line_spectra.pdf

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Line Spectra

Physics 83 HZ-2L

Institute of Chemistry, University of the Philippines- Los Banos

[email protected]

Abstract

Excited atoms (Hydrogen, Helium, Krypton, Argon) in gas tubes are produced in an electric discharge.

These atoms radiate light at discrete wavelengths, some of which lie in the visible region of the spectrum. Using

diffraction grating spectrometer; the visible light is spread and detected. The wavelength determines the position of

the lines in the spectrum and these wavelengths are compared to the literature value. Furthermore, the experiment

attempt to explain the wavelength value observed in terms of the transition made by electrons.

Keywords: line spectra, Hydrogen atom, Balmer series, spectroscopy

1 Introduction

The emission of light of certain wavelengths occurs when atoms are excited. The emitted light can be

observed as a series of colored lines with dark spaces between; this series of colored lines is known as line or atomic

spectra. Each element has a unique set of spectral lines. Thus, investigation of spectral lines are useful in identifying

elements.

Niels Bohr, a Danish physicist (1913), hypothesized of photons with specific energies from the atom of that

element. During the emission of a photon, the internal energy of the atom changes by by anamount equal to the

enegy of the photon. Thus he concluded that each atom must be able to exist with only certain specific values of

internal energy. This internal energy now called, energy level are quantized and cannot have intermediate energy

between levels. (Young, Freedman at al. ,2009)

In electric discharge tubes, atoms are excited to higher energy levels mainly through inelastic collision

(Young, Freedman at al. ,2009) The excitation implies electron transition from one energy level to a lower level by

emitting a photon with energy equal to the energy difference between the initial and final levels. In an electric

discharge tube of Hydrogen, atomic hydrogen emits a series of lines. The visble line has the lowest frequency and

thus longest wavelbngth, is in the red, the next color is in blue-green. Johan Balmer (1825-1898) gives a formula

that gives the wavelengths of these lines which are now called the Balmer series:

Where is the wavelngth, R is a constant called the Rydberg constant and n may have the integer values

3,4,5,. R has a value of 1.097 x 10

7

m

-1

. This formula gives a direct relationship to Bohrs hypothesis about energylevels. The photon energy tat corresponds to the wavelength of the Balmer series is given by the equation

This experiment aims to determine in the visible region in the emission spectrum of Hydrogen, Krypton,

Helium and Argon gases. The energy emitted by an electron of a Hydrogen atom undergoing transitions will be

computed. Furthermore, the characteristic of line spectra of many electron atoms will be observed and described.
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2. Methodology

The set-up is shown in Figure 1. A gas tube with Hydrogen is placed inside and the circuit is turned on. By

using eyepiece of the spectroscope, spectra produced by the element are observed. The wavelength projected in the

viewing screen are identified through Lab Quest. Other gas tube used are Helium, Argon and Krypton.

Figure 1. Experimental Set-up for viewing line spectrum

3 Results and Discussion

The experiment employed a device called diffraction grating spectrometer that allows a single beam of light

to split into many familiar colors (e.g. Red, Orange, Yellow, Green, Blue, Indigo, Violet). Spectral tubes or tube

containing different elements are plugged into the wall of spectrometer and by introducing electricity, energy is

added to the gas element. This cause Hydrogen for instance, to become excited and thus electrons jump into high

energy levels. This electron eventually relaxed and moves into lower energy state (ground state) and emits energy.

Table 1. Color bands in Hydrogen and in many-electron atoms in visible region.

Gas in the tube Color observed Wavelength, nm Literature value of

Hydrogen Red 656.0 656.2

Green 468.0 486.1

Helium Orange 668.0 667.8

Yellow 588.0 501.5

Green 501.0 585.5

Green 447.0 447.1

Blue 388.0 Out of Vis range

violet 707.0 706.5

Argon Blue 486.0 486.5

Red 697.0 650.4

Red 751.0 Out of Vis range

Red 764.0 Out of Vis range

white 812.0 Out of Vis range

Krypton Blue 431.0 431.7

Green 516.0 512.5

Yellow 587.0 587.0

Yellow 557.0 557.0

Blue 468.0 468.0

A shell of atom corresponds to a specific energy level which is designated by a quantum number n. The

quantum number n is always an integer value (n=1,2,3,4) since electron cannot exist between two values. (Tipler,


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1994). When the electron is in ground state as mention earlier, it is in the lowest energy (n=1) and is closest to the

nucleus.

The simple explanation of relaxation of Hydrogen electrons is explained by Figure 2. The illustration is

based on the Bohr model of the Hydrogen atom. The energy of the photon emitted by an electron is calculated from

Ephoton =RH (1/ni21/nf

2)

Figure 2. The Bohr model of a Hydrogen atom

In the experiment, the lab quest allowed us to approximate the wavelength of the lines found in the

spectrum of Hydrogen (Figure 3). Again, this spectrum is produced by exciting the gas tube of Hydrogen and

viewed through a diffraction grating. For Hydrogen, with atomic number of 1, a wavelength of 656.0 nm is from the

transition of the electron from third energy level to second energy leve (Figure 2). It give a quntum energy of

1.889eV. Table 2 shows other wavelength and transition of Hydrogen electron. In addition Table 3 shows the energy

emtted by Hydrogen electron.

Figure 3. Line spectrum of Hydrogen showing the line spectrum

The energy emitted are simply calculated from the formula given by Balmer series. Other spectral series for

Hydrogen have been discovered. Therse series are names after their discoverers as Lyman, Paschen, Barckett and

Pfund series. Their wavelbngths can be represented by formulas similar to Balmers formula:


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Lyman series

n=2,3,4,

Paschen series

n=4,5,6,

Brackett series

n= 5, 6, 7

Pfund series

n=6,7,8..

While Balmer series is in Visible region, Lyman series is in the ultraviolet, and the Paschen, Brakett and P fund

series are in the infrared.( Young, Freedman at al. ,2009)

Table 2Wavelngth transition ans electron transition of Hydrogen electron.

Wavelength(nm)

RelativeIntensity

Transition Color

383.5384 5 9 -> 2 Violet

388.9049 6 8 -> 2 Violet397.0072 8 7 -> 2 Violet

410.174 15 6 -> 2 Violet

434.047 30 5 -> 2 Violet

486.133 80 4 -> 2 Bluegreen (cyan)656.272 120 3 -> 2 Red

656.2852 180 3 -> 2 Red

Table 3. Energy emitted of the elctron based on the experimental wavelength

Observed wavelength, nm Transition Energy emitted, eV

468 4 -> 2 2.55106837656 3 -> 2 1.88968028

How other electrons produces lines in each spectrum is explain in the same way, the Hydrogen electron

transition is explain. The only differences is that, many-electron atom like Helium and Krypton makes many

transition because they have many electrons in each energy level. The greater the number of electron, the greater

the number of transition and thus producing more number of lines. The figure below shows all spectrum of the

element used in the experiment.

a. Helium

b. Argon

c. Krypton

Figure 4. Line spectra of Helium, Argon and Krypton


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The application of emission of atoms is seen in atomic spectroscopy. Since the emission spectrum is

different for every element, it acts as an atomic fingerprint by which elements can be identified. Some elements

were discovered by the analysis of their atomic spectrum. Helium, for example, was discovered while scientists were

analyzing the absorption spectrum of the sun. Emission spectra is especially useful to astronomers who use emission

and absorption spectra to determine the makeup of faraway stars and other celestial bodies. (Mindtouch core, 2010)

4 Conclusion

The wavelength in the visible region in the emsiion spectrum of Hydrogen, Helium, Krypton and Argon were

determined by using diffraction grating spectrometer. The energy emitted by an electron of a Hydrogen atom

undergoing traistion was computed. The experimental value were compared to the literature value and this

confirmed that the line spectra observed is for each element. The Bohr model as well as Balmer series was applied

in explaining the line spectra observed and the wavelength. The difference in the line spectra of many-electron atom

and Hydrogern is the number of electrons that can make transition from different energy level.

5. References:

H. Young, R Freedman and L. Ford University Physics with Modern Physics. 12th ed Pearson Education South Asia

Pte Ltd, Singapore, 2009.

P. Tipler. Physics:for Scientists and Engineers 4 th ed

Internet source:

http://www.uncp.edu/home/mcclurem/courses/chm226/Atomic_Spectrum_Hydrogen.pdf

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