mc ch.6 (quantum theory)

Chapter 6 - Quantum Theory

Due: 11:00pm on Sunday, October 25, 2009

Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy

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Electromagnetic Radiation

Electromagnetic radiation behaves both as particles (called photons) and as waves. Wavelength ( ) and frequency ( ) are

related according to the equation

where is the speed of light ( ). The energy ( in joules) contained in one quantum of electromagnetic

radiation is described by the equation

where is Planck's constant ( ). Note that frequency has units of inverse seconds ( ), which are

more commonly expressed as hertz ( ).

Part A

A microwave oven operates at 2.40 . What is the wavelength of the radiation produced by this appliance?

Hint A.1 How to approach the problem

Hint not displayed

Hint A.2 Convert gigahertz to hertz

Hint not displayed

Hint A.3 Calculate the wavelength in meters

Hint not displayed

Express the wavelength numerically in nanometers.

ANSWER: = 1.25!108

Correct

Some people lose their wireless Internet connection at home while their microwave oven is turned on because both

happen to operate at 2.40 .

Part B

There are two types of ultraviolet light, UVA and UVB, that are both components of sunlight. Their wavelengths range

from 320 to 400 for UVA and from 290 to 320 for UVB. Compare the energy of of microwaves, UVA, and

UVB.

Hint B.1 How to approach the problem

Hint not displayed

Hint B.2 Determine the relationship between wavelength and energy

Hint not displayed

Hint B.3 Which has greater energy, UVA or UVB?

Hint not displayed

Rank from greatest to least energy per photon. To rank items as equivalent, overlap them.

ANSWER:

View

Correct

[ Print ]

UVB radiation causes sunburn whereas UVA radiation does not. However, UVA, which causes tanning, is thought to

be even more dangerous. The precise wavelengths of ultraviolet light that contribute to the formation of skin cancers

still need to be determined by scientists.

Properties of Waves

Learning Goal: To understand electromagnetic radiation and be able to perform calculations involving wavelength,

frequency, and energy.

Several properties are used to define waves. Every wave has a wavelength, which is the distance from peak to peak or

trough to trough. Wavelength, typically given the symbol (lowercase Greek "lambda"), is usually measured in meters.

Every wave also has a frequency, which is the number of wavelengths that pass a certain point during a given period of

time. Frequency, given the symbol (lowercase Greek "nu"), is usually measured in inverse seconds ( ). Hertz ( ),

another unit of frequency, is equivalent to inverse seconds.

The product of wavelength and frequency is the speed in meters per second ( . For light waves, the speed is constant.

The speed of light is symbolized by the letter and is always equal to in a vacuum; that is,

Another term for "light" is electromagnetic radiation, which encompasses not only visible light but also gamma rays, X

rays, UV rays, infrared rays, microwaves, and radio waves. As you could probably guess, these different kinds of radiation

are associated with different energy regimes. Gamma rays have the greatest energy, whereas radio waves have the least

energy. The energy (measured in joules) of a particular kind of light wave is equal to its frequency times a constant called

Planck's constant, symbolized

where

These two equations can be combined to give an equation that relates energy to wavelength:

Part A

A radio station's channel, such as 100.7 FM or 92.3 FM, is actually its frequency in megahertz ( ), where

. Calculate the broadcast wavelength of the radio station 102.7 FM.


Hint not displayed

Hint A.2 Convert frequency to hertz

Hint not displayed

Hint A.3 Choose a formula for frequency

Hint not displayed

Express your answer in meters to four significant figures.

ANSWER: = 2.919

Correct

Part B

Green light has a frequency of about . What is the energy of green light?


Hint not displayed

Hint B.2 Choose a formula for energy

Hint not displayed

Express your answer in joules.

ANSWER: = 3.98!10"19

Correct

Part C

Hospital X-ray generators emit X rays with wavelength of about 15.0 nanometers ( ), where . What

is the energy of the X rays?

Hint C.1 How to approach the problem

Hint not displayed

Hint C.2 Convert nanometers to meters

Hint not displayed

Hint C.3 Choose a formula for energy

Hint not displayed

Express your answer in joules.

ANSWER: = 1.32!10"17

Correct

Using Microwave Radiation to Heat Coffee

Microwave ovens use microwave radiation to heat food. The microwaves are absorbed by the water molecules in the food,

which is transferred to other components of the food. As the water becomes hotter, so does the food.

Part A

Suppose that the microwave radiation has a wavelength of 11.6 . How many photons are required to heat 275 of

coffee from 25.0 to 62.0 ? Assume that the coffee has the same density, 0.997 , and specific heat capacity,

4.184 , as water over this temperature range.


First, determine the amount of energy in joules needed to heat the coffee using the following equation:

in which is the quantity of heat transferred, is the specific heat capacity, is the mass of the substance, and is

the temperature change. Second, determine the energy of a photon with a wavelength of 11.6 using the relationship

in which is the wavelength in meters, is Planck's constant ( ), and is the speed of light (

). Lastly, use the total energy and the energy per photon to determine the number of photons needed.

Hint A.2 Determine the total energy required

How much energy in joules is required to heat 275 of coffee from 25.0 to 62.0 ? Assume that the coffee has

the same density, 0.997 , and specific heat capacity, 4.184 , as water over this temperature range.

Hint A.2.1 Determine the mass of coffee

Hint not displayed

Hint A.2.2 Determine the temperature change

Hint not displayed

Express your answer numerically in joules.

ANSWER: = 4.24!104

Correct

Hint A.3 Determine the energy of a single photon

What is the energy of a photon with a wavelength of 11.6 ?

Hint A.3.1 Relation between energy and wavelength

Hint not displayed

Hint A.3.2 Determine the wavelength in meters

Hint not displayed

Express your answer numerically in joules per photon.

ANSWER:1.71!10"24

Correct

Hint A.4 Identify how to find the number of photons

If is the total energy in joules, and is the number of joules per photon, which choice shows how to calculate the

number of photons?

ANSWER:

Correct

Plug in the values of and and calculate the number of photons based on units:

Express the number of photons numerically.

ANSWER:2.48!1028

Correct

Electromagnetic radiation in this region of the spectrum is also used for cellular phones, radar, and wireless Internet.

The Photoelectric Effect

Electrons are emitted from the surface of a metal when it's exposed to light. This is called the photoelectric effect. Each

metal has a certain threshold frequency of light, below which nothing happens. Right at this threshold frequency, an electron

is emitted. Above this frequency, the electron is emitted and the extra energy is transferred to the electron.

The equation for this phenomenon is

where is the kinetic energy of the emitted electron, is Planck's constant, is the frequency of

the light, and is the threshold frequency of the metal.

Also, since , the equation can also be written as

where is the energy of the light and is the threshold energy of the metal.

Here are some data collected on a sample of cesium exposed to various energies of light.

Light energy

( )

Electron emitted? Electron

( )

3.87 no —

3.88 no —

3.89 yes 0

3.90 yes 0.01

3.91 yes 0.02

Part A

What is the threshold frequency of cesium?

Note that

Hint A.1 How to approach this problem

First use the chart to determine the threshold energy in electron volts. Then convert that energy to joules. Then use that

value to calculate the corresponding frequency.

Hint A.2 Determine the threshold energy in electron volts

What is the threshold energy in electron volts?

Hint A.2.1 How to approach the problem

Hint not displayed

ANSWER: = 3.89

Correct

Hint A.3 Determine the threshold energy in joules

Hint not displayed

Hint A.4 Useful formulas

Here are some handy formulas:

where is the energy in joules, is the frequency in hertz, is the wavelength in meters, is

Planck's constant, and is the speed of light.

Express your answer in hertz.

ANSWER: = 9.39!1014

Correct

Part B

Red light has a wavelength of about . Will exposure to red light cause electrons to be emitted from cesium?

Hint B.1 How to approach this problem

Hint not displayed

Hint B.2 Threshold energy of cesium

Hint not displayed

Hint B.3 Find the energy of red light

Hint not displayed

Hint B.4 Useful formulas

Hint not displayed

ANSWER: yes

no

Correct

Part C

What is the kinetic energy of the emitted electrons when cesium is exposed to UV rays of frequency ?

Hint C.1 How to approach this problem

Hint not displayed

ANSWER: = 3.72!10"19

Correct

The Rydberg Equation

An astrophysicist working at an observatory is interested in finding clouds of hydrogen in the galaxy. Usually hydrogen is

detected by looking for the Balmer series of spectral lines in the visible spectrum. Unfortunately, the instrument that detects

hydrogen emission spectra at this particular observatory is not working very well and only detects spectra in the infrared

region of electromagnetic radiation. Therefore the astrophysicist decides to check for hydrogen by looking at the Paschen

series, which produces spectral lines in the infrared part of the spectrum. The Paschen series describes the wavelengths of

light emitted by the decay of electrons from higher orbits to the level.

Part A

What wavelength should the astrophysicist look for to detect a transition of an electron from the to the

level?


The Rydberg formula is given by

where is the wavelength in meters, , and is the Rydberg constant in inverse meters.

Plug in the values for the lower level, , and the higher level, , and the Rydberg constant, then solve for

.

Hint A.2 Calculate the parenthetical term of the Rydberg equation

Calculate the value of

Express your answer numerically using three significant figures.

ANSWER:9.07!10"2

Correct

Enter your answer numerically in meters.

ANSWER: = 1.00!10"6

Correct

Atomic Spectra

Learning Goal: To calculate the wavelengths of the lines in the hydrogen emission spectrum.

Atoms give off light when heated or otherwise excited. The light emitted by excited atoms consists of only a few

wavelengths, rather than a full rainbow of colors. When this light is passed through a prism, the result is a series of discrete

lines separated by blank areas. The visible lines in the series of the hydrogen spectrum are caused by emission of energy

accompanying the fall of an electron from the outer shells to the second shell. The wavelength ( ) of the lines can be

calculated using the Balmer-Rydberg equation

where is an integer, is an integer greater than , and is the Rydberg constant.

Part A

In the Balmer-Rydberg equation, what value of is used to determine the wavelengths of the Balmer series?

Hint A.1 Explanation of n and m

Hint not displayed

Hint A.2 Classify the series

There are several named series, defined by their value of . Match the values of to the correct series.

Drag each item to the appropriate bin.

ANSWER:

View

Correct

If an excited electron drops to the second shell, the light emitted will be in the Balmer series:

Express your answer as an integer.

ANSWER:= 2

Correct

If an excited electron drops to the second shell, the light emitted will be in the Balmer series.

Part B

The image shows the wavelengths (in nanometers) of the

four visible lines in the Balmer series for hydrogen. Match

each line to its corresponding transition.


Hint not displayed

Hint B.2 Identify which transition will emit the shortest wavelength

Hint not displayed

Hint B.3 Identify which transition will emit the longest wavelength

Hint not displayed


ANSWER:

View

Correct

Part C

If our eyes could see a slightly wider region of the electromagnetic spectrum, we would see a fifth line in the Balmer

series emission spectrum. Calculate the wavelength associated with the fifth line.


Hint not displayed

Hint C.2 What values of m and n should be used?

Hint not displayed

Hint C.3 Substitute the values of m and n in the equation

Hint not displayed

Express the wavelength numerically in nanometers.

ANSWER: = 397

Correct

Electromagnetic radiation at 397 lies outside of the visible region shown here.

A wavelength of 397 is in the ultraviolet region, which would be to the left of the spectrum shown.

The Bohr Equation

The electron from a hydrogen atom drops from an excited state into the ground state. When an electron drops into a lower-

energy orbital, energy is released in the form of electromagnetic radiation.

Part A

How much energy does the electron have initially in the n=4 excited state?

Hint A.1 Use the Bohr equation

The Bohr equation states that the energy of an electron in a particular orbit is given by

where

= 1.10!107 (the Rydberg constant)

= 6.63!10"34 (Planck's constant)

and

= 3.00!108 (the speed of light in a vacuum)

Enter your answer numerically in joules.

ANSWER: = !1.36"10!19

Correct

Part B

What is the change in energy if the electron from Part A now drops to the ground state?


You found the energy of = 4.00 in Part A. Now find the energy of the ground state. Then subtract the two energies:

Hint B.2 Define the ground state

What is the value of in the ground state?

Enter your answer numerically.

ANSWER: = 1

Correct

Enter your answer numerically in joules.

ANSWER: = !2.05"10!18

Correct

Energy was released in this transition, so we express as a negative number (it is a net loss of energy from the

point of view of the system). However, you should use the absolute value of for the remaining calculations.

Part C

What is the wavelength of the photon that has been released in Part B?

Hint C.1 Relationship of energy to wavelength

Hint not displayed

Express your answer numerically in meters.

ANSWER: = 9.72!10"8

Correct

Part D

What might the photon from Part C be useful for?

Hint D.1 How to approach the problem

Hint not displayed

ANSWER: Warming up a frozen hot dog

Getting a suntan

Checking for broken bones

Night-vision goggles

Listening to music

Correct

Problem 6.34

Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen.

Part A

from 2 to 6 state,

ANSWER: Energy is emitted.

Energy is absorbed.

Correct

Part B

from an orbit of radius 4.76 to one of radius 0.529 ,


Energy is absorbed.

Correct

Part C

from the 6 to the 9 state.


Energy is absorbed.

Correct

The de Broglie Relation and the Wavelength of a Particle

Just as light waves have particle behavior, a moving particle has a wave nature. The faster the particle is moving, the higher

its kinetic energy and the shorter its wavelength. The wavelength, , of a particle of mass , and moving at velocity , is

given by the de Broglie relation

where is Planck's constant.

This formula applies to all objects, regardless of size, but the de Broglie wavelength of macro objects is miniscule compared

to their size, so we cannot observe their wave properties. In contrast, the wave properties of subatomic particles can be seen

in such experiments as diffraction of electrons by a metal crystal.

Part A

The mass of an electron is . If the de Broglie wavelength for an electron in a hydrogen atom is

, how fast is the electron moving relative to the speed of light? The speed of light is .


First, solve the de Broglie equation for velocity:

With mass in kilograms and wavelength in meters, the velocity can be calculated in meters per second. Once you know

the velocity, express it as a percentage of the speed of light, .

Hint A.2 Calculate the velocity of the electron in meters per second

What is the velocity of the electron?

Express your answer numerically in meters per second.

ANSWER: = 2.20!106

Correct

Express your answer numerically as a percentage of the speed of light.

ANSWER: 0.732

Correct

Part B

The mass of a golf ball is 45.9 . If it leaves the tee with a speed of 80.0 , what is its corresponding wavelength?


Hint not displayed

Hint B.2 Convert the mass to kilograms

Hint not displayed


ANSWER: = 1.80!10"34

Correct

The de Broglie wavelength of the golf ball is insignificant compared to the size of the ball itself. That is why we do

not observe the wave properties of objects in everyday life.

On the atomic scale, we cannot observe the dual nature of subatomic particles directly because we can't see atoms,

but the wave/particle description works well as a mathematical model of the behavior of elementary particles.

The Heisenberg Uncertainty Principle

A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of = 0.200 (where a

femtogram, , is ) and is swimming at a velocity of = 1.00 , with an uncertainty in the velocity of

2.00 . E. coli bacterial cells are around 1 ( ) in length. The student is supposed to observe the bacterium and

make a drawing. However, the student, having just learned about the Heisenberg uncertainty principle in physics class,

complains that she cannot make the drawing. She claims that the uncertainty of the bacterium's position is greater than the

microscope's viewing field, and the bacterium is thus impossible to locate.

Part A

What is the uncertainty of the position of the bacterium?


Hint not displayed

Hint A.2 Determine the mass of the bacterium in kilograms

Hint not displayed

Hint A.3 Convert the velocity to meters per second

Hint not displayed

Hint A.4 Determine the uncertainty of the bacterium's momentum

Use the mass (in kilograms), the velocity (in meters per second), and the percent uncertainty to calculate , the

uncertainty in the bacterium's momentum.

Hint A.4.1 How to find the uncertainty in the momentum

Hint not displayed

Express your answer numerically in kilogram meters per second.

ANSWER: = Answer not displayed


ANSWER: = 1.32!10"8

Answer Requested

Part B

By looking at the uncertainty of the bacterium's position, did the student have a valid point?

Hint B.1 Size of E. coli

Hint not displayed

ANSWER: The student has a point. The uncertainty of the bacterium's position is much larger than the bacterium

itself.

The bacterium's size and the uncertainty of its position are about the same magnitude. The student

should have little trouble finding the bacterium in the microscope

The student is wrong. The uncertainty of the bacterium's position is tiny compared to the size of the

bacterium itself.

Correct

Quantum Number Rules

Learning Goal: To learn the restrictions on each quantum number.

Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum

numbers.

The principal quantum number corresponds to the shell in which the electron is located. Thus can therefore be any

integer. For example, an electron in the 2p subshell has a principal quantum number of because 2p is in the second

shell.

The azimuthal or angular momentum quantum number corresponds to the subshell in which the electron is located. s

subshells are coded as 0, p subshells as 1, d as 2, and f as 3. For example, an electron in the 2p subshell has . As a

rule, can have integer values ranging from 0 to .

The magnetic quantum number corresponds to the orbital in which the electron is located. Instead of , , and ,

the three 2p orbitals can be labeled 1, 0, and 1, but not necessarily respectively. As a rule, can have integer values

ranging from to .

The spin quantum number corresponds to the spin of the electron in the orbital. A value of 1/2 means an "up" spin,

whereas 1/2 means a "down" spin.

Part A

What is the only possible value of for an electron in an s orbital?


Hint not displayed

Hint A.2 Determine the value of

Hint not displayed

ANSWER: 0

Correct

Part B

Classify each set of quantum numbers (ordered , , , ) as possible or not possible for an electron in an atom.


Hint not displayed

Hint B.2 Identify issues with an example set of quantum numbers

Hint not displayed

Drag the appropriate items to their respective bins.

ANSWER:

View

All attempts used; correct answer displayed

Quantum Numbers

Every electron in an atom is described by a unique set of four quantum numbers: , , , and . The principal quantum

number, , identifies the shell in which the electron is found. The angular-momentum quantum number, , indicates the

kind of subshell. The magnetic quantum number, , distinguishes the orbitals within a subshell. The spin quantum

number, , specifies the electron spin.

Part A

Identify which sets of quantum numbers are valid and which are invalid. Each set is ordered ( ).

Hint A.1 Identify the restrictions on the principal quantum number

Hint not displayed

Hint A.2 Identify the restrictions on the angular momentum quantum number

Hint not displayed

Hint A.3 Identify the restrictions on the magnetic quantum number

Hint not displayed

Hint A.4 Identify the restrictions on the spin quantum number

Hint not displayed


ANSWER:

View

Answer Requested

Part B

Identify the sets of quantum numbers that describe all the electrons in a neutral beryllium atom, . Each set is ordered

( ).

Hint B.1 Determine the number of electrons in a Be atom

Hint not displayed

Hint B.2 Determine the first set of quantum numbers

Hint not displayed

Hint B.3 Determine the last set of quantum numbers

Hint not displayed


ANSWER:

View

Correct

Characteristics of an Atomic Orbital

Wave functions provide information about an electron's probable location in space. This can be represented by an electron-density distribution diagram, called an

orbital. An orbital is characterized by a size, shape, and orientation in space.

Part A

What is the azimuthal quantum number, , for the orbital shown here?

Hint A.1 Match orbital shapes with letter designations

Hint not displayed

Hint A.2 Match letter designations with values of the azimuthal quantum number

Hint not displayed

Express your answer numerically as an integer.

ANSWER:= 2

Correct

For the known elements, only s, p, d, and f orbitals are used. However, quantum theory predicts the existence of orbitals with values higher than . For

example, an orbital with would be given the letter designation of g.

Part B

What is the label for this orbital that indicates the type of orbital and its orientation in space?


The label for a p orbital is based on its orientation with respect to the , , and axes. The p orbital that lies along the axis is labeled , the p orbital that

lies along the axis is labeled , and the p orbital that lies along the axis is labeled . The label for a d orbital is related to its orientation with respect to

the xy, xz, and zy planes. For example, the orbital that is bisected by the xz plane is labeled . Identify which plane bisects this particular orbital to determine

the appropriate label.

Hint B.2 Match orbital orientation with coordinate plane location

Based on the orientation of the following orbitals, identify the coordinate plane that bisects the orbital.


ANSWER:

View

Correct

Express your answer using appropriate letters (e.g., ).

ANSWER:

Correct

Part C

Compare the orbital shown in Parts A and B to the orbital shown here in size, shape, and orientation.

Which quantum number(s) would be different for these two orbitals?


Hint not displayed

Hint C.2 Identify the significance of the quantum numbers

Associate the quantum numbers with their specific orbital properties.

Match the words in the left-hand column with the appropriate blank in the sentences on the right. Make certain each sentence is complete before

submitting your answer.

ANSWER:

Answer

not

displayed

ANSWER: only

only

only

and

, , and

Correct

The label for this orbital would be .

The actual value of assigned to a given orientation is not arbitrary. It is determined based on how the hydrogen atom behaves in a magnetic field. This

also accounts for the name given to this quantum number.

Part D

How would the orbital in the shell compare to the orbital in the subshell?

A. The contour of the orbital would extend further out along the and axes.

B. The value of would increase by 2.

C. The radial probability function would include two more nodes.

D. The orientation of the orbital would be rotated 45 along the xy plane.

E. The value would be the same.

Hint D.1 Identify the significance of the quantum numbers

Hint not displayed

Hint D.2 The radial probability function

Hint not displayed


ANSWER:

View

Correct

A following representation of this orbital, shown when it is bisected by the xy plane,

shows the effect of the radial nodes on the orbital contours.

Orbital Diagrams

Learning Goal: To understand how to draw orbital diagrams, and how they are used to write electron configurations.

The electron configuration of an element is the arrangment of its electrons in their atomic orbitals. Electron configurations

can be used to predict most of the chemical properties of an element.

Orbital diagrams are a useful tool to aid in the derivation of the electron configuration of an element. Orbital diagrams are

filled using the aufbau principle, the Pauli principle, and Hund's rule.

Aufbau is German for "building up." The aufbau principle simply states that electrons are added to an orbital diagram one at

a time to the lowest energy orbital available, and that the orbital diagram is thus "built up." However, due to shielding of the

nucleus, the energies of orbitals are not always in order of energy level ( ). For example, the orbital is lower in energy

than the orbital for elements with more than one electron. To aid in remembering the energy order of orbitals, draw a

diagram with the energy levels (1 through 8) down the left of the diagram, and the subshells of each

energy level across in rows, with each row offset by one (so is below , is below , etc).

To determine the order in which orbitals fill, read the diagram from top to bottom, left to right. This

results in the order , etc. This order is often called the "aufbau order."

The Pauli principle states that no two electrons in an atom can have the same value of all four

quantum numbers ( , , , and ). The first three quantum numbers ( , , and ) specify a

particular orbital, such as . The fourth quantum number ( ) specifies the spin of the electron.

Since there are only two possibly values for ( and ), only two electrons can occupy any given orbital.

Remember that subshells consist of three separate orbitals ( , , and ), for a total of up to six electrons in a given

subshell. Similarly, subshells consist of five separate orbitals, and subshells consists of seven separate orbitals.

Finally, Hund's rule states that the lowest energy electron configuration for an atom is one having the maximum number of

electrons with parallel spins in degenerate orbitals. In other words, when three electrons begin to fill a subshell (which

consists of three degenerate orbitals, meaning three orbitals with the same energy), the lowest energy configuration consists

of one electron in each orbital, all with either spin up or spin down.

Part A

Draw an orbital diagram for boron.


First, determine the number of electrons in an atom of boron ( ). Next, fill the orbitals one electron at a time, from

lowest energy to highest energy.

Use this tool to draw the orbital diagram.

ANSWER:

View

Correct

Part B

Draw an orbital diagram for scandium (Sc).


Hint not displayed

Hint B.2 The aufbau principle

Remember that the orbital fills before the orbitals.

Use this tool to draw the orbital diagram.

ANSWER:

View

Correct

Part C

Electron configurations are a shorthand form of an orbital diagram, describing which orbitals are occupied for a given

element. For example, is the electron configuration of boron.


Hint not displayed

Hint C.2 The aufbau principle

Hint not displayed

Use this tool to generate the electron configuration of arsenic (As).

ANSWER:

View

Correct

Orbital-Filling Diagrams

Learning Goal: To learn to create orbital-filling diagrams.

An orbital-filling diagram shows the number of electrons in each orbital, which are shown in order of energy. The

placement of electrons in orbitals follows a certain set of rules.

1. Lower energy subshells fill before higher energy subshells. The order of filling is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s,

4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. The periodic table can be used to help you remember this order.

2. An orbital can hold up to two electrons, which must have opposite spins.

3. Hund's rule states that if two or more orbitals with the same energy are available, one electron goes in each until all

are half full. The electrons in the half-filled orbitals all have the same value of their spin quantum number.

Part A

How many orbitals are there in the third shell ( )?


Hint not displayed

Hint A.2 Determine how many orbitals are in the 3s subshell

Hint not displayed

Hint A.3 Determine how many orbitals are in the 3p subshell

Hint not displayed

Hint A.4 Determine how many orbitals are in the 3d subshell

Hint not displayed


ANSWER: 9

Correct

Nine orbitals (one s, three p, and five d) can hold a maximum of 18 electrons.

Part B

Show the orbital-filling diagram for (nitrogen). Stack the subshells in order of energy, with the lowest-energy subshell

at the bottom and the highest-energy subshell at the top.


Hint not displayed

Hint B.2 How many electrons are in a neutral atom of N?

Hint not displayed

Hint B.3 How to use the orbital-filling tool

Hint not displayed

Use the buttons at the top of the tool to add orbitals. Click within the orbital to add electrons.

ANSWER:

View

Correct

Part C

Show the orbital-filling diagram for (sulfur). Stack the subshells in order of energy, with the lowest-energy subshell at

the bottom and the highest-energy subshell at the top.


Hint not displayed

Hint C.2 How many electrons are in a neutral atom of S?

Hint not displayed


ANSWER:

View

Correct

Part D

Show the orbital-filling diagram for (bromine). Stack the subshells in order of energy, with the lowest-energy subshell

at the bottom and the highest-energy subshell at the top.

Hint D.1 How to approach the problem

Hint not displayed

Hint D.2 Determine the number of electrons in a neutral atom of Br

Hint not displayed


ANSWER:

View

Correct

Electron Configurations of Atoms and Ions

The electron configuration of an atom tells us how many electrons are in each orbital. For example, helium has two

electrons in the 1s orbital. Therefore the electron configuration of is .

Part A

What is the ground-state electron configuration of a neutral atom of cobalt?

Hint A.1 Determine cobalt's block

Look at a periodic table. In which block is cobalt found?

ANSWER: s

p

d

f

Correct

Enter the electron configuration (e.g., [Ne]3s^23p^1).

ANSWER: [Ar]4s^23d^7

Correct

Part B

What is the ground-state electron configuration of the oxide ion ?

Hint B.1 Determine the number of electrons

Hint not displayed

Enter the electron configuration (e.g., 1s^22s^2).

ANSWER: 1s^22s^22p^6

Correct

Part C

Which element has the following configuration: ?

Hint C.1 Count electrons

Hint not displayed

Enter the symbol for the element.

ANSWER: Ce

Correct

Quantum Numbers and Electron Identification

Quantum numbers are used to uniquely identify an electron in an atom. The Pauli exclusion principle states that no two

electrons in an atom may have the same set of four quantum numbers.

Part A

List a possible set of four quantum numbers ( , , , ) in order, for the highest energy electron in gallium, .

Refer to the periodic table as necessary.

Hint A.1 Descriptions of the four quantum numbers

Hint not displayed

Hint A.2 Identify the subshell

In which specific subshell is the highest energy electron in found?

Hint A.2.1 Identify the principal energy level

Hint not displayed

Hint A.2.2 Identify the type of subshell

Hint not displayed

ANSWER: 4s

3s

4p

2s

3d

3p

4d

4f

2p

1s

Correct

Based on this subshell designation you can identify the values of and for the electron. The possible values of

can be determined based on the value of . For any electron, the possible values of are 1/2 or +1/2

regardless of other factors.

Hint A.3 Identify the value

What is the value for an electron in a p subshell?


ANSWER: 1

Correct

The value can be thought of as a code for the type of subshell:

Subshell

s 0

p 1

d 2

f 3

Enter four numbers separated by commas (e.g., 3,2,-2,1/2).

ANSWER: 4,1,0,1/2

Correct

The first two numbers, and , specify the 4p subshell.

Although we typically fill orbitals in a given subshell from left to right and "up" before "down" when making an

orbital diagram, the "last" electron in gallium may go into any of the three 4p orbitals and may have either spin.

Thus, the possible values of are 1, 0, or 1 (restricted to integers from to ) and the possible values of

are +1/2 or 1/2.

Problem 6.26

The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of 941 is

required to break the nitrogen-nitrogen bond in .

Part A

What is the longest wavelength of radiation that possesses the necessary energy to break the bond?

ANSWER: = 1.27!10"7

Correct

Part B

What type of electromagnetic radiation is this?

ANSWER: radiowaves

infrared

gamma rays

X rays

microwaves

visible light

ultraviolet

Correct

In part D, light with the wavelength of 439 nm is used.

Problem 6.30

It requires a photon with a minimum energy of to emit electrons from sodium metal.

Part A

What is the minimum frequency of light necessary to emit electrons from sodium via the photoelectric effect?

ANSWER: = 6.66!1014

Correct

Part B

What is the wavelength of this light?

ANSWER: = 450

Correct

Part C

If sodium is irradiated with light of 439 , what is the maximum possible kinetic energy of the emitted electrons?

Express your answer using two significant figures.

ANSWER: = 1.2!10"20

Correct

Part D

What is the maximum number of electrons that can be freed by a burst of light whose total energy is 1.00 ?

ANSWER: = 2.21!1012

Correct electrons

Score Summary:

Your score on this assignment is 94.7%.You received 62.49 out of a possible total of 66 points.

mc ch.6 (quantum theory)

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