

Supervisor: Dr. Chirag Jhala

Word Count: 3722

ABSTRACT

The purpose of paper is to investigate the working and limitations of a DIY[i] Spectrophotometer

by designing and testing a low cost prototype. Spectrophotometers have applications in the

field of Chemistry and education, but the designing demonstrates Physics concepts.

Commercial Spectrophotometers are expensive devices and not available in many less

economically developed places for uses in education. The designed Spectrophotometer is

constructed in around 13.38 USD, which is around one fiftieth of the cost of a Commercial

educational Spectrophotometer that the readings were compared to – the Vernier SpectroVis

Plus. The testing was a rigorous process in which a total of 23 solutions of 4 different colours

were used to determine the efficiency of the DIY Spectrophotometer. The results obtained

(graphs of Absorbance against Wavelength) followed similar qualitative trends, with

substantial, but expected quantitative errors (varying amount of deviation for each

wavelength). Thus, the designed Spectrophotometer should not be looked upon as a substitute

for a commercial Spectrophotometer, but an educational tool. The further scope of this

research is remarkable. The DIY Spectrometer can become an effective learning tool for

students in Grades 8, 9 and 10 to teach concepts of Optical Physics, Programming, Electronics,

and Product Design. Suggestions or modifications to the designed model to improve accuracy,

are also given in the paper.

Word Count: 213

[i] Do It Yourself

TABLE OF CONTENTS

1 Introduction ............................................................................................................................ 1

1.1 Research Question ........................................................................................................... 1

1.2 Rationale .......................................................................................................................... 1

1.3 Background Literature ..................................................................................................... 1

2 Design of the Spectrophotometer .......................................................................................... 3

2.1 Operation Mechanism ..................................................................................................... 3

2.2 Diagram of the Apparatus ................................................................................................ 4

2.3 Circuit Diagram ................................................................................................................ 7

2.4 Primary Components ....................................................................................................... 8

2.4.1 Light Source ............................................................................................................... 8

2.4.2 Diffraction grating ..................................................................................................... 9

2.4.3 Light Dependent Resistor (LDR) .............................................................................. 11

2.4.4 Computer (Arduino) ................................................................................................ 14

2.5 Peripheral Components ................................................................................................. 15

2.5.1 Collimator ................................................................................................................ 15

2.5.2 Slit............................................................................................................................ 15

2.5.3 Cuvette .................................................................................................................... 16

2.6 Bill of Materials .............................................................................................................. 17

3 Testing the Spectrophotometer ........................................................................................... 18

3.1 Variables......................................................................................................................... 18

3.1.1 Independent Variable ............................................................................................. 18

3.1.2 Dependent Variable ................................................................................................ 18

3.1.3 Controlled Variables................................................................................................ 18

3.2 Data Collection ............................................................................................................... 20

3.2.1 Construction of the Spectrophotometer ................................................................ 20

3.2.2 Making the stock solutions ..................................................................................... 20

3.2.3 Finding Wavelength with respect to angle of the Servo ........................................ 21

3.2.4 Obtaining readings from DIY Spectrophotometer .................................................. 22

3.2.5 Obtain readings from commercial Spectrophotometer ......................................... 23

3.3 Data Processing .............................................................................................................. 24

4 Analysis of Results ................................................................................................................. 34

4.1 Error Analysis ................................................................................................................. 34

4.2 Additional Sources of Error ............................................................................................ 40

4.3 Findings .......................................................................................................................... 42

5 Further Scope of Investigation .............................................................................................. 43

5.1 Proposed Optimized Model ........................................................................................... 43

5.2 Applications of the DIY Spectrophotometer .................................................................. 43

6 Appendix ............................................................................................................................... 44

Section 1: Working of the Circuit .............................................................................................. 44

Section 2: Comparison between instruments for Light Dispersion .......................................... 45

Section 3: Multiple slit Interference ......................................................................................... 46

Section 4: Program of the Arduino ........................................................................................... 48

Section 5: Building guide of the Spectrophotometer ............................................................... 49

Section 6: Calculations and Preparation of Stock Solutions ..................................................... 57

Section 7: Procedure for finding Wavelength with respect to Theta ....................................... 59

Section 8: Table for organizing collected data from the Arduino ............................................ 61

Section 9: Data obtained from Arduino for all solutions .......................................................... 62

Section 10: Processed data for all solutions ............................................................................. 66

Section 11: Graphs of the solutions with error bars ................................................................. 70

Section 12: Examples of solutions showing increase in error after Absorbance > 2 ................ 72

Section 13: Alternatives to the LDR .......................................................................................... 73

Section 14: Projected cost of the optimized model ................................................................. 75

7 Bibliography .......................................................................................................................... 76

1

1 INTRODUCTION

1.1 RESEARCH QUESTION Investigating the working and limitations of a DIY Spectrophotometer by designing and testing a

low cost prototype.

1.2 RATIONALE Commercially available spectrometers are expensive and uncommon in my city. Through this

research, I wanted to devise a way to design a low cost Spectrophotometer, which can be built

by any student with commonly available materials. This will help the maker to experiment and

learn at a viable cost. Along with this juniors in my high school can construct and understand

the working of a Spectrophotometer.

1.3 BACKGROUND LITERATURE Figure 1.3.1 - Principle of the working of a typical Spectrophotometer[ii][1].

In a typical spectrophotometer, a polychromatic light[iii] is focused onto the Polychromator[iv],

using a Collimator[v]. The focused beam of light falls on the Polychromator, which splits the light

into its constituent wavelengths by generating a spectrum. The slit selects a particular

wavelength of light and allows it to pass through a solution placed in a cuvette that is optically

transparent. The detector then measures the intensity of the light transmitted (IT), and the

[ii] http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Reaction_Rates/Experimental_Determination_of_Kinetcs/Spectrophotometry [iii] White light, which is a mixture of other colours. [iv] A Polychromator is a device which causes the dispersion of white light into a spectrum. For example – A prism, or a diffraction grating (Discussed ahead). [v] A collimator is a device used to focus a beam of light on a spot. Could be a lens, reflector, or any focussing mechanism.

Polychromator

2

intensity of the incident light (I0). The data is collected and processed by a computer, which

outputs the Absorbance.

Absorbance (A) is a ratio indicating the capacity of a substance to absorb a particular

wavelength of light [2]. The mathematical relation between Absorbance and Intensity is [3]:

𝐴 = −𝑙𝑜𝑔10(𝐼𝑇/𝐼0) (1)

A spectrophotometer only works because different liquids selectively absorb different

frequencies of visible light, to different degrees [vi] [4].The dependence of concentration of the

liquid on the absorbance, is expressed by the Beer-Lambert Law [5]:

𝐴 = 𝜖𝐶𝐿 (2)

Where ε is the Molar Absorption Coefficient (mol-1 dm3 cm-1), C is the concentration (mol dm-3),

and L is the path-length or the width of the cuvette (cm).

The spectrometer is widely used in applications in chemistry, but the construction and the

components used, demonstrate complex physics concepts.

[vi] This is because the electrons in the molecules of liquids vibrate at different frequencies. When light of the same frequency strikes the electron, the photon is absorbed. The number of electrons absorbing photons, depends on the number of molecules of the compound present in the liquid, and thus, the concentration. The greater the concentration, greater the absorbance for a specific wavelength.

3

2 DESIGN OF THE SPECTROPHOTOMETER

2.1 OPERATION MECHANISM Figure 2.1.1 - Flowchart representing the working of the designed Spectrophotometer. The loop

is continued until the full spectrum is covered.

Diffraction Grating [vii]

LDR [viii]

Arduino Board [ix]

[vii] A diffraction grating is an optical device that contains closely spaced slits or groves. When a beam of light passes through, the light undergoes the process of diffraction and splits into its constituent wavelengths, forming a spectrum. Diffraction is the phenomena that occurs when a wave passes through a slit. [viii]LDR is a device which alters its resistance based on the intensity of light received. As the intensity of light increases, the electrical resistance decreases. Further details are present in Section 2.4.3 [ix] A microprocessor and microcontroller. (www.arduino.cc)

4

2.2 DIAGRAM OF THE APPARATUS Figure 2.2.1 – Diagrams of the Spectrophotometer from the top

(a)

(b)

Note: The LDR head is embedded on

the inside of the cuvette holder and is

not visible in the representations.

The 3D diagrams are created using

Google Sketchup Pro.

(c) (d)

(e)

(f)

(g)

(h)

(i)

(j) (a)

(b)

(c)

(d)

(e)

(f)

(k)

(j) (k)

5

Figure 2.2.2 – Measurements of the DIY Spectrophotometer

19.3 cm

12

cm

4 cm

3 cm

7 cm

2 cm 2 cm 5 cm

2.5 cm 8 cm

2.5 cm 2.5 cm

0.8 cm

0.8 cm

2 cm 2 cm

4 cm 3 cm

4 cm

5 cm

0.5 mm

5 cm

5 cm

5.7 cm 5.7 cm

12 cm

(a)

(b) (c)

6

Figure 2.2.3 – Working of the DIY Spectrophotometer. The figure shows the effect of the rotation of the servo on the position of the

spectrum and thus, the wavelength of the light passing through the slit.

Position B Position A

Change in

position of

the

spectrum

Slit

DVD Central

maxima

Light Source,

Collimator,

and Servo

(Discussed

ahead)

7

2.3 CIRCUIT DIAGRAM One of the primary aspects of the apparatus is the circuit.

Figure 2.3.1 - Circuit diagram of the electronics used in the spectrophotometer.[x]

The circuit works as a Potential Divider (PD) circuit. The voltage across the LDR (Vout) is

measured, and sent to the Analog input pin (A0). The Voltage input (Vin) is 5V from the AB.

According to Ohm’s Law, the Voltage is directly proportional to resistance[6]. Therefore, as the

Resistance of the LDR (RL) increases, Vout increases. The equation of Vout in this case is[xi][7]:

𝑉𝑜𝑢𝑡 =𝑉𝑖𝑛 × 𝑅𝐿(𝑅𝐿 + 𝑅2)

R2 is the resistance of the additional resistor (150 kΩ). The function of the second resistor is

altering the resolution of Vout. Through experimentation, we found that 150 kΩ is adequate to

bring the readings to a scale having an optimum resolution and hence, a greater sensitivity to

[x] Note: Figure 2.3.1 is a representation of the electrical connections in the circuit. The position of each component in the Spectrophotometer will vary. [xi] See Appendix Section 1 for derivation.

Light

Dependent

Resistor (LDR)

Resistor (150 kΩ)

Potential

divider circuit

Power supply

(5V)

Servo

Analog input pin

Servo Power

supply

Servo data wire (Pin 9)

(3)

8

changes in RL [xii]. The A0 pin reads the voltage and the processor converts it to bytes, the

maximum being 1024 bytes (1 kilobyte).

The other part of the circuit is the servo. The servo shares the 5V power supply of the Arduino

board. The data wire of the servo is connected to Pin 9 of the board, which signals the servo to

rotate to a specific position. The black wires in the figure show the negative terminals

connected to the ground (GND) pin.

2.4 PRIMARY COMPONENTS

2.4.1 Light Source

Figure 2.4.1 – Light source, Collimator, and the Servo in the DIY Spectrophotometer

[xii] Refer the Appendix Section 1 for further details on the working of the circuit

Light Source (Cost

effective Head torch)

Collimator (Reflector inside

the head torch was inverted

and used as a Collimator)

Servo motor (Hitec HS-485HB)

9

2.4.2 Diffraction grating

The principle of the working of a grating is based on the principle of multiple slit interference

[xiii].

Our Spectrophotometer uses a DVD as the grating. DVDs contain numerous concentric lines,

on which data is stored. These lines or groves are like slits on a grating. A spectrum can be

obtained using a prism through the phenomenon of dispersion, but a prism occupies greater

space and the spectrum obtained is narrower, with lesser distance between wavelengths[xiv].

Figure 2.4.2.1 – Stripped DVD in the DIY Spectrophotometer

A DVD contains 1350 lines per mm[8]. The more the lines per mm, the greater the diffraction. A

DVD was used to make the device more cost effective, and to highlight the commonness of

some complex looking materials in the world around us. However, the DVD is not an ultimate

replacement because it contains concentric lines which produce an imperfect spectrum.

However, using a small section of the DVD as the usable section reduces the length if the lines

considered, making them almost straight, just like tangents of a circle[xv].

[xiii] Refer to the Appendix Section 3 for details. [xiv] See Appendix Section 2 for comparison between different Light dispersion devices [xv] Shown in Figure 2.4.2.2.

Temporary white screen

to observe spectrum

Stripped DVD

Light Source

Solid Epoxy putty

holding the DVD

10

Figure 2.4.2.2 - Distribution of lines on a DVD/CD, and the movement of a beam of light across

the ‘usable’ area.[xvi]

Figure 2.4.2.3 – Light falling on the DVD in the DIY Spectrometer

[xvi] Note: Figure 2.4.2.1 does not show the actual lines/grooves, but only their position and direction on the DVD. The lines on a DVD are concentric, and not straight like in a normal diffraction grating. Thus, the spectrum produced, is often distorted. To overcome this, only a small section of the DVD was used as the functional part. Notice that in the small section, the lines become almost straight (tangents of the circle).

12 cm

Example of

a usable

section

Beam of

light

Path of motion

Concentric

Lines or

grooves

In a small section, the

lines are almost

straight (tangents of a

circle)

Temporary white screen

to observe spectrum

Faint spectrum visible (faint

due to external light)

Stripped DVD

Central Maxima of Diffraction

Usable section (Refer to Figure

2.4.2.2)

Beam of light

Light Source

Solid Epoxy putty

holding the DVD

11

In the diffraction pattern, not all wavelengths have the same intensity[xvii]. Since the grating

does not have exactly straight lines or grooves, the wavelength with respect to the angle of

rotation of the servo cannot be calculated accurately using the standard equation. To

overcome this, the Pasco Amadeus[9] was used[xviii].

2.4.3 Light Dependent Resistor (LDR)

The model number of the LDR used is PGM5526, which is a Cadmium sulphide (CdS) resistor.

The sensitivity of an LDR depends on the wavelength. For a particular wavelength, the LDR will

detect a change in intensity more accurately than some other wavelength. This is Relative

Sensitivity (RS).

Figure 2.4.3.1 - The Relative Sensitivity of the LDR to different wavelengths[10]. (From the

manufacturer)

From the RS of LDR, we can predict the trend of the uncertainty in the readings obtained.

The relation between the intensity of light and the resistance of the LDR is expressed by the

formula[11]:

𝐼

𝐼0= (

𝑅𝐿𝑅0)−𝛾

Where I is the intensity of light to be calculated, R0 is the resistance of the LDR at a controlled

intensity, I0 is the intensity of light which was used to measure R0, and ϒ is a constant of the

LDR[xix].

[xvii] As we go away from the Central maxima, the intensity of the light decreases due to the increase in distance from the source. [xviii] Refer Section 3.2.3 for details. [xix] Given in the Datasheet

(4)

The visible

spectrum ranges

from 380 nm to

780 nm.

12

Table 2.4.3.1 - The values for I0, R0, and ϒ of the LDR used in the design[xx]. (Values obtained

from Datasheet)

Constant Value

I0 10 lx

R0 8 < R0 < 20 kΩ ≈ 14 kΩ

ϒ 0.6

Therefore, the equation becomes:

𝐼

10 𝑙𝑥= (

14 𝑘𝛺

𝑅𝐿)0.6

The problem in this equation is that the Intensity is actually in form of the Brightness or

Illuminance[xxi], (unit ‘lux’). It is important to convert the illuminance to intensity to apply the

formula. The formula for converting illuminance to intensity is[12]:

𝑃𝑜𝑤𝑒𝑟 (𝑊) =𝐼𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑛𝑐𝑒 (𝑙𝑥) × 𝐴𝑟𝑒𝑎 (𝑚2)

𝐿𝑢𝑚𝑖𝑛𝑜𝑢𝑠 𝐸𝑓𝑓𝑖𝑐𝑎𝑐𝑦 (𝑙𝑚𝑊)

Since intensity is Power by unit Area;

𝑃𝑜𝑤𝑒𝑟 (𝑊)

𝐴𝑟𝑒𝑎 (𝑚2)= 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 =

𝐼𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑛𝑐𝑒 (𝑙𝑥)

𝐿𝑢𝑚𝑖𝑛𝑜𝑢𝑠 𝐸𝑓𝑓𝑖𝑐𝑎𝑐𝑦 (𝑙𝑚𝑊)

Luminous efficacy (LE) is a wavelength dependent constant which describes the response of

the human eye to a particular wavelength or frequency of light[13]. The LE of the light under

which R0 was measured[xxii] is 15 lm W-1[14]. Therefore, I0 is: 10 𝑙𝑥

15𝑙𝑚𝑊

≈ 0.667 𝑊 𝑚−2

Thus, I becomes:

𝐼 = (14 𝑘𝛺

𝑅𝐿)0.6

× 0.667 𝑊 𝑚−2

The Arduino outputs the resistance in form of Voltage values, scaled between 0 and 1024.

Therefore, the Arduino Reading (Ar) can be converted to voltage, and then using the voltage,

RL can be calculated.

𝑉𝑜𝑢𝑡 =𝐴𝑟1024

× 5𝑉

[xx] http://www.gotronic.fr/pj-1284.pdf. The constants are considered to have no uncertainty. [xxi] A measure of how bright the human eye perceives different wavelengths to be. [xxii] The Luminous Efficacy was measured under a Tungsten Incandescent light bulb, according to the manufacturer.

(5)

(6)

(7)

13

𝑉𝑜𝑢𝑡 =𝑉𝑖𝑛 × 𝑅1(𝑅𝐿 + 𝑅2)

𝐴𝑟1024

× 5𝑉 =5 𝑉 × 𝑅𝐿

(𝑅𝐿 + 150 𝑘𝛺)

Making RL the subject of the formula:

𝑅𝐿 =150000 𝛺 × 𝐴𝑟1024 − 𝐴𝑟

∴ 𝐼 = (14000 𝛺 × (1024 − 𝐴𝑟)

150000 𝛺 × 𝐴𝑟)0.6

× 0.667 𝑊 𝑚−2

As absorbance is the logarithmic function of Intensities according to Beer-Lambert’s Law:

𝐴 = log10 (𝐼𝑠𝑎𝑚𝑝𝑙𝑒

𝐼𝑠𝑜𝑙𝑣𝑒𝑛𝑡)

𝐴 = log10

(

14000 𝛺 × (1024 − 𝐴𝑟𝑠𝑜𝑙𝑣𝑒𝑛𝑡)

150000 𝛺 × 𝐴𝑟𝑠𝑜𝑙𝑣𝑒𝑛𝑡

14000 𝛺 × (1024 − 𝐴𝑟𝑠𝑎𝑚𝑝𝑙𝑒)

150000 𝛺 × 𝐴𝑟𝑠𝑎𝑚𝑝𝑙𝑒 )

0.6

+ log10 (0.667 𝑊 𝑚−2

0.667 𝑊 𝑚−2)

𝐴 = 0.6 log10 (𝐴𝑟𝑠𝑎𝑚𝑝𝑙𝑒 × (1024 − 𝐴𝑟𝑠𝑜𝑙𝑣𝑒𝑛𝑡)

𝐴𝑟𝑠𝑜𝑙𝑣𝑒𝑛𝑡 × (1024 − 𝐴𝑟𝑠𝑎𝑚𝑝𝑙𝑒))

(8)

(3)

Merging (3) and (7)

14

2.4.4 Computer (Arduino)

Figure 2.4.4.1 - Flow of the Arduino program[xxiii]

[xxiii] For the complete code, refer the Appendix Section 6.

Recieving Voltage data from the

potential divider circuit.

Taking 10 samples

Averaging the 10 samples to obtain a whole number

(integer)

Printing the value on the serial

monitor

Signaling the servo to rotate by

1˚

15

2.5 PERIPHERAL COMPONENTS

2.5.1 Collimator

Narrowing the beam using a collimator helps in eliminating unwanted parts of the spectrum

which is formed when light scatters. The narrowed beam also goes through only a part of the

concentric lines, which improves the quality of the spectrum.

2.5.2 Slit

The slit, formed using two razor blades, is exactly rectangular, and thin, but not so thin that it

reduces the intensity of light.

Figure 2.5.2 – Slit in the DIY Spectrophotometer, with width[xxiv]

[xxiv] Note: This image was taken before the part shown was sprayed completely black.

Slit with blue light coming

out (0.50 ± 0.01 mm)

Razor blades covered

with tape

16

2.5.3 Cuvette

The cuvette should be optically pure so that the light can pass through with minimum

attenuation[xxv]. One side of the cuvette will be exposed to light, while the other side will have

an LDR close to it for detection.

Figure 2.5.3 – Image of the Cuvette used in the experiment with the path-length.

The path length of the cuvette is an important factor when equation (2) is used.

[xxv] Loss of intensity.

Path-length = 5.0 mm

Cuvette

17

2.6 BILL OF MATERIALS An important factor to be considered while making the design of the Spectrometer was the

cost. The materials used have to be cost effective and should have the potential to be mass

produced and supplied or maximum application of the design.

Table 2.6.1 - Summary of the materials used and the estimated cost. Note: 1 USD = 63.54

INR[xxvi]

Total Cost: 852 INR ≈ 850 INR ≈ 13.38 USD.

Vernier SpectroVis Plus[15] (used to compare the data in this investigation): 659 USD[xxviii].

[xxvi] http://www.xe.com/currencyconverter/convert/?From=USD&To=INR (12:48 pm, 20th July, 2015) [xxvii] The Controller used in this design is Arduino Uno, which is more expensive (Rs. 515), but there is a cost effective alternative of using a minimalistic ATtiny85 chip. Also, when commercially mass produced, the cost will be greatly reduced as a different IC will be used specific to the one program which is to be executed. [xxviii] Inclusive of the cuvette.

Material Quantity Purpose Cost (INR)

Plywood 1 Casing of the device 50

Head torch 1 Light source 50

Collimator 1 Collimation of light 0

DVD 1 Diffraction grating 20

Servo 1 Rotation of light source 550

Razor blades 2 Slit 1

Cuvette 1 Holding the Sample 10

LDR 1 Sensing light 5

150 kΩ resistor 1 Potential divider circuit 1

Cardboard sheet 1 Internal compartments 5

Electrical Wires ≈100 cm Electrical connections 10

Micro Controller 1 Processing the data 150[xxvii]

18

3 TESTING THE SPECTROPHOTOMETER

3.1 VARIABLES

3.1.1 Independent Variable

The concentration of 5 different solutions used is the independent variable. The wavelength of

light passing through the cuvette is not the independent variable because for each trial, the

change is same. The only change across trials is of the concentration.

3.1.2 Dependent Variable

IT is the dependent variable, which is measured by the LDR[xxix]. The absorption and the

transmission of the liquid at a particular wavelength will be determined based on the change

in intensity.

3.1.3 Controlled Variables

Table 3.1.3 - Summary of the factors that were controlled.

Variable Value How it was controlled

Lines per mm of grating

1350 lines mm-1 [16] Using the same DVD for all the readings.

Position of the grating

The DVD was fixed at the same point throughout.

Brightness of the power source

Maximum possible AA Batteries which were fully charged and give

out full 1.5V were used for all readings.

Axis and point of rotation of light

source

The light source was fixed on a servo motor which was fixed to the base.

LDR sensitivity ϒ = 0.6 The same LDR was used for all readings. LDR resistance

range Dark resistance =

1.0 MΩ

Operation temperature

≈ 27°C Air conditioner was used.

Slit width 0.50 ± 0.01 mm Two razor blades were fixed at a constant

distance.

Position of the LDR The position of the LDR was not change

throughout the investigation.

Position of the cuvette

A cuvette holder was constructed which so that

the cuvette was in the same position.

Path length of the cuvette

5.0 ± 0.1 mm The cuvettes used in the experiment were the

same models from the same manufacturer.

[xxix] The uncertainty in measurement is discussed in later sections.

19

External light The Spectrophotometer was covered completely.

The inside walls were painted jet black to minimize reflection.

Resistance of second resistor

150 kΩ Same resistor was used throughout the

investigation.

Input Voltage from the Arduino

5 V The supply from Arduino is always constant[xxx].

Input Current from the Arduino

450mA[xxxi][17] The current is fairly constant.

[xxx] This is due to an in built 5V DC converter. [xxxi] The Arduino receives around 500mA from the computer’s USB port and around 50mA are used for the internal processing.

20

3.2 DATA COLLECTION

Figure 3.2.1 - Diagram representing the procedure of experimentation

3.2.1 Construction of the Spectrophotometer

For the complete building guide, please refer the Appendix Section 5[xxxii].

3.2.2 Making the stock solutions

Stock solutions of a total of 4 different salts were created, with different concentrations of

each. To make the particular concentration of the solution, a fixed mass of the compound was

added to a 50 ml of distilled water[xxxiii].

Table 3.2.2.1 - Masses of salt required to prepare 50 ml of desired concentrations.

Compound Color Molar Mass

Mass required (g)

0.1 mol dm-3

0.2 mol dm-3

0.3 mol dm-3

0.4 mol dm-3

0.5 mol dm-3

Nickel Sulphate hexahydrate Green 262.86 1.314 2.629 3.943 5.257 6.572

Copper sulphate pentahydrate Blue 249.68 1.248 2.497 3.745 4.994 6.242

Potassium dichromate Yellow 294.19 1.471 2.942 4.413 5.884 7.355

Potassium chromate Orange 194.2 0.971 1.942 2.913 3.88422 4.855[xxxiv]

[xxxii] The complete building guide is not included in the main article due to length restrictions. Please refer Appendix Section 5 for a comprehensive guide. The model of the Spectrophotometer created, was inspired from http://www.instructables.com/id/Light-Spectrometer-from-a-head-inspection-lamp/, but significantly dissimilar to it. [xxxiii] For detailed calculations and procedure, please refer the Appendix Section 6. [xxxiv] Note: 0.4 and 0.5 mol dm-3 concentration of Potassium chromate might not be possible to create because the solution gets saturated before this point at room temperature. Heating the solution slightly might dissolve the salt completely.

Design

Construction of the Spectrophotometer

Making the stock solutions

Finding Wavelength with

respect to the angle of the

Servo

Obtaining readings from DIY

Spectrophotometer

(Calibration and Testing)

Obtaining readings from Commercial

Spectrophotometer

Comparing the readings obtained

21

Figure 3.2.2.1 – Picture of the solutions prepared

3.2.3 Finding Wavelength with respect to angle of the Servo

For finding the wavelength at a particular angle, the Pasco Amadeus was used. One end of the

optical fibre connected to the device was placed near the slit, perpendicular to it. Due to this,

the wavelength of light which is separated by the slit will enter the optical fibre and will be

detected. When set in the “Analyse light” mode, the graph created by the device will show a

peak on the corresponding wavelength[xxxv]. The process was repeated 5 times and the average

of the readings was taken.

Table 3.2.3 – Average Value of Wavelength with respect to the position of the servo

Position (°)

Wavelength (nm)

Standard Deviation (± nm)

25 385.17 4.19

24 392.36 3.73

23 407.08 4.80

22 421.03 6.06

21 441.89 5.08

20 461.35 5.58

19 471.58 3.47

18 496.99 3.79

17 507.98 5.32

16 525.69 4.04

15 541.56 6.69

14 559.54 5.68

[xxxv] For the complete procedure and readings, please refer to the Appendix Section 7

Nickel Sulphate

solutions

Copper Sulphate

solutions

Potassium Chromate

solutions

Potassium Dichromate

solutions

22

13 573.82 5.81

12 591.18 4.81

11 613.65 5.82

10 626.21 4.66

9 641.06 6.40

8 666.68 6.92

7 670.76 5.08

6 692.18 5.75

5 713.74 3.14

4 718.47 4.71

3 743.54 6.00

2 763.23 7.78

1 770.15 3.32

3.2.4 Obtaining readings from DIY Spectrophotometer

1. Connect the Arduino board to a PC with the Arduino IDE[xxxvi] installed.

2. Connect the external circuit to the AB as shown in Figure 2.3.1.

3. Download the program from the IDE to the AB.

4. Fill a cuvette with distilled water using a dropper and place it into the cuvette holder.

Figure 3.2.4.1 – Placing the cuvette into the cuvette holder

5. Turn on the light source.

6. Cover the device using the top cover and keep some weight on it to ensure that

external light does not enter.

[xxxvi] https://www.arduino.cc/en/main/software (IDE is Integrated Development Environment)

23

Figure 3.2.4.2 – Collecting the readings from the DIY Spectrophotometer

7. Launch the serial monitor in the IDE[xxxvii]. The monitor will display readings.

8. Press the reset button on the AB when you are ready to start collecting data.

9. After 5 complete cycles highlight and copy the readings[xxxviii]. Paste the data in a

spreadsheet and organize it according to Table 7.8.1[xxxix].

10. Repeat steps 4 to 9 for other salt solutions and record your readings similarly.

After the readings are in place, cover the Spectrophotometer completely such that LDR is in

the darkest condition possible. Measure the Arduino reading. In this research it was 29. This is

the lowest threshold of light. In a commercial spectrophotometer, this reading is the ‘Dark

calibration’. Subtract the minimum number from all readings obtained.

3.2.5 Obtain readings from commercial Spectrophotometer

For this research, the readings from Vernier SpectroVis Plus were taken for comparison[xl]. The

data was then recorded on a spreadsheet.

[xxxvii] Press Ctrl + Shift + M on the PC when the Arduino Programming Environment is open, to launch the serial monitor. [xxxviii] You might have to deselect the “Autoscroll” option in the serial monitor. [xxxix] See Appendix Section 8 [xl] Find procedure here: http://www2.vernier.com/booklets/svis.pdf

24

3.3 DATA PROCESSING For the sample calculation, one of the examples is taken from both – the DIY spectrometer and

the Commercial spectrometer. [xli]

Table 3.3.1 - Arduino readings for Distilled water and 0.1 mol dm-3 Nickel Sulphate solution.

The least count for the bytes is 1 byte.

Wavelength

(nm)

Distilled water Nickel Sulphate 0.1 mol dm-3

Trial 1

(bytes)

Trial 2

(bytes)

Trial 3

(bytes)

Trial 4

(bytes)

Trial 5

(bytes)

Trial 1

(bytes)

Trial 2

(bytes)

Trial 3

(bytes)

Trial 4

(bytes)

Trial 5

(bytes)

385.17 ±4.19 620 617 619 620 620 963 962 962 961 962

392.36 ±3.73 609 607 609 608 609 884 885 884 886 886

407.08 ±4.80 590 590 590 594 593 892 890 892 892 889

421.03 ±6.06 525 523 523 524 526 762 758 759 758 758

441.89 ±5.08 518 516 517 515 515 704 702 701 703 701

461.35 ±5.58 440 439 438 438 438 499 502 501 499 501

471.58 ±3.47 362 359 359 361 360 369 370 368 370 370

496.99 ±3.79 299 298 296 297 298 304 302 302 302 304

507.98 ±5.32 274 272 275 276 275 275 279 275 276 278

525.69 ±4.04 254 253 256 254 256 258 254 258 257 254

541.56 ±6.69 242 244 240 244 240 242 246 242 244 245

559.54 ±5.68 243 240 244 244 240 258 261 262 260 259

573.82 ±5.81 255 254 256 255 254 269 267 269 269 267

591.18 ±4.81 276 275 279 276 278 303 300 302 302 301

613.65 ±5.82 309 310 310 311 313 380 378 380 376 378

626.21 ±4.66 349 353 349 351 351 469 472 473 471 473

641.06 ±6.40 376 376 377 377 374 492 490 489 490 492

666.68 ±6.92 407 405 408 405 407 617 616 617 617 616

670.76 ±5.08 414 415 415 416 414 561 562 562 560 564

692.18 ±5.75 486 484 484 485 486 616 616 618 618 618

713.74 ±3.14 502 506 506 505 505 685 686 685 688 686

718.47 ±4.71 430 430 427 429 427 558 557 558 554 555

743.54 ±6.00 582 584 580 580 581 756 754 753 755 756

763.23 ±7.78 604 604 602 601 603 731 732 732 732 732

770.15 ±3.32 615 615 617 618 616 718 714 714 716 718

The next step is taking the average of the readings across all five trials. The uncertainty of the

average can be calculated using the Standard deviation of the values.

[xli] The complete data obtained for each of the solutions and the final processed data is attached in the Appendix Section 9 and 10 respectively.

25

Sample Calculation for Wavelength = 385.17 nm, Distilled water:

∴ 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 =620 + 617 + 619 + 620 + 620

5= 619.2 ≈ 619 𝑏𝑦𝑡𝑒𝑠

Subtracting the lowest threshold of light, we get:

619 − 29 = 590 𝑏𝑦𝑡𝑒𝑠

Uncertainty:

The standard deviation in values is given by the formula[18]:

𝜎 = √∑ (𝑥𝑖 − 𝑥𝑎𝑣𝑔)

2𝑛𝑖=1

𝑛

𝜎 = 1.3 𝑏𝑦𝑡𝑒𝑠 ≈ 1 𝑏𝑦𝑡𝑒

Sample Calculation for Wavelength = 385.17 nm, Nickel Sulphate 0.1 mol dm-3:

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 =963 + 962 + 962 + 961 + 962

5= 962 𝑏𝑦𝑡𝑒𝑠

962 − 29 = 933 𝑏𝑦𝑡𝑒𝑠

Uncertainty:

Using the standard deviation equation:

𝜎 = 0.7 𝑏𝑦𝑡𝑒𝑠 ≈ 1 𝑏𝑦𝑡𝑒

Similar calculations were done for all the readings.

26

Table 3.3.2 - Average of the readings along with the uncertainties.

Wavelength (nm)

Distilled water Average (bytes)

Nickel Sulphate 0.1 mol dm-3 Average

(bytes)

385.17 ±4.19 590 ±1 933 ±1

392.36 ±3.73 579 ±1 856 ±1

407.08 ±4.80 562 ±2 862 ±1

421.03 ±6.06 495 ±1 730 ±2

441.89 ±5.08 487 ±1 673 ±1

461.35 ±5.58 410 ±1 471 ±1

471.58 ±3.47 331 ±1 340 ±1

496.99 ±3.79 269 ±1 274 ±1

507.98 ±5.32 245 ±2 248 ±2

525.69 ±4.04 226 ±1 227 ±2

541.56 ±6.69 213 ±2 215 ±2

559.54 ±5.68 213 ±2 231 ±2

573.82 ±5.81 226 ±1 239 ±1

591.18 ±4.81 248 ±2 273 ±1

613.65 ±5.82 282 ±2 349 ±2

626.21 ±4.66 322 ±2 443 ±2

641.06 ±6.40 347 ±1 462 ±1

666.68 ±6.92 377 ±1 588 ±1

670.76 ±5.08 386 ±1 533 ±2

692.18 ±5.75 456 ±1 588 ±1

713.74 ±3.14 476 ±2 657 ±1

718.47 ±4.71 400 ±2 527 ±2

743.54 ±6.00 552 ±2 726 ±1

763.23 ±7.78 574 ±1 703 ±0

770.15 ±3.32 587 ±1 687 ±2

In the next step, the formula derived in Section 2.4.3 is applied.

𝐴 = 0.6 log10 (𝐴𝑟𝑠𝑎𝑚𝑝𝑙𝑒 × (1024 − 𝐴𝑟𝑠𝑜𝑙𝑣𝑒𝑛𝑡)

𝐴𝑟𝑠𝑜𝑙𝑣𝑒𝑛𝑡 × (1024 − 𝐴𝑟𝑠𝑎𝑚𝑝𝑙𝑒))

Sample Calculation of Absorbance (Wavelength = 385.17 nm, Nickel Sulphate 0.1 mol dm-3):

𝐴 = (0.6) log10 ((933 ± 1) × (1024 − (590 ± 1))

(590 ± 1) × (1024 − (933 ± 1)))

𝐴 = 0.5264867816 ≈ 0.526

27

Uncertainty:

𝐴 = 0.6 log10

(

(933 ± (

1933 × 100)) × (

(1024 − 590) ± (1

1024 − 590× 100))

(590 ± (1590

× 100)) × ((1024 − 933) ± (1

1024 − 933 × 100)))

𝐴 = 0.6 log10 ((933 ± 0.10%) × (434 ± 0.23%)

(590 ± 0.17%) × (91 ± 1.10%))

𝐴 = 0.6 log10 (404922 ± 0.33%

53690 ± 1.27%)

𝐴 = 0.6 log10(7.542 ± 1.60%)

𝐴 = 0.6 log10( 7.542) ± 0.016 [19]

𝐴 = 0.526 ± 0.016

Similarly, calculations were done for all the values of Absorbance[xlii].

Table 3.3.3 - Absorbance for different wavelengths of 0.1 mol dm-3 Nickel Sulphate solution.

Wavelength (nm)

Absorbance

385.17 ±4.19 0.526 ±0.016

392.36 ±3.73 0.356 ±0.011

407.08 ±4.80 0.385 ±0.015

421.03 ±6.06 0.254 ±0.013

441.89 ±5.08 0.195 ±0.008

461.35 ±5.58 0.063 ±0.008

471.58 ±3.47 0.010 ±0.009

496.99 ±3.79 0.007 ±0.010

507.98 ±5.32 0.004 ±0.021

525.69 ±4.04 0.001 ±0.017

541.56 ±6.69 0.003 ±0.024

559.54 ±5.68 0.027 ±0.023

573.82 ±5.81 0.019 ±0.011

591.18 ±4.81 0.034 ±0.016

613.65 ±5.82 0.080 ±0.018

626.21 ±4.66 0.132 ±0.017

641.06 ±6.40 0.123 ±0.008

666.68 ±6.92 0.219 ±0.008

670.76 ±5.08 0.152 ±0.008

[xlii] See Appendix Section 10 for full processed data, tabulated.

28

692.18 ±5.75 0.135 ±0.008

713.74 ±3.14 0.188 ±0.012

718.47 ±4.71 0.131 ±0.016

743.54 ±6.00 0.191 ±0.013

763.23 ±7.78 0.141 ±0.004

770.15 ±3.32 0.109 ±0.013

Figure 3.3.1 - Graph of Absorbance vs Wavelength for 0.1 mol dm-3 Nickel Sulphate solution.

For the same, the data gathered from the Vernier SpectroVis Plus was plotted on a graph.

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Absorbance vs Wavelength of 0.1 mol dm-3 NiSO4

29

Figure 3.3.2 - Graph of Absorbance vs Wavelength for 0.1 mol dm-3 Nickel Sulphate solution

from DIY Spectrometer (blue) and Vernier SpectroVis Plus (black)[xliii].

Similarly, this process was repeated for all the different solutions and concentrations.

[xliii] The commercial instrument is assumed to have no uncertainty.

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Absorbance vs Wavelength of 0.1 mol dm-3 NiSO4

30

Figure 3.3.3 - Absorbance vs Wavelength of different concentrations of Nickel Sulphate from

Vernier SpectroVis Plus.

Figure 3.3.4 - Absorbance vs Wavelength of different concentrations of Nickel Sulphate from

DIY Spectrometer.[xliv]

[xliv] The error bars are not shown because they are unclear when represented. For the graph with error bars, refer the Appendix Section 11.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Absorbance vs Wavelength of Nickel(II) Sulphate solutions

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Absorbance vs Wavelength of Nickel(II) Sulphate solutions

0.1 mol dm-3

31

Figure 3.3.5 - Absorbance vs Wavelength of different concentrations of Copper Sulphate from

Vernier SpectroVis Plus.

Figure 3.3.6 - Absorbance vs Wavelength of different concentrations of Copper Sulphate from

DIY Spectrophotometer.[xlv]

[xlv] The error bars are not shown because they are unclear when represented. For the graph with error bars, refer the Appendix Section 11. Specific marked areas in the graph are discussed in Section 4.1

0

0.5

1

1.5

2

2.5

3

3.5

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Absorbance vs Wavelength of Copper Sulphate solutions

0

0.5

1

1.5

2

2.5

3

3.5

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Absorbance vs Wavelength of Copper Sulphate solutions

0.3 mol dm-3

0.4 mol dm-3

0.5 mol dm-3

0.2 mol dm-3

0.3 mol dm-3

0.4 mol dm-3

0.5 mol dm-3

High Error region

32

Figure 3.3.7 - Absorbance vs Wavelength of different concentrations of Potassium Chromate

from Vernier SpectroVis Plus.

Figure 3.3.8 - Absorbance vs Wavelength of different concentrations of Potassium Chromate

from DIY Spectrophotometer.[xlvi]

[xlvi] The error bars are not shown because they are unclear when represented. For the graph with error bars, refer the Appendix Section 11. Specific marked areas in the graph are discussed in Section 4.1

0

0.5

1

1.5

2

2.5

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Absorbance vs Wavelength of Potassium Chromate solutions

0.1 mol dm-3

0.2 mol dm-3

0.3 mol dm-3

0.4 mol dm-3

0.5 mol dm-3

-0.5

0

0.5

1

1.5

2

380.00 430.00 480.00 530.00 580.00 630.00 680.00 730.00 780.00

Ab

sorb

ance

Wavelength (nm)

Absorbance vs Wavelength of Potassium Chromate solutions

Unknown feature(discussed in section 4.1)

0.1 mol dm-3

0.2 mol dm-3

0.3 mol dm-3

0.4 mol dm-3

0.5 mol dm-3

Mixing of values

33

Figure 3.3.9 - Absorbance vs Wavelength of different concentrations of Potassium Dichromate

from Vernier SpectroVis Plus.

Figure 3.3.10 - Absorbance vs Wavelength of different concentrations of Potassium

Dichromate from DIY Spectrophotometer.[xlvii]

[xlvii] The error bars are not shown because they are unclear when represented. For the graph with error bars, refer the Appendix Section 11. Specific marked areas in the graph are discussed in Section 4.1

0

0.5

1

1.5

2

2.5

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Absorbance vs Wavelength of Potassium Dichromate solutions

-0.5

0

0.5

1

1.5

2

2.5

380.00 430.00 480.00 530.00 580.00 630.00 680.00 730.00 780.00

Ab

sorb

ance

Wavelength (nm)

Absorbance vs Wavelength of Potassium Dichromate solutions

0.1 mol dm-3

0.2 mol dm-3

0.3 mol dm-3

0.1 mol dm-3

0.2 mol dm-3

0.3 mol dm-3

High Error Region

(a) (b)

34

4 ANALYSIS OF RESULTS

The results obtained are quite encouraging. The salient qualitative features, like the shape and

magnitude of the graph, are maintained in the DIY Spectrometer, though the quantitative data

contains errors. In Figure 3.3.2 the readings obtained follow the same trend that the ideal

values should. This statement holds true for all the other solutions and their graphs.

4.1 ERROR ANALYSIS Possible sources of errors are discussed in the coming sections. Firstly, to quantify the

difference between the ideal value and the observed value of Absorbance, the Quantitative

deviation can be calculated for each reading. If the experimental uncertainty for the points is

lesser than the deviation from the ideal value, we can confirm that there are other sources of

error acting.

𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑎𝑡𝑖𝑣𝑒 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = |𝐼𝑑𝑒𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒|

Sample Calculation of Quantitative Deviation (Wavelength = 385.17 nm, Nickel Sulphate 0.1

mol dm-3):

Experimental Value: 0.526 ± 0.016

Ideal Value: 0.411

𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑎𝑡𝑖𝑣𝑒 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = |0.411 − 0.526|

𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑎𝑡𝑖𝑣𝑒 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 0.115

0.115 > 0.016

𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑎𝑡𝑖𝑣𝑒 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 > 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

This tells us that there are multiple other sources of error in the experiment.

35

Figure 4.1.2 – Quantitative Deviation vs Wavelength for 0.1 mol dm-3 Nickel Sulphate.

The error in Figure 4.1.2 matches the model of RS as the lower wavelengths demonstrate

greater error, the middle wavelengths demonstrate lesser error and the higher wavelengths

demonstrate considerable error. However, there are two points (marked in red) which are

misfits. The error in the region is considerable less. This could be simply due to the

randomness in the investigation in spite of the 5 trials conducted. These anomalies also show

the limitations of this model to analyse the error.

However, the error features in Figure 4.1.2 could be due to the features of the Figure 3.3.4,

which shows greater amount of absorbance in the lower wavelength region and lesser

absorbance in the middle region, for the same solution. Thus, error features in Figure 4.1.2

could be because a greater value of absorbance will have a greater quantitative error than a

smaller value. To ensure that this pattern continues in the other solutions, the Absorbance of a

Copper Sulphate solution is taken into consideration.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

380 430 480 530 580 630 680 730 780

Qu

anti

tati

ve D

evia

tio

n

Wavelength (nm)

Quantitative deviation vs Wavelength

Misfits/Anomaly

High Error region

Lesser Error region

Considerable Error

36

Figure 4.1.3 – Quantitative deviation vs Wavelength of 0.3 mol dm-3 Copper Sulphate solution.

Figure 4.1.3 also, follows the RS model to some extent. The extremely lower wavelengths do

show some error, but not as prominently as the Nickel Sulphate solutions. The mid-wavelength

regions show a lesser error, and the higher wavelengths show a substantial amount of error,

just like the RS model.

However, it is noticeable in the case of Copper Sulphate that the error after a certain value of

absorbance is crossed, increases dramatically. When visually observed the readings are quite

inaccurate in the region when the Absorbance should be greater than 2 in the marked region

in Figure 3.3.6 and Figure 3.3.8 (a). This brings in a different error altogether.

0

0.2

0.4

0.6

0.8

1

1.2

380 430 480 530 580 630 680 730 780

Qu

anti

tati

ve d

evia

tio

n

Wavelength (nm)

Quantitative deviation vs Wavelength

Considerable Error

Lesser Error region

Higher Error region

37

Figure 4.1.4 – Graph of Quantitative error vs Absorbance for 0.3 mol dm-3 Copper sulphate.

Figure 4.1.4 proves that there is a sudden increase in the error after Absorbance has crossed 2.

This is because- after Ar has reached a value above 1020, there is little scope for increase as at

the 1024, the value of the equation inside the logarithmic function becomes zero, the result of

which is undefined. Thus, the only possible maximum value of the Arduino output is 1023.

Also, the resolution of the device reduces as it reaches higher absorbance values as the

function relating Ar and A is logarithmic. Another factor affecting this is the quality of the

spectrum. Near the blue region, there is a reduction in the intensity or the spectrum[xlviii].

This analysis helps in revealing a limitation of the device, which is that the accuracy of

measurement reduces after the absorbance is greater than 2[xlix].

[xlviii] Refer Figure 4.1.5 [xlix] For graphs of other solutions exhibiting a similar behaviour, refer the Appendix Section 12.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3

Qu

anti

tati

ve E

rro

r

Ideal Value of Absorbance

Quantitative Error vs Absorbance

Sharp increase in

Error

38

Another factor governing this result is the quality of the spectrum. The intensity of the lower

and the higher wavelengths is relatively less, and the spectrum is faded [l]. This creates

problems in sensing.

Figure 4.1.5 – Defects in the spectrum [li]

The Figure 4.1.5 highlights some significant problems with the spectrum which is produced,

which could lead to errors. These defects are caused due to the DVD which was used instead

of a grating. The shape of the spectrum turns out to be elliptical. The spectrum is not also

evenly distanced for all wavelengths as it is supposed to be, for instance, the green and red

regions are much longer than they should be in relation to the blue region which is short. This

happens because the concentric grooves on the DVD diffract light in a non-uniformed manner,

where in some rays are diffracted more when they strike a relatively sharply curved part of a

groove. This is also the reason for the elliptical shape. Because of this shape, uneven amounts

of light fall on the LDR for each wavelength, which leads to different resolution for different

wavelengths because the relation between Absorbance and Intensity is logarithmic. Simply

put, the change in an intensity which is faint, is harder to detect than the same change in a

brighter intensity. Furthermore, due to the disproportionate wavelength regions, the step size

between wavelengths will vary in an erratic manner, which is evident. This leads to

uncertainties.

Also, another prominent observation from the quality of the spectrum that is produced is that

at the convergence of the green and blue region, there is an overlap of wavelengths, the blue

wavelength above the green one; which is a result of the concentric lines on the DVD. This

means that at that point, there will be two different wavelengths passing through the slit and

striking the LDR. Perhaps the effect of this confluence can be seen distinctly in the Potassium

Dichromate solution (Figure 3.3.10 (b)).

[l] Refer to Figure 4.1.5 [li] Defects are due to usage of DVD instead of proper Diffraction grating. Image captured from the actual spectrophotometer created

Fading of

higher

wavelengths

Sudden

change in

Wavelength

Overlapping

Green and Blue

wavelengths

Fading of

lower

wavelengths

Spectrum is

elliptically

shaped

39

The sudden change in wavelength observed in Figure 4.1.5 again shows the effect it would

have on the step size of the wavelengths in the experiment.

Overall, considering the sources of errors, there are multiple factors affecting the same thing,

so it is difficult to conclude which factor affects the results the most.

One of the preeminent limitations of the device is that the current hardware of the

spectrophotometer does not allow it to accurately distinguish absorbance values which are

close to each other. For instance, the colours of the five concentrations of Potassium

Chromate are almost impossible to distinguish[lii]. From Figures 3.3.7 and 3.3.8, it is evident

that SpectroVis distinguishes colours better than the DIY spectrophotometer. Here, the

limitation is caused due to the sensing device, which is an LDR, as compared to high accuracy,

expensive light sensors in SpectroVis.

A similar problem is observed in the Potassium Dichromate solutions[liii]. The reason for this

could be the lesser resolution of wavelengths. The difference between each wavelength is

significantly large as compared to SpectroVis.

Additionally, there are interesting features is observed in Figures 3.3.8 and 3.3.10(b)[liv] which

are not present in the ideal graphs[lv]. These ‘anomalies’ in the readings cannot be defined by

any error model discussed previously. Hence, there are various other sources of errors

affecting the DIY Spectrophotometer.

[lii] Refer to marked region in Figure 3.3.8 [liii] Refer to Figures 3.3.9 and 3.3.10 (Marked region) [liv] Marked with circles [lv] Figures 3.3.7 and 3.3.9 respectively

40

4.2 ADDITIONAL SOURCES OF ERROR The table below summarizes the other sources of error in the investigation

Table 4.2.1 – Sources of errors in the experiment, their implications, and improvements; other

than the ones discussed before.

Source of Error Type of Error Description and effects Improvements

Motion of the servo

Random The servo spline does not move with complete accuracy, and on any given fixed position, the servo will rotate slightly (<1°) about that position.

A better quality servo can be used. Also, an alternate mechanism of changing the position of the slit (and keeping the position of the spectrum constant) can be tried as the change in position of the slit will be lateral motion which can be carried out with greater accuracy and not rotational motion like the servo. Small error in the rotational motion can cause a relatively greater lateral error. Alternatively, a stepper motor can be used which is more accurate as it has a greater holding torque. Both of these improvements will increase the cost.

Difference between Wavelengths

Systematic There is a big and variable step size of wavelengths in the device. Due to this, reaction of the solution to the wavelengths in between is unknown and the overall curve of the Absorbance vs wavelength contains errors

The alternate mechanism discussed above can be used. This will drastically reduce the step size. Alternatively, a Charge Coupled Device (CCD) can be used. The spectrum can be projected on the CCD directly, so that the complete spectrum would be captured as it is[lvi].

Optical resistance of the cuvette

Random Any deformations or marks on the cuvette can lead to errors

A high quality and optically pure cuvette can be used. The same cuvette used in the calibration (reading of distilled water) can be used for the other readings.

[lvi] This would increase the cost significantly. Refer Appendix Section 14 for cost analysis of an optimized model.

41

Quality of the spectrum

Systematic Due to the DVD, the quality of the spectrum produced is not as impressive as it would be in a commercial grating[lvii].

A proper commercial grating with straight lines can be used. To prevent fading of certain wavelengths, a high intensity light source can be used. However, this will increase the hindrance of the central maxima to the other wavelengths[lviii].

Response time of the LDR

Random An LDR takes time to adjust to the new light falling on it. Not always is this time uniform. A 2 second gap is given to each wavelength by the program. This might not be enough sometimes. Increasing the time for each position will increase the time for one reading dramatically, which might not be very practical.

A better quality LDR can be used.

RS of the LDR Systematic This can result in greater deviation in the reading in the regions with lesser RS.

A suggested alternative to the LDR is the Light to frequency converter (TSL235R) by SparkFun[lix]. Also, a Charge coupled device (CCD) can be used for the same[lx].

Hindrance to spectrum from Central maxima

Systematic Even though the box is painted in black from the inside, there is still some light reflected from the central maxima, which could enter the slit along with the selected wavelength, causing a disturbance in the readings.

A wall can be constructed between the central maxima and the spectrum to block excess light.

[lvii] For a view of the spectrum and the deformities which lead to uncertainties, refer to Figure 4.1.5. These features will result into errors in the readings. [lviii] Discussed further [lix] Refer to the Appendix Section 14. This would increase the cost, but not very significantly, compared to the accuracy it can provide. For an explanation on the TSL235R, refer the Appendix Section 13. [lx] Refer to Appendix section 14 for a brief analysis.

42

Battery drain from the light source.

Reduction in voltage output from the battery could reduce the intensity of light emitted from the source. A difference between the intensity of light emitted during calibration and testing solutions could result in errors.

The light source can be powered from the mains, connected to a DC adapter, which outputs fixed voltage.

4.3 FINDINGS Some important findings from the investigation are summarized below:

The prime features of the graph of Absorbance vs Wavelength are maintained.

This device can be used in finding unknown concentrations provided that the colours

are visibly distinct.

There is a tremendous scope of improvement in the design to reduce the errors and

convert it into a commercial prototype.

Multiple limitations of the current model have emerged like:

o Limited to detecting absorbance below 2. Can be eliminated by using better

sensors instead of the LDR

o RS of the LDR prevents accurate readings for all wavelengths.

o The device is inefficient in distinguishing solutions which are of almost similar

colours. Can be improved by using better sensors, and accurate wavelength-

shifting mechanisms.

o Less resolution is offered, owing to the larger step size in wavelengths.

Overall, the limitations can be acceptable considering the cost and the availability of the

materials used to make the device.

43

5 FURTHER SCOPE OF INVESTIGATION

The investigation can be taken further by finding the molar absorption co-efficient of

compounds using the Beer Lambert Law. Other scopes are discussed further.

5.1 PROPOSED OPTIMIZED MODEL [lxi] The next version of the DIY Spectrophotometer can have various improvements, while

increasing the cost to some extent for improving the accuracy.

Using a TSL235R Sensor instead of an LDR

Using a commercial grating instead of a DVD. A grating with higher number of lines per

mm[lxii].

Keeping the Light source fixed, and moving the slit area instead. This will ensure

accuracy in the motion and a reduced step size. A stepper motor and a rack and pinion

mechanism can be used.

Converting the Arduino program and circuitry into a commercially viable hardwired

circuit.

A wall between the central maxima and the spectrum.

A light source of higher intensity.

An interface to obtain readings from a computer with alterable number of averages per

reading and other settings, similar to the SpectroVis Plus.

5.2 APPLICATIONS OF THE DIY SPECTROPHOTOMETER This DIY spectrophotometer could have multiple applications:

The model can be useful in education in places with limited resources like my town.

Can be used in applications in Chemistry – finding concentrations, rates of reaction,

etc.

Students can construct the spectrophotometer on their own as it is open source

hardware, and learn more about Electronics, Programming, Optical Physics, and

Machine Design; while maintaining their interest in the subject.

An online data bank can be created where users upload their graphs and spectra like

the PublicLab[20].

[lxi] Refer Appendix Section 14 for cost analysis of an optimized model. [lxii] This will widen the spectrum and thus make the spectrophotometer more compact.

44

6 APPENDIX

SECTION 1: WORKING OF THE CIRCUIT The circuit used in the Spectrophotometer is a simple potential divider circuit. The black wires

represent negative terminal connections and the red wires represent the positive terminal

connections. When a Voltage of 5V is supplied to the circuit from the Arduino, it is divided

amongst the two resistances in the circuit – the 150 kΩ resistor and the LDR. At any given

point, with no light received by the LDR, its resistance is maximum. Thus, according to the

Ohm’s law, the voltage across the LDR will increase (Voltage is directly proportional to

Resistance when the Current is constant). Thus, a dark environment will result in a greater

value of Voltage detected by the Arduino and a well-lit environment will result in a lesser value

of Voltage. From this change in voltage, it is possible to determine the change in Intensity of

light, using the relation discussed in Section 2.3.

A resistance of 150 kΩ was chosen through trial and error, such that the voltage divided across

the LDR could have a larger range, leading to greater sensitivity to light intensities.

The derivation of the Voltage divider rule can be done as follows:

Figure 7.1.1 – Potential Divider circuit [lxiii]

The Ohm’s law is:

𝑉 = 𝐼𝑅

For Vout, the law becomes:

𝑉𝑜𝑢𝑡 = 𝐼2 × 𝑅2

For this circuit, we are assuming that the current is

constant throughout. Thus, the Current I1 = I2 = I. Thus:

𝐼 = 𝐼1 = 𝐼2 =𝑉𝑖𝑛

𝑅1 + 𝑅2

Therefore, when equated with the previous equation,

the final equation we obtain is:

𝑉𝑜𝑢𝑡 = 𝑅2 ×𝑉𝑖𝑛

𝑅1 + 𝑅2

In our case, R2 is the resistance of the LDR and R1 is the fixed resistance.

[lxiii] https://learn.sparkfun.com/tutorials/voltage-dividers/extra-credit-proof

45

SECTION 2: COMPARISON BETWEEN INSTRUMENTS FOR LIGHT DISPERSION

Figure 7.2.1 – Spectrum Produced by Diffraction Grating vs Spectrum produced by Prism

(a)

(b)

Figure 7.2.1 (a) is a spectrum generated by a diffraction grating with 590 lines per mm while

Figure 7.2.1 (b) is a spectrum produced by a prism of 4cm sides. Both the spectra are captured

from the same distance from the screen. It is evident that diffraction is an efficient solution for

dispersion of light, than using a prism. This is because the lines on a grating are quite uniform

and closely spaced, which enables better dispersion of light. A grating with greater lines per

mm will give an even broader spectrum, which is further away from the central maxima.

46

SECTION 3: MULTIPLE SLIT INTERFERENCE Figure 7.3.1 - Multiple slit interference phenomenon[21]

(a) (b)

The equation of the phase difference (S2Z) using trigonometry, is

𝑆2𝑍 = 𝑑 sin (𝜃)

Where d is the distance between the slits, S2 is the second slit, and θ is the angle of incidence of

the light on the grating.

When there is maximum intensity projected, it is a result of constructive interference, when

both the waves superimpose without any phase difference, or a phase difference in multiples

of the wavelength. Thus, for constructive interference, the phase difference must be 𝑛𝜆,

where λ is the wavelength and n represents the order of the considered maxima from the

central maxima. Therefore:

𝑑 sin(𝜃) = 𝑛𝜆

Where θ is very small, as in this case,

sin(𝜃) ≈ 𝜃 ≈ tan(𝜃)

According to Figure ___ (b),

tan(𝜃) =𝑆𝑛𝐷

Where Sn is the distance between the ‘nth’ maxima and the central maxima, and D is the

distance between the slit and the screen.

Thus, when replaced in place of sin(θ), the equation becomes:

𝑆𝑛 =𝑛𝜆𝐷

𝑑

47

Using this equation, the distance of a particular wavelength from the central maxima can be

calculated, and it can be determined which wavelength is passing through the slit at a given

angle of the source. Also, as n increases, the intensity of the maxima, and consequently the

wavelengths of light in the spectrum reduces.

The figure below shows how polychromatic light would be diffracted into its constituent

wavelengths using a diffraction grating.

Figure 7.3.2 - Formation of a spectrum using a diffraction grating.[lxiv]

[lxiv] http://memidastouch.blogspot.in/2011/06/diy-simple-cd-spectroscope.html

Light Source

Diffraction Grating

Central Maxima

Screen

Beam of light

First order maxima (n = 1)

Second order maxima (n = 2)

48

SECTION 4: PROGRAM OF THE ARDUINO #include <Servo.h> // Include the Servo Library const int numReadings = 10; // Number of readings taken before average. int readings[numReadings]; // Array for storing the readings from the Analog pin int index = 0; // the index of the current reading int total = 0; // the total of all the readings int pos = 24; // Position of the servo int inputPin = A0; // Defining the Analog input pin (A0) Servo servo; // Naming the servo ‘servo’. void setup(){ // Function to begin basics of the program pos = 24; // Set position of the servo to 24 (initial position) servo.attach(9); // Define the pin to which the servo is attached Serial.begin(9600); // Open Serial Port for communication at 9600 baud rate Serial.println("Position\tAverage"); // Print the headings for the columns in Serial Monitor initialize(); } // Run the initialize() function

void initialize(){ // This function resets all the readings to 0 for (int thisReading = 0; thisReading < numReadings; thisReading++) readings[thisReading] = 0; } // Set all values of the array to 0

void loop() { // This function collects the data for the device pos = pos > 49 ? 25 : pos; // Setting a range between which the Servo can rotate pos += 1; // Increase the value of ‘pos’ by 1 servo.write(pos); // Move servo to the new ‘pos’ value delay(2000); // Delay of 2 seconds to allow LDR to adjust logReadings(pos); } // Function to record the readings to the array

void logReadings(int p) { for (int thisReading = 0; thisReading < numReadings; thisReading++) readings[thisReading] = analogRead(inputPin); // Record the values from the printArray(p); // Function to Print the array which is recorded initialize(); } // Reset the array

void printArray(int p){ int total; for (int thisReading =0; thisReading < 10; thisReading++){ total = total + readingsthisReading; // Add all the readings to ‘total’ delay(2);} // Short delay for calculations Serial.print(p); // Print ‘p’ which is the position of the array Serial.print("\t"); // Print a tabspace Serial.print(total/numReadings); // Print the Average Serial.print("\n"); }

49

SECTION 5: BUILDING GUIDE OF THE SPECTROPHOTOMETER

The following section contains 3D rendered graphics of how the Spectrophotometer can be

built.

Table 7.5.1 – Materials required for building the Spectrophotometer.

Material Code Dimensions (l x b x h) (cm) Quantity Purpose

Plywood sheets P1 25.4 x 13.4 x 0.7 2 Base and the Cover

Plywood sheets P2 24.0 x 13.0 x 0.7 2 Side walls of the device

Plywood sheets P3 13.4 x 13.0 x 0.7 2 Top and bottom walls

Plywood sheet P4 12.0 x 13.0 x 0.7 1 Centre Partition

Plywood block P5 7.0 x 5.0 x 1.4 1 Base to hold DVD

Cardboard box C1 7.0 x 3.0 x 5.0 1 Mount for Cuvette holder

Cardboard pieces

C2 0.8 x 3.0 x 0.1 3 Cuvette holder

Razor Blades B1 ≈ 2.0 x 4.0 2 Slit

Servo S1 Model no. HS-485HB 1 Rotation of the Light

source

Head lamp L1 Quechua HL 50 1 Light source

DVD D1 12.0 cm diameter 1 Diffraction grating

Light Dependent Resistor

LDR Model no. PGM5526 1 Sensing Light Intensity

Table 7.5.2 – Other additional materials required for constructing the spectrometer.

Material/Equipment Purpose

Grinder Cutting the plywood sheets

Ruler Measuring lengths

Strong Adhesive Attaching Servo to the light source

Furniture Glue Attaching the plywood pieces together

Sanding tool Smoothening the edges of the plywood

Black Acrylic spray Colouring the interiors black

Epoxy Putty Holding the DVD

Scissors Cutting the DVD

Transparent Tape Preparing the Diffraction grating

Note: The procedure contains the hardware part of the Device. For the electrical connections,

refer to the circuit diagram in Figure 2.3.1, and for the Programming, refer Section 2.4.4 and

Appendix Section 4.

50

Procedure:

1. Firstly, cut out all the plywood pieces of the sizes mentioned in Table 6.5.1, by marking

them on a big plywood sheet and then cutting them out using a grinder. Sand their

edges to get a smooth surface.

2. Next, attach a P3 and the two P2s to one of the P1 as shown below using Furniture

Glue.

P1 P1 P2 P2

P3 P3 P4

P1

P3

P2

P2

51

3. Take the head lamp and open up the front end. Remove the dome shaped reflector

from the inside and invert it and attach it outside the head lamp so that the light

emitted by the LED inside is in form of a single beam. Stick the reflector/collimator to

the rim of the device.

4. Until the joints dry, take the Servo, and on the rotating end of the servo, using a strong

adhesive like Fevikwik®, stick the base of the light source as shown below. When you

do it, make sure that the servo is turned to its minimum position.

5. After the joints made in Step 2 have dried, stick the servo contraption into the casing as

shown below using a strong adhesive

Light Source

Servo

2 cm

2 cm

52

6. Now cut and stick P5 in the device as shown in the figure below, using furniture glue.

7. While P5 sticks to P1, the DVD needs to be converted into a diffraction grating. Take

the DVD and using a blade or a knife, separate the two visible layers on it partially.

Once the layers are apart, use your hands to gently pull them apart. Discard the plastic

layer with the branding which is on the top.

8. Using a transparent tape, remove the shining foil from the remaining layer of the DVD

by sticking the transparent tape on it and the slowly removing it. Be careful not to

disturb the surface of the layer by inflicting scratches. Protect it from the glue in the

cellophane tape.

9. After the foil is removed completely, tae the layer and under running water, gently

wash it with liquid soap and a towel to remove the purplish dye. Once the layer is

completely transparent, dry it using a cotton towel.

10. Next, take P4 and using a grinder, make a slit in the area on P4 shown below

2.5 cm

8 cm

P5

6 cm 6 cm

6.5 cm

6.5 cm

3 cm

0.6 cm

Slit region

53

11. The slit can be improved in shape using the sanding tool.

12. Next, attach P4 to the rest of the device like shown in the figure below, using furniture

glue.

13. While the glue settles, ready a small, round lump of Epoxy putty by mixing both of the

semi solids together. Place the putty on P5 on the region shown below.

4 cm

2.5 cm 2.5 cm

2.5 cm

Area to place

Epoxy

54

14. On the epoxy putty, pierce the DVD such that it is places as shown below.

15. Once the DVD is firmly attached, using a pair of scissors, cut out the part from the top

which is emerging out of the box, as shown in the image below.

60°

Portion of DVD cut

off

55

16. Next, take C1 and attach it to the device as shown below using furniture glue.

17. Next, take the B1s and stick it to P5 as shown in the figure below, using a strong

adhesive. Be sure to maintain an equal distance between their edges. Keep a very small

distance of 0.5 mm between the blades. This can be done by keeping a few sheets of

paper between them while sticking them which are exactly 0.5 mm apart, measured

using a micrometer.

2.5 cm 2.5 cm

C1

≈4 cm ≈4 cm

Slit Width of 0.5 mm

B1 B1

56

18. Next, using all three C2s, construct a 3 sided enclosure around the slit as shown below.

19. Take the LDR and pass it from the inside of the cuvette holder, such that the terminals

poke out from the holders as shown below. Make sure the LDR is centred.

20. Finally, the device can be covered completely by attaching the remaining P3 to the

open side using furniture glue, as shown below.

3 cm 3 cm

Cuvette Holder by 3 C2s

LDR head

LDR terminal

P3

57

SECTION 6: CALCULATIONS AND PREPARATION OF STOCK SOLUTIONS Table 7.6.1 – Apparatus required

Name Quantity Uncertainty

50 ml Measuring cylinder 1 ± 0.1 ml

Digital balance 1 ± 0.0005 g

50 ml glass beakers 20 -

Stirrer (Glass rod) 1 -

Watch glass 1 -

Dropper 1 -

Aluminium foil 1 -

Procedure:

1. Place the watch glass on the digital balance and calibrate the balance so that it reads

0.000 gm.

2. Weigh the desired amount of salt (as given in Table __) using the balance.

3. Measure 50 ml of distilled water using the Measuring cylinder and pour it into a 50 ml

beaker.

4. Drop the measured quantity of salt from the watch glass to the beaker. Be sure to scrap

of any remaining particles off the watch glass into the beaker.

5. Using a glass rod/stirrer, stir the solution until all of the salt dissolves.

6. Cover the beaker with a square of aluminium foil to prevent the contents from reacting

with the atmosphere or prevent impurities from falling in. Label the beaker with the

compound name and concentration

7. Repeat steps 1 to 6 for all the salt solutions. In the end, you should have 20 filled

beakers. Arrange them in ascending order based on their concentration for ease of

access.

Figure 7.6.1 – Arrangement of coloured solutions.

58

The stock solutions of various compounds were prepared by adding a calculated amount of the

solid mass to distilled water of a fixed volume. The concentrations of 0.1 to 0.5 mol dm-3

solutions were prepared. This section summarizes the method of calculation used in deciding

the amount of the solid compound that should be added to a specific amount of distilled

water. The volume to be prepared per solution was 50 mL, which was known.

The equation -

𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 =𝑀𝑜𝑙𝑒𝑠

𝑉𝑜𝑙𝑢𝑚𝑒

- was used. The molar mass of the compound (on its container) tells us the mass of the

compound which corresponds to one mole.

𝑀𝑜𝑙𝑎𝑟 𝑀𝑎𝑠𝑠 =𝑀𝑎𝑠𝑠

𝑀𝑜𝑙𝑒𝑠

We know the number of moles we want per unit volume (i.e. 0.1, 0.2, 0.3, etc.). We know the

volume that we want at the end is 50 mL or 50 cm3 which is 0.05 dm3. Thus,

𝑀𝑜𝑙𝑒𝑠 = 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 × 𝑉𝑜𝑙𝑢𝑚𝑒

𝑀𝑎𝑠𝑠 = 𝑀𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 × 𝑀𝑜𝑙𝑒𝑠

Combining the two equations, we get:

𝑀𝑎𝑠𝑠 = 𝑀𝑜𝑙𝑎𝑟 𝑀𝑎𝑠𝑠 × 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 × 𝑉𝑜𝑙𝑢𝑚𝑒

Using this equation, we can find the required mass for creating any of the solutions required in

the investigation. For example, for making 0.1 mol dm-3 of Nickel Sulphate solution, we require

the Nickel sulphate hexahydrate powder which has the Molar Mass of 262.86 g mol-1.

Sample calculation:

Molar Mass = 262.86 g mol-1

Concentration = 0.1 mol dm-3

Volume = 0.05 dm3

𝑀𝑎𝑠𝑠 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 = 262.86 (𝑔

𝑚𝑜𝑙) × 0.1 (

𝑚𝑜𝑙

𝑑𝑚3) × 0.05(𝑑𝑚3)

𝑀𝑎𝑠𝑠 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 = 1.3143 ≈ 1.314 𝑔

The same method was used to calculate the masses required for all the solutions.

59

SECTION 7: PROCEDURE FOR FINDING WAVELENGTH WITH RESPECT TO THETA This section describes how the Wavelength was found with respect to the change in angle of

the servo.

1. A hole was drilled from the back of the Spectrophotometer to the slit region.

2. An optical fibre connected to the Amadeus system was inserted through the hole such

that it was perpendicular to the light falling through the slit.

Figure 7.7.1 – Image of hole drilled from the back to insert optical fibre to the slit.

3. When the light was analysed using the ‘Analyse Light’ option in the software, the graph

showed a peak on the wavelength which was coming through the slit.

4. The position of the servo was changed

5. The process was repeated five times for all the positions of the servo.

6. An average of the values was taken.

Hole

Slit visible

60

Table 7.7.1 - Readings for wavelength with respect to the Position of the servo

Position of the Servo

Trial 1 Trial 2 Trial 3 Trial 4 Trial 5

Wavelength (nm)

Wavelength (nm)

Wavelength (nm)

Wavelength (nm)

Wavelength (nm)

46 386.92 381.53 391.09 380.85 385.45

45 392.59 389.97 387.86 397.61 393.77

44 409.26 407.81 406.02 412.62 399.67

43 422.93 423.16 414.76 429.12 415.19

42 440.60 435.05 449.08 441.20 443.50

41 459.27 464.52 460.65 453.75 468.56

40 476.94 468.12 471.26 469.06 472.55

39 490.76 497.31 500.05 500.03 496.81

38 509.39 516.14 506.56 506.09 501.73

37 524.42 521.80 524.55 532.54 525.14

36 541.62 533.15 537.78 544.42 550.83

35 559.66 566.64 560.76 550.77 559.89

34 574.35 567.76 570.11 573.87 583.01

33 595.42 590.79 586.90 586.11 596.69

32 610.67 619.96 605.72 618.52 613.38

31 628.86 628.16 631.24 622.94 619.87

30 644.62 650.67 636.12 637.37 636.51

29 663.31 656.67 667.46 673.01 672.97

28 672.94 676.63 666.85 664.23 673.17

27 695.13 699.78 692.93 687.50 685.58

26 709.33 714.32 715.88 711.96 717.21

25 722.28 715.21 724.04 712.77 718.03

24 744.56 751.91 735.42 744.62 741.18

23 762.73 770.79 754.83 771.43 756.38

22 772.24 770.07 772.27 771.72 764.44

61

SECTION 8: TABLE FOR ORGANIZING COLLECTED DATA FROM THE ARDUINO This section provides the format of a table that can be used to collect and organize data when

collected from the Arduino Serial Monitor.

Table 7.8.1 – Example Table for recording data from Arduino.

Servo Position (°)

Wavelength (nm)

Arduino Reading of 0.1 mol dm-3 Nickel Sulphate (bytes) (±1)

Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 25 385.17 ±4.19 24 392.36 ±3.73 23 407.08 ±4.80 22 421.03 ±6.06 21 441.89 ±5.08 20 461.35 ±5.58 19 471.58 ±3.47 18 496.99 ±3.79 17 507.98 ±5.32 16 525.69 ±4.04 15 541.56 ±6.69 14 559.54 ±5.68 13 573.82 ±5.81 12 591.18 ±4.81 11 613.65 ±5.82 10 626.21 ±4.66 9 641.06 ±6.40 8 666.68 ±6.92 7 670.76 ±5.08 6 692.18 ±5.75 5 713.74 ±3.14 4 718.47 ±4.71 3 743.54 ±6.00 2 763.23 ±7.78 1 770.15 ±3.32

A similar format can be used for recording data for other solutions.

62

SECTION 9: DATA OBTAINED FROM ARDUINO FOR ALL SOLUTIONS This section provides all the data that was collected from the Arduino for all the solutions of all the concentrations, some of which is used

in the article.

Table 7.9.1 – Arduino Readings for Nickel Sulphate solutions. The uncertainty is 1 byte.

Wavelength (nm)

Nickel Sulphate 0.1 mol dm-3 Nickel Sulphate 0.2 mol dm-3 Nickel Sulphate 0.3 mol dm-3 Nickel Sulphate 0.4 mol dm-3 Nickel Sulphate 0.5 mol dm-3

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

385.17 ±4.19 934 933 933 932 933 1005 1003 1004 1001 1005 1016 1014 1017 1014 1016 1017 1016 1016 1019 1016 1018 1018 1018 1017 1019

392.36 ±3.73 855 856 855 857 857 1012 1009 1011 1011 1008 1016 1015 1019 1018 1016 1019 1019 1022 1021 1021 1022 1023 1024 1021 1022

407.08 ±4.80 863 861 863 863 860 993 994 995 993 992 1010 1014 1012 1011 1012 1023 1020 1019 1022 1022 1020 1022 1023 1020 1020

421.03 ±6.06 733 729 730 729 729 938 935 938 936 937 975 978 977 979 978 980 978 981 981 981 1000 1002 1000 1002 1002

441.89 ±5.08 675 673 672 674 672 689 687 686 687 688 891 887 888 887 890 873 872 870 874 871 848 849 848 849 847

461.35 ±5.58 470 473 472 470 472 507 507 507 508 508 550 551 549 552 552 578 580 581 580 579 606 608 610 610 609

471.58 ±3.47 340 341 339 341 341 381 381 380 381 382 396 396 394 394 395 408 410 410 407 406 423 421 420 424 422

496.99 ±3.79 275 273 273 273 275 289 290 292 292 291 296 296 297 297 299 305 307 304 306 308 311 309 311 309 309

507.98 ±5.32 246 250 246 247 249 260 260 263 262 264 260 261 259 259 259 277 277 275 275 278 280 281 279 281 277

525.69 ±4.04 229 225 229 228 225 243 246 245 243 244 249 251 249 250 247 262 261 264 262 262 269 269 268 267 266

541.56 ±6.69 213 217 213 215 216 235 237 236 236 239 248 246 246 250 246 261 259 258 257 260 270 268 269 268 271

559.54 ±5.68 229 232 233 231 230 256 252 255 253 254 278 278 277 277 276 277 277 281 279 280 302 303 301 302 304

573.82 ±5.81 240 238 240 240 238 275 275 276 274 274 306 307 306 305 306 338 335 338 335 337 363 363 364 361 365

591.18 ±4.81 274 271 273 273 272 355 355 353 356 356 409 408 407 411 411 463 464 464 466 464 519 519 519 516 519

613.65 ±5.82 351 349 351 347 349 436 436 439 436 437 540 542 540 540 538 631 630 630 633 630 712 713 714 715 713

626.21 ±4.66 440 443 444 442 444 609 612 610 610 612 719 719 716 716 719 858 856 858 858 854 920 918 920 918 917

641.06 ±6.40 463 461 460 461 463 671 672 674 673 673 817 817 816 816 818 896 898 898 897 896 957 958 959 960 959

666.68 ±6.92 588 587 588 588 587 772 770 770 772 770 912 910 910 912 911 971 973 974 972 973 993 994 992 992 991

670.76 ±5.08 532 533 533 531 535 791 792 790 789 789 905 903 907 906 904 964 964 964 964 963 994 990 991 994 994

692.18 ±5.75 587 587 589 589 589 811 808 808 807 809 961 960 963 959 963 976 976 977 977 975 1009 1010 1010 1006 1007

713.74 ±3.14 656 657 656 659 657 862 862 864 864 864 957 955 955 953 953 996 996 996 997 993 1010 1010 1010 1014 1012

718.47 ±4.71 529 528 529 525 526 853 853 852 853 853 924 925 923 922 923 975 978 974 975 978 1010 1008 1009 1012 1012

743.54 ±6.00 727 725 724 726 727 890 889 890 888 887 949 951 947 951 949 1000 1000 997 996 999 1016 1012 1013 1012 1016

763.23 ±7.78 702 703 703 703 703 857 860 860 861 860 960 961 961 963 962 983 984 987 987 986 1000 1002 1000 1002 1001

770.15 ±3.32 689 685 685 687 689 898 896 894 894 895 908 909 907 908 909 970 971 967 970 971 992 991 989 990 990

63

Table 7.9.2 – Arduino Readings for Copper Sulphate solutions. The uncertainty is 1 byte

Wavelength (nm)

Copper Sulphate 0.1 mol dm-3 Copper Sulphate 0.2 mol dm-3 Copper Sulphate 0.3 mol dm-3 Copper Sulphate 0.4 mol dm-3 Copper Sulphate 0.5 mol dm-3

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

385.17 ±4.19 834 831 832 833 832 872 873 871 872 873 893 894 891 893 894 849 847 845 846 847 1018 1018 1018 1017 1019

392.36 ±3.73 784 782 784 785 784 704 704 705 703 705 749 745 749 746 748 730 730 730 732 730 1022 1023 1024 1021 1022

407.08 ±4.80 647 650 648 651 649 770 766 766 770 769 700 700 703 701 699 702 702 701 701 702 1020 1022 1023 1020 1020

421.03 ±6.06 654 656 656 657 653 572 575 573 575 572 605 604 601 603 602 657 656 659 658 656 1000 1002 1000 1002 1002

441.89 ±5.08 638 638 639 636 639 551 554 551 551 554 578 579 581 577 578 583 581 582 585 584 848 849 848 849 847

461.35 ±5.58 450 452 452 452 453 564 564 565 564 565 590 586 589 586 586 594 592 590 593 592 606 608 610 610 609

471.58 ±3.47 464 466 463 465 463 378 378 378 378 380 395 397 399 398 398 402 403 401 405 405 423 421 420 424 422

496.99 ±3.79 294 297 297 298 298 309 306 307 307 309 322 322 324 324 323 334 332 333 336 336 311 309 311 309 309

507.98 ±5.32 266 264 265 266 264 278 279 279 282 278 286 288 286 287 286 309 309 311 310 309 280 281 279 281 277

525.69 ±4.04 246 245 245 246 242 258 261 258 261 260 273 272 274 274 275 289 290 291 293 292 269 269 268 267 266

541.56 ±6.69 232 230 233 234 231 245 247 244 247 244 253 253 256 254 253 271 275 271 275 271 270 268 269 268 271

559.54 ±5.68 243 240 241 243 242 272 271 269 268 270 302 302 306 303 304 335 333 333 334 335 302 303 301 302 304

573.82 ±5.81 267 267 264 264 268 310 310 312 312 311 360 362 363 362 363 406 409 407 408 409 363 363 364 361 365

591.18 ±4.81 317 315 313 316 317 393 392 394 391 395 481 482 482 481 484 563 564 565 565 565 519 519 519 516 519

613.65 ±5.82 389 390 391 393 393 508 509 507 510 511 633 633 635 635 635 741 743 741 742 742 712 713 714 715 713

626.21 ±4.66 501 500 499 500 498 681 680 680 682 682 829 826 830 827 830 920 922 921 919 923 920 918 920 918 917

641.06 ±6.40 600 600 603 602 602 819 820 817 817 817 944 946 943 942 946 994 996 994 996 995 957 958 959 960 959

666.68 ±6.92 736 737 738 739 735 941 940 940 941 941 1002 1002 1005 1003 1003 1020 1017 1021 1019 1017 993 994 992 992 991

670.76 ±5.08 795 792 795 796 794 976 977 973 977 977 1014 1015 1014 1017 1016 1022 1024 1020 1021 1022 994 990 991 994 994

692.18 ±5.75 924 921 924 925 923 1016 1014 1013 1013 1014 1024 1021 1023 1024 1023 1021 1023 1023 1022 1023 1009 1010 1010 1006 1007

713.74 ±3.14 967 968 965 967 964 1018 1021 1020 1022 1019 1023 1023 1021 1023 1023 1023 1021 1023 1023 1023 1010 1010 1010 1014 1012

718.47 ±4.71 975 974 974 973 974 1021 1021 1024 1022 1020 1022 1023 1023 1023 1023 1023 1022 1023 1023 1023 1010 1008 1009 1012 1012

743.54 ±6.00 1006 1006 1010 1009 1010 1023 1024 1022 1024 1022 1023 1023 1023 1022 1024 1022 1021 1023 1023 1024 1016 1012 1013 1012 1016

763.23 ±7.78 1011 1009 1012 1008 1011 1023 1022 1022 1023 1023 1022 1023 1023 1024 1022 1023 1023 1024 1022 1022 1000 1002 1000 1002 1001

770.15 ±3.32 1014 1011 1015 1011 1014 1021 1021 1022 1024 1023 1022 1024 1022 1021 1024 1024 1022 1023 1023 1022 992 991 989 990 990

64

Table 7.9.3 - Arduino Readings for Potassium chromate solutions. The uncertainty is 1 byte

Wavelength (nm)

Potassium chromate 0.1 mol dm-3 Potassium chromate 0.2 mol dm-3 Potassium chromate 0.3 mol dm-3 Potassium chromate 0.4 mol dm-3 Potassium chromate 0.5 mol dm-3

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

385.17 ±4.19 1023 1021 1020 1019 1023 1023 1024 1021 1021 1023 1021 1020 1023 1019 1022 1019 1023 1022 1022 1020 1024 1020 1021 1022 1023

392.36 ±3.73 1023 1023 1023 1023 1022 1023 1023 1023 1023 1023 1023 1023 1023 1022 1023 1023 1023 1023 1023 1022 1024 1021 1024 1021 1023

407.08 ±4.80 1022 1023 1023 1023 1022 1023 1023 1023 1023 1023 1021 1023 1022 1022 1023 1023 1023 1022 1021 1023 1023 1022 1024 1022 1021

421.03 ±6.06 1021 1023 1023 1023 1023 1021 1022 1023 1023 1023 1023 1023 1023 1023 1023 1023 1021 1023 1023 1021 1023 1023 1024 1022 1022

441.89 ±5.08 1021 1023 1023 1023 1021 1023 1022 1023 1023 1023 1021 1023 1023 1024 1022 1024 1023 1024 1023 1022 1023 1023 1021 1024 1023

461.35 ±5.58 1019 1018 1019 1021 1020 1023 1020 1024 1021 1023 1022 1023 1022 1024 1020 1021 1019 1020 1022 1020 1020 1020 1022 1021 1019

471.58 ±3.47 989 991 988 987 990 1016 1016 1015 1014 1016 1009 1009 1010 1006 1008 1021 1019 1018 1019 1019 1013 1013 1009 1009 1013

496.99 ±3.79 720 719 718 718 716 819 817 819 818 817 957 956 957 958 956 972 972 972 972 973 964 962 964 963 965

507.98 ±5.32 299 296 298 299 300 305 304 305 308 306 354 352 355 354 354 491 491 487 489 491 436 435 436 435 437

525.69 ±4.04 274 274 275 275 273 231 230 231 228 231 252 251 253 253 253 257 254 257 255 257 269 268 266 267 269

541.56 ±6.69 284 283 283 280 280 260 263 261 262 263 293 297 296 296 296 338 336 337 335 337 331 333 333 332 330

559.54 ±5.68 243 243 241 245 245 222 223 225 221 223 228 228 231 230 231 211 211 212 213 210 236 236 236 234 237

573.82 ±5.81 237 237 235 236 238 222 220 221 222 220 226 227 227 224 225 228 227 229 231 229 232 233 234 234 232

591.18 ±4.81 261 261 261 263 260 257 258 258 257 256 253 257 257 254 256 260 262 260 260 259 260 263 259 260 260

613.65 ±5.82 300 300 297 301 299 295 295 295 296 298 289 291 288 288 290 296 293 293 295 295 299 298 302 298 299

626.21 ±4.66 340 339 340 339 340 326 328 328 330 327 340 341 338 339 340 342 345 346 342 342 345 347 343 343 344

641.06 ±6.40 357 356 358 358 356 362 360 360 362 360 363 363 366 365 362 362 365 363 366 364 368 367 367 368 370

666.68 ±6.92 390 389 390 386 388 386 384 384 385 388 393 391 390 391 391 396 395 395 396 393 396 399 400 400 398

670.76 ±5.08 401 402 401 402 401 395 397 397 398 395 403 402 402 400 402 400 403 404 400 402 398 397 396 396 399

692.18 ±5.75 462 461 461 461 463 482 482 483 480 484 477 476 477 475 476 478 480 478 477 478 486 485 486 485 483

713.74 ±3.14 494 496 494 494 498 493 491 490 490 489 483 485 482 483 481 501 499 497 497 501 494 493 493 497 493

718.47 ±4.71 407 405 405 404 407 420 419 417 421 418 409 408 412 410 410 424 424 424 426 426 422 422 423 419 419

743.54 ±6.00 570 572 568 572 570 565 565 567 568 565 560 561 558 558 562 561 561 563 564 563 567 565 564 567 565

763.23 ±7.78 581 579 580 581 581 585 584 585 585 585 594 596 594 592 592 595 596 594 596 593 600 601 600 601 601

770.15 ±3.32 604 601 605 601 603 603 604 603 600 600 601 604 604 604 601 605 601 605 602 604 604 604 607 604 604

65

Table 7.9.4 - Arduino Readings for Potassium dichromate solutions. The uncertainty is 1 byte.

Wavelength (nm)

Potassium dichromate 0.1 mol dm-3

Potassium dichromate 0.2 mol dm-3

Potassium dichromate 0.3 mol dm-3

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

385.17 ±4.19 1019 1018 1016 1020 1018 1024 1023 1023 1023 1022 1020 1020 1019 1020 1019

392.36 ±3.73 1024 1023 1024 1022 1023 1023 1023 1023 1024 1023 1023 1023 1023 1023 1024

407.08 ±4.80 1023 1023 1022 1024 1021 1021 1022 1024 1021 1023 1021 1023 1021 1023 1023

421.03 ±6.06 1023 1022 1023 1023 1023 1023 1022 1021 1022 1023 1022 1023 1022 1023 1021

441.89 ±5.08 1024 1022 1022 1024 1024 1023 1023 1022 1022 1023 1022 1023 1022 1021 1024

461.35 ±5.58 1020 1020 1020 1020 1023 1023 1023 1021 1023 1023 1023 1023 1023 1024 1020

471.58 ±3.47 1020 1020 1021 1020 1019 1022 1018 1019 1018 1022 1023 1023 1023 1024 1023

496.99 ±3.79 1020 1021 1018 1020 1019 1016 1015 1016 1019 1015 1021 1023 1022 1021 1019

507.98 ±5.32 1021 1020 1017 1017 1018 1019 1022 1019 1023 1023 1021 1022 1020 1021 1023

525.69 ±4.04 965 965 967 964 965 1012 1009 1009 1009 1011 1012 1010 1011 1009 1012

541.56 ±6.69 1013 1013 1013 1013 1012 1019 1018 1018 1021 1019 1021 1019 1020 1020 1018

559.54 ±5.68 344 341 341 342 343 379 379 379 378 382 413 410 410 412 410

573.82 ±5.81 251 252 248 250 249 262 265 262 262 263 279 282 281 283 281

591.18 ±4.81 253 253 252 251 249 256 259 256 256 256 259 259 260 261 258

613.65 ±5.82 282 283 282 282 285 286 285 283 287 287 283 285 283 284 283

626.21 ±4.66 322 324 322 321 321 321 323 323 325 324 324 322 322 324 324

641.06 ±6.40 344 347 347 345 345 349 349 349 347 347 349 345 349 346 345

666.68 ±6.92 378 379 377 379 379 377 379 376 376 377 377 377 375 376 378

670.76 ±5.08 384 384 387 385 383 386 386 383 386 384 384 384 384 388 388

692.18 ±5.75 458 456 458 456 454 455 458 456 455 458 456 458 457 458 456

713.74 ±3.14 474 475 473 475 475 478 475 475 479 479 474 475 475 476 475

718.47 ±4.71 399 400 401 400 399 399 401 399 399 401 399 403 401 399 403

743.54 ±6.00 556 554 554 554 553 554 550 550 550 551 554 550 551 550 554

763.23 ±7.78 573 572 572 574 573 575 573 573 571 572 571 571 572 573 574

770.15 ±3.32 588 591 591 588 591 588 591 591 589 587 586 590 589 589 587

66

SECTION 10: PROCESSED DATA FOR ALL SOLUTIONS This section provides all the processed data for all the solutions of all the concentrations, some of which is used in the article.

Table 7.10.1 – Processed data for Nickel Sulphate solutions.

Wavelength (nm)

0.1 mol dm-3 Nickel Sulphate 0.2 mol dm-3 Nickel Sulphate 0.3 mol dm-3 Nickel Sulphate 0.4 mol dm-3 Nickel Sulphate 0.5 mol dm-3 Nickel Sulphate

AVG (bytes)

STDEV ABSOR ± ERR AVG

(bytes) STDEV ABSOR ± ERR

AVG (bytes)

STDEV ABSOR ± ERR AVG

(bytes) STDEV ABSOR ± ERR

AVG (bytes)

STDEV ABSOR ± ERR

385.17 4.19 933 1 0.526 0.016 1004 2 0.940 0.107 1015 1 1.151 0.117 1017 1 1.217 0.149 1018 1 1.258 0.173

392.36 3.73 856 1 0.356 0.011 1010 2 1.046 0.148 1017 2 1.229 0.291 1020 1 1.375 0.255 1022 1 1.556 0.505

407.08 4.80 862 1 0.385 0.015 993 1 0.852 0.041 1012 1 1.105 0.092 1021 2 1.468 0.676 1021 1 1.468 0.342

421.03 6.06 730 2 0.254 0.013 937 1 0.637 0.018 977 2 0.808 0.050 980 1 0.826 0.029 1001 1 1.001 0.050

441.89 5.08 673 1 0.195 0.008 687 1 0.211 0.010 889 2 0.517 0.022 872 2 0.481 0.021 848 1 0.435 0.012

461.35 5.58 471 1 0.063 0.008 507 1 0.100 0.008 551 1 0.145 0.008 580 1 0.175 0.008 609 2 0.205 0.012

471.58 3.47 340 1 0.010 0.009 381 1 0.056 0.010 395 1 0.071 0.010 408 2 0.085 0.014 422 2 0.100 0.014

496.99 3.79 274 1 0.007 0.010 291 1 0.028 0.011 297 1 0.036 0.010 306 2 0.047 0.015 310 1 0.052 0.010

507.98 5.32 248 2 0.004 0.021 262 2 0.023 0.018 260 1 0.021 0.013 276 1 0.042 0.013 280 2 0.047 0.018

525.69 4.04 227 2 0.001 0.017 244 1 0.026 0.013 249 1 0.033 0.013 262 1 0.051 0.013 268 1 0.059 0.013

541.56 6.69 215 2 0.003 0.024 237 2 0.036 0.023 247 2 0.050 0.023 259 2 0.066 0.022 269 1 0.079 0.017

559.54 5.68 231 2 0.027 0.023 254 2 0.059 0.023 277 1 0.090 0.017 279 2 0.092 0.022 302 1 0.121 0.017

573.82 5.81 239 1 0.019 0.011 275 1 0.068 0.010 306 1 0.106 0.009 337 2 0.143 0.014 363 1 0.173 0.009

591.18 4.81 273 1 0.034 0.016 355 1 0.132 0.013 409 2 0.191 0.017 464 1 0.248 0.013 518 1 0.303 0.013

613.65 5.82 349 2 0.080 0.018 437 1 0.175 0.011 540 1 0.281 0.011 631 1 0.375 0.012 713 1 0.468 0.012

626.21 4.66 443 2 0.132 0.017 611 1 0.305 0.012 718 2 0.425 0.017 857 2 0.629 0.022 919 1 0.768 0.018

641.06 6.40 462 1 0.123 0.008 673 1 0.344 0.010 817 1 0.532 0.011 897 1 0.684 0.014 959 1 0.875 0.022

666.68 6.92 588 1 0.219 0.008 771 1 0.431 0.011 911 1 0.685 0.016 973 1 0.909 0.026 992 1 1.036 0.038

670.76 5.08 533 1 0.152 0.008 790 1 0.448 0.009 905 2 0.660 0.022 964 0 0.854 0.003 993 2 1.034 0.070

692.18 5.75 588 1 0.135 0.008 809 2 0.403 0.016 961 2 0.767 0.038 976 1 0.842 0.026 1008 2 1.137 0.131

713.74 3.14 657 1 0.188 0.012 863 1 0.474 0.014 955 2 0.721 0.038 996 2 0.967 0.080 1011 2 1.171 0.162

718.47 4.71 527 2 0.131 0.016 853 0 0.535 0.006 923 1 0.692 0.017 976 2 0.901 0.050 1010 2 1.231 0.151

743.54 6.00 726 1 0.191 0.013 889 1 0.450 0.015 949 2 0.621 0.035 998 2 0.910 0.086 1014 2 1.163 0.209

763.23 7.78 703 0 0.141 0.004 860 2 0.368 0.020 961 1 0.647 0.022 985 2 0.778 0.058 1001 1 0.920 0.050

770.15 3.32 687 2 0.109 0.013 895 2 0.428 0.023 908 1 0.459 0.015 970 2 0.676 0.044 990 1 0.802 0.036

67

Table 7.10.2 – Processed data for Copper Sulphate solutions.

Wavelength (nm)

0.1 mol dm-3 Copper Sulphate 0.2 mol dm-3 Copper Sulphate 0.3 mol dm-3 Copper Sulphate 0.4 mol dm-3 Copper Sulphate 0.5 mol dm-3 Copper Sulphate

AVG (bytes)

STDEV ABSOR ± ERR AVG

(bytes) STDEV ABSOR ± ERR

AVG (bytes)

STDEV ABSOR ± ERR AVG

(bytes) STDEV ABSOR ± ERR

AVG (bytes)

STDEV ABSOR ± ERR

385.17 4.19 832 1 0.302 0.012 872 1 0.375 0.013 893 1 0.420 0.014 847 1 0.328 0.012 856 2 0.344 0.019

392.36 3.73 784 1 0.240 0.009 704 1 0.137 0.008 747 2 0.190 0.013 730 1 0.168 0.008 740 2 0.181 0.013

407.08 4.80 649 2 0.092 0.016 768 2 0.235 0.018 701 2 0.151 0.017 702 1 0.152 0.012 701 2 0.151 0.017

421.03 6.06 655 2 0.167 0.014 573 2 0.080 0.013 603 2 0.111 0.013 657 1 0.169 0.009 676 2 0.190 0.014

441.89 5.08 638 1 0.156 0.009 552 2 0.066 0.013 579 2 0.094 0.013 583 2 0.098 0.013 580 1 0.095 0.009

461.35 5.58 452 1 0.044 0.008 564 1 0.158 0.008 587 2 0.182 0.012 592 1 0.187 0.008 589 1 0.184 0.008

471.58 3.47 464 1 0.144 0.010 378 1 0.053 0.01 397 2 0.073 0.014 403 2 0.080 0.014 412 1 0.089 0.010

496.99 3.79 297 2 0.036 0.015 308 1 0.049 0.01 323 1 0.067 0.010 334 2 0.080 0.015 331 2 0.076 0.015

507.98 5.32 265 1 0.027 0.013 279 2 0.045 0.018 287 1 0.056 0.013 310 1 0.084 0.013 306 2 0.079 0.017

525.69 4.04 245 2 0.027 0.018 260 2 0.048 0.018 274 1 0.066 0.013 291 2 0.088 0.017 293 2 0.091 0.017

541.56 6.69 232 2 0.028 0.023 245 2 0.047 0.023 254 1 0.059 0.017 273 2 0.085 0.022 270 2 0.081 0.022

559.54 5.68 242 1 0.043 0.018 270 2 0.081 0.022 303 2 0.122 0.022 334 1 0.159 0.017 357 1 0.186 0.016

573.82 5.81 266 2 0.056 0.015 311 1 0.113 0.009 362 1 0.171 0.009 408 1 0.221 0.009 447 2 0.262 0.013

591.18 4.81 316 2 0.087 0.018 393 2 0.174 0.017 482 1 0.267 0.013 564 1 0.350 0.013 635 1 0.425 0.013

613.65 5.82 391 2 0.127 0.016 509 2 0.249 0.015 634 1 0.379 0.012 742 1 0.504 0.012 821 2 0.616 0.020

626.21 4.66 500 1 0.191 0.011 681 1 0.382 0.012 828 2 0.579 0.020 921 2 0.774 0.029 969 0 0.951 0.008

641.06 6.40 601 1 0.266 0.009 818 1 0.533 0.011 944 2 0.817 0.032 995 1 1.095 0.041 1012 1 1.330 0.090

666.68 6.92 737 2 0.386 0.015 941 1 0.773 0.019 1003 1 1.148 0.054 1019 2 1.526 0.408 1023 1 1.947 1.007

670.76 5.08 794 2 0.454 0.015 976 2 0.916 0.047 1015 1 1.362 0.116 1022 1 1.756 0.504 1022 1 1.756 0.504

692.18 5.75 923 2 0.634 0.026 1014 1 1.261 0.105 1023 1 1.863 1.005 1022 1 1.682 0.505 1023 0 1.863 0.004

713.74 3.14 966 2 0.770 0.043 1020 2 1.481 0.508 1023 1 1.843 1.007 1023 1 1.843 1.007 1023 0 1.843 0.006

718.47 4.71 974 1 0.890 0.027 1022 2 1.741 1.008 1023 0 1.922 0.006 1023 0 1.922 0.006 1023 0 1.922 0.006

743.54 6.00 1008 2 1.039 0.134 1023 1 1.765 1.008 1023 1 1.765 1.008 1023 1 1.765 1.008 1023 0 1.765 0.007

763.23 7.78 1010 2 1.051 0.150 1023 1 1.743 1.006 1023 1 1.743 1.006 1023 1 1.743 1.006 1023 1 1.743 1.006

770.15 3.32 1013 2 1.102 0.189 1022 1 1.548 0.506 1023 1 1.729 1.006 1023 1 1.729 1.006 1023 1 1.729 1.006

68

Table 7.10.3 – Processed data for Potassium Chromate solutions.

Wavelength (nm)

0.1 mol dm-3 Potassium chromate 0.2 mol dm-3 Potassium chromate 0.3 mol dm-3 Potassium chromate 0.4 mol dm-3 Potassium chromate 0.5 mol dm-3 Potassium chromate

AVG (bytes)

STDEV ABSOR ± ERR AVG

(bytes) STDEV ABSOR ± ERR

AVG (bytes)

STDEV ABSOR ± ERR AVG

(bytes) STDEV ABSOR ± ERR

AVG (bytes)

STDEV ABSOR ± ERR

385.17 4.19 1021 2 1.439 0.674 1022 1 1.545 0.506 1021 2 1.439 0.674 1021 2 1.439 0.674 1022 2 1.545 1.007

392.36 3.73 1023 0 1.737 0.004 1023 0 1.737 0.004 1023 0 1.737 0.004 1023 0 1.737 0.004 1023 2 1.737 2.006

407.08 4.80 1023 1 1.755 1.009 1023 0 1.755 0.008 1022 1 1.574 0.509 1022 1 1.574 0.509 1023 1 1.755 1.009

421.03 6.06 1023 1 1.823 1.006 1022 1 1.642 0.506 1023 0 1.823 0.005 1022 1 1.642 0.506 1023 1 1.823 1.006

441.89 5.08 1022 1 1.651 0.506 1023 0 1.831 0.005 1023 1 1.831 1.006 1023 1 1.831 1.006 1023 1 1.831 1.006

461.35 5.58 1019 1 1.491 0.205 1022 2 1.730 1.006 1022 1 1.730 0.505 1020 1 1.549 0.255 1020 1 1.549 0.255

471.58 3.47 989 2 1.063 0.065 1015 1 1.424 0.118 1008 2 1.272 0.133 1019 1 1.578 0.207 1011 2 1.327 0.162

496.99 3.79 718 1 0.491 0.010 818 1 0.628 0.012 957 1 0.962 0.022 972 0 1.032 0.006 964 1 0.992 0.023

507.98 5.32 298 2 0.069 0.018 306 2 0.079 0.017 354 1 0.135 0.012 490 2 0.279 0.016 437 1 0.225 0.012

525.69 4.04 274 1 0.066 0.013 230 1 0.006 0.013 252 1 0.037 0.013 256 1 0.042 0.013 267 1 0.057 0.013

541.56 6.69 282 2 0.096 0.022 262 1 0.070 0.017 296 2 0.114 0.021 337 1 0.163 0.016 331 1 0.156 0.016

559.54 5.68 243 2 0.044 0.023 223 1 0.015 0.018 230 2 0.026 0.023 211 1 -0.003 0.018 235 1 0.033 0.018

573.82 5.81 237 1 0.016 0.010 221 1 -0.007 0.011 226 1 0.000 0.010 229 1 0.004 0.010 234 1 0.012 0.010

591.18 4.81 261 1 0.018 0.014 257 1 0.012 0.014 255 2 0.010 0.019 260 1 0.016 0.014 261 2 0.018 0.019

613.65 5.82 299 2 0.021 0.017 296 1 0.018 0.012 289 1 0.009 0.012 294 1 0.015 0.012 300 2 0.023 0.017

626.21 4.66 340 1 0.021 0.012 328 1 0.007 0.012 340 1 0.021 0.012 343 2 0.024 0.016 345 2 0.027 0.016

641.06 6.40 357 1 0.011 0.010 361 1 0.016 0.010 364 2 0.019 0.014 364 2 0.019 0.014 369 1 0.025 0.010

666.68 6.92 389 2 0.013 0.014 385 2 0.009 0.014 391 1 0.015 0.010 395 1 0.020 0.010 398 2 0.023 0.014

670.76 5.08 401 1 0.016 0.008 396 1 0.011 0.008 402 1 0.017 0.008 402 2 0.017 0.012 398 1 0.013 0.008

692.18 5.75 462 1 0.006 0.008 482 1 0.027 0.008 476 1 0.021 0.008 478 1 0.023 0.008 484 1 0.029 0.008

713.74 3.14 495 2 0.019 0.014 491 2 0.015 0.014 483 1 0.007 0.010 499 2 0.023 0.014 495 2 0.019 0.014

718.47 4.71 406 1 0.006 0.010 419 2 0.020 0.014 410 1 0.011 0.010 425 1 0.026 0.010 421 2 0.022 0.014

743.54 6.00 570 2 0.018 0.014 566 1 0.014 0.011 560 2 0.008 0.014 562 1 0.010 0.011 565 1 0.013 0.011

763.23 7.78 580 1 0.006 0.009 585 0 0.011 0.005 594 2 0.021 0.013 595 1 0.022 0.009 599 1 0.026 0.009

770.15 3.32 603 2 0.017 0.013 602 2 0.016 0.013 603 2 0.017 0.013 603 2 0.017 0.013 606 1 0.020 0.009

69

Table 7.10.3 – Processed data for Potassium Chromate solutions.

Wavelength (nm)

0.1 mol dm-3 Potassium dichromate 0.2 mol dm-3 Potassium dichromate 0.3 mol dm-3 Potassium dichromate

AVG (bytes)

STDEV ABSOR ± ERR AVG

(bytes) STDEV ABSOR ± ERR

AVG (bytes)

STDEV ABSOR ± ERR

385.17 4.19 1018 1 1.258 0.173 1023 1 1.545 0.506 1018 1 1.364 0.256

392.36 3.73 1023 1 1.737 1.005 1023 0 1.737 0.004 1023 0 1.737 0.004

407.08 4.80 1023 1 1.755 1.009 1022 1 1.755 1.009 1023 1 1.755 1.009

421.03 6.06 1023 0 1.823 0.005 1022 1 1.823 1.006 1023 1 1.823 1.006

441.89 5.08 1023 1 1.831 1.006 1023 1 1.831 1.006 1023 1 1.831 1.006

461.35 5.58 1021 1 1.730 0.505 1023 1 1.730 0.505 1021 2 1.730 1.006

471.58 3.47 1020 1 1.636 0.257 1020 2 1.636 0.508 1020 0 1.998 0.006

496.99 3.79 1020 1 1.654 0.207 1016 2 1.566 0.293 1020 1 1.788 0.34

507.98 5.32 1019 2 1.687 0.410 1021 2 1.821 0.677 1019 1 1.926 0.509

525.69 4.04 965 1 1.062 0.026 1010 1 1.444 0.080 965 1 1.463 0.086

541.56 6.69 1013 0 1.552 0.012 1019 1 1.734 0.213 1013 1 1.734 0.213

559.54 5.68 342 1 0.170 0.017 379 2 0.211 0.021 342 1 0.245 0.016

573.82 5.81 250 2 0.034 0.015 263 1 0.053 0.010 250 1 0.075 0.01

591.18 4.81 252 2 0.004 0.019 257 1 0.014 0.014 252 1 0.016 0.014

613.65 5.82 283 1 0.001 0.012 286 2 0.004 0.017 283 1 0.004 0.012

626.21 4.66 322 1 0.000 0.012 323 1 0.001 0.012 322 1 0.001 0.012

641.06 6.40 346 1 -0.001 0.010 348 1 0.000 0.010 346 2 0.000 0.014

666.68 6.92 378 1 0.000 0.010 377 1 0.001 0.010 378 1 0.000 0.01

670.76 5.08 385 2 -0.001 0.012 385 1 -0.001 0.008 385 2 0.000 0.012

692.18 5.75 456 2 0.000 0.012 456 2 0.001 0.012 456 1 0.001 0.008

713.74 3.14 474 1 -0.001 0.010 477 2 0.001 0.014 474 1 -0.001 0.01

718.47 4.71 400 1 0.001 0.010 400 1 0.001 0.010 400 2 0.001 0.014

743.54 6.00 554 1 0.002 0.011 551 2 0.000 0.014 554 2 0.000 0.014

763.23 7.78 573 1 0.000 0.009 573 1 -0.001 0.009 573 1 -0.001 0.009

770.15 3.32 590 2 0.002 0.013 589 2 0.002 0.013 590 2 0.001 0.013

70

SECTION 11: GRAPHS OF THE SOLUTIONS WITH ERROR BARS This section contains the graphs of all the solutions like in Section 3.3, but with error bars. The

error bars were eliminated from the original graphs as they were unclear and a hindrance to

the trend line.

Figure 7.11.1 – Graph of absorbance vs wavelength for Nickel Sulphate, with error bars, from

the DIY Spectrophotometer

Figure 7.11.2 – Graph of absorbance vs wavelength for Copper Sulphate, with error bars, from

the DIY Spectrophotometer

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Nickel Sulphate Absorbance vs Wavelength

0

0.5

1

1.5

2

2.5

3

3.5

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Copper Sulphate Absorbance vs Wavelength

71

Figure 7.11.3 – Graph of absorbance vs wavelength for Potassium Chromate, with error bars,

from the DIY Spectrophotometer

Figure 7.11.4 – Graph of absorbance vs wavelength for Potassium Dichromate, with error bars,

from the DIY Spectrophotometer

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Potassium chromate Absorbance vs Wavelength

-0.5

0

0.5

1

1.5

2

2.5

3

380 430 480 530 580 630 680 730 780

Ab

sorb

ance

Wavelength (nm)

Potassium Dichromate Absorbance vs Wavelength

72

SECTION 12: EXAMPLES OF SOLUTIONS SHOWING INCREASE IN ERROR AFTER ABSORBANCE > 2 This section shows multiple other graphs of Quantitative deviation vs Absorbance, to

demonstrate that there is a sharp increase in the error after the absorbance is greater than 2.

Figure 7.12.1 – Copper sulphate 0.2 mol dm-3 solution Quantitative error vs Absorbance.

Figure 7.12.2 – Potassium chromate 0.3 mol dm-3 solution Quantitative error vs Absorbance.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5

Qu

anti

tati

ve e

rro

r

Absorbance

Quantitative Error vs Absorbance

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.5 1 1.5 2 2.5

Qu

anti

tati

ve E

rro

r

Absorbance

Quantitative Error vs Absorbance

Increase in error

after Absorbance > 2

Increase in error

after Absorbance ≈ 2

73

SECTION 13: ALTERNATIVES TO THE LDR This section discusses the alternatives to the LDR that were considered. The primary

alternatives are using the SparkFun TSL235R, or a Charge Coupled Device (CCD).

TSL235R:

Extracts from the description of the device according to its seller is given below[22].

“The TSL235R light-to-frequency converter outputs a square wave (50% duty cycle) with

frequency directly proportional to light intensity (irradiance). The device has been temperature

compensated for the ultraviolet-to-visible light range of 320 nm to 700 nm and responds over

the light range of 320 nm to 1050 nm.

Features:

High-resolution conversion of light intensity to frequency with no external components

Communicates directly with a microcontroller

Nonlinearity error typically 0.2% at 100kHz

Stable 150 ppm/°C temperature coefficient

The TSL235R light-to-frequency converter combines a silicon photodiode and a current-to-

frequency converter on a single monolithic CMOS integrated circuit.”

The price of this component id relatively cheap, at 2.95 USD. This is a fair alternative to the LDR.

For this research, this component was later purchased and tested. The results obtained were

definitely of a higher accuracy.

Figure 7.13.1 – The TSL235R

74

CCD:

For information on what a Charge Coupled Device is, and how it works please follow the link

given below:

http://www.specinst.com/What_Is_A_CCD.html

Figure 7.13.2 – A Charged Coupled Device[23]

A CCD completely captures the image of the Spectrum, unlike the LDR and the TSL235R. The

benefit of this is the higher resolution in terms of the wavelengths captured. Also, another

benefit would be that the spectrum would not have to be shifted. The polychromatic light can

be passed through a sample and then can be diffracted into a spectrum, which can be projected

on a CCD strip. The device will completely capture every wavelength and its intensity. This can

give a higher resolution.

On the other hand, the device can become expensive to integrate into the spectrophotometer.

75

SECTION 14: PROJECTED COST OF THE OPTIMIZED MODEL

Table 6.14 – The materials that would go into the optimized modellxv

Total Cost: 1311 INR ≈ 20.10 USD

lxv The cost of developing a computer interface is not consideres [lxvi] The Controller used in this design is Arduino Uno, which is more expensive (Rs. 515), but there is a cost effective alternative of using a minimalistic ATtiny85 chip. Also, when commercially mass produced, the cost will be greatly reduced as a different IC will be used specific to the one program which is to be executed.

Material Quantity Purpose Cost (INR)

Plywood 1 Casing of the device 50

Plywood barrier 1 Extra wall between Central maxima and spectrum

5

High power light bulb 1 Light source 100

Voltage adapter 1 Powering the light source 250

Collimator 1 Collimation of light 20

Commercial grating 1 Diffraction grating 500

Stepper motor 1 Linear movement of slit 300

Rack and pinion 1 Rotational to linear motion 50

Black spray paint 1 Colouring the interiors black 60

Razor blades 2 Slit 1

Cuvette 1 Holding the Sample 10

TSL235R 1 Sensing light 200

Cardboard sheet 1 Internal compartments 5

Electrical Wires ≈100 cm Electrical connections 10

Micro Controller 1 Processing the data 150[lxvi]

76

7 BIBLIOGRAPHY

[1] Chemwiki – Spectrophotometry

http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Reaction_Rates/Experimental_Deter

mination_of_Kinetcs/Spectrophotometry

[2] Dictionary.com – Definition of Absorbance

http://dictionary.reference.com/browse/absorbance

[3] Chemwiki – Spectrophotometry

http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Reaction_Rates/Experimental_Deter

mination_of_Kinetcs/Spectrophotometry

[4] Physics Classroom – Light Absorption, Reflection, and Transmission

http://www.physicsclassroom.com/class/light/Lesson-2/Light-Absorption,-Reflection,-and-

Transmission

[5] Durham University – Absorption Spectroscopy

https://www.dur.ac.uk/chemistry/outreach/spectroscopy_in_a_suitcase/absorption_spectrosc

opy/

[6] HyperPhysics© 2014 C.R.Nave – Ohm’s Law

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmlaw.html

[7] HyperPhysics© 2014 C.R.Nave – Voltage Divider

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/voldiv.html

[8] Jim’s Homemade Spectrometers

http://www.inpharmix.com/jps/CD_spectro.html

[9] Pasco Amadeus Spectrometer system

http://www.pasco.com/legacy/SE/SE-7183_amadeus-spectrometer-system/index.cfm

[10] Token – LDR Datasheet

http://www.gotronic.fr/pj-1284.pdf (Datasheet of the LDR)

77

[11] Joachim Köppen (Institut für Theoretische Physik und Astrophysik) – Photometry with

Light dependent resistors

http://astro.u-strasbg.fr/~koppen/blueskies/photometer.html

[12] Rapid Tables – Lux to watt Conversion

http://www.rapidtables.com/calc/light/lux-to-watt-calculator.htm

[13] HyperPhysics© 2014 C.R.Nave – Luminous Efficacy Tables

http://hyperphysics.phy-astr.gsu.edu/hbase/vision/efficacy.html

[14] Rapid Tables – Lux to Watt Conversion (Luminous Efficacy of Tungsten bulb)

http://www.rapidtables.com/calc/light/lux-to-watt-calculator.htm

[15] Vernier SpectroVis Plus Product Page

http://www.vernier.com/products/sensors/spectrometers/visible-range/svis-pl/

[16] NASA Spaceplace Classroom Activities – Make your own Spectroscope

http://spaceplace.nasa.gov/review/classroom-activities/pdf/tes_spectroscope.pdf

[17] Arduino UNO Product Information

http://arduino.cc/en/Main/ArduinoBoardUno

[18] MathIsFun – Standard Deviation

https://www.mathsisfun.com/data/standard-deviation-formulas.html

[19] Capilano University – Uncertainty in Logarithms

http://phys114115lab.capuphysics.ca/App%20A%20-%20uncertainties/appA%20propLogs.htm

[20] Public Lab Spectrometer Project page

http://publiclab.org/wiki/spectrometer

[21] Page Number 626, Physics for the IB Diploma, Fifth Edition – KA Tsokos (Print)

[22] SparkFun TSL235R Datasheet

https://www.sparkfun.com/datasheets/Sensors/Imaging/TSL235R-LF.pdf

[23] Image of a CCD

https://upload.wikimedia.org/wikipedia/commons/a/a1/CCD.jpg