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Homework 6 Chapter 06
Homework 6 Chapter 06
Due: 11:59pm on Wednesday, November 2, 2016
You will receive no credit for items you complete after the assignment is due. Grading Policy
Sample Exercise 6.2 Practice Exercise 1 with feedback
Part A ­ Calculating Frequency from Wavelength
Consider the following three statements:
i. For any electromagnetic radiation, the product of the wavelength and the frequency is a constant.
18
ii. If a source of light has a wavelength of 3.0 Å, its frequency is 1.0 × 10 Hz.
iii. The speed of ultraviolet light is greater than the speed of microwave radiation.
Which of these three statements is or are true?
ANSWER:
Only one statement is true
Statements (i) and (ii) are true
Statements (i) and (iii) are true
Statements (ii) and (iii) are true
All three statements are true
Correct
The only false statment is (iii), "The speed of ultraviolet light is greater than the speed of microwave radiation" is false
because the speed of any electromagnetic radiation is constant regardless the type of radiation.
Sample Exercise 6.4 Practice Exercise 1 with feedback
Part A ­ Electronic Transitions in the Hydrogen Atom
In the top part of image below, the four lines in the H atom spectrum are due to transitions from a level for which ni > 2 to
the nf = 2 level. What is the value of ni for the blue­green line in the spectrum?
ANSWER:
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Homework 6 Chapter 06
3
4
5
6
7
Correct
Sample Exercise 6.5 Practice Exercise 1 with feedback
Part A ­ Matter Waves
Consider the following three moving objects:
i. A golf ball with a mass of 45.9 g moving at a speed of 50.0 m/s .
ii. An electron moving at a speed of 3.5 × 10 5 m/s.
iii. A neutron moving at a speed of 2.3 × 10 2 m/s.
List the three objects in order from shortest to longest de Broglie wavelength.
ANSWER:
i < ii < iii
i < iii < ii
ii < iii < i
iii < i < ii
iii < ii < i
Correct
If you calculate the de Broglie wavelength for each object, you should obtain the following:
i. The de Broglie wavelength of the golf ball is 2.89 × 10 −34
ii. The de Broglie wavelength of the electron is 21 Å.
.
m
iii. The de Broglie wavelength of the neutron 17 Å.
The de Broglie wavelength is inversely proportional to the momentum. So, the order from shortest to longest de
Broglie wavelength is i < iii < ii.
Sample Exercise 6.7 Practice Exercise 1 with feedback
Part A ­ Orbital Diagrams and Electron Configurations
How many of the elements in the second row of the periodic table (Li through Ne) will have at least one unpaired electron
in their electron configurations?
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Homework 6 Chapter 06
ANSWER:
3
4
5
6
7
Correct
There are six elements in the second row of the periodic table that have at least one unpaired electron in their electron
configurations: Li, B, C, N, O, F.
Sample Exercise 6.8 Practice Exercise 1 with feedback
Part A ­ Electron Configurations for a Group
A certain atom has an ns2 np6 electron configuration in its outermost occupied shell. Which of the following elements
could it be?
ANSWER:
Si
Kr
I
Be
Rb
Correct
electron configuration indicates eight valence electrons. Krypton, Kr has eight electrons its outermost
10
occupied shell. The electron configuration for Kr is [Ar] 3d 4s2 4p6
2
ns np
6
± 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 12.4 cm . How many photons are required to heat 305 mL of
coffee from 25.0 ∘ C to 62.0 ∘ C? Assume that the coffee has the same density, 0.997 g/mL , and specific heat capacity,
4.184 J/(g ⋅ K) , as water over this temperature range.
Express the number of photons numerically.
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Hint 1. How to approach the problem
First, determine the amount of energy in joules needed to heat the coffee using the following equation:
q = Cs × m × ΔT
in which q is the quantity of heat transferred, Cs is the specific heat capacity, m is the mass of the substance, and
ΔT is the temperature change. Second, determine the energy of a photon with a wavelength of 12.4 cm using the
relationship
E=
hc
λ
in which λ is the wavelength in meters, h is Planck's constant (6.626 × 10 −34 J ⋅ s), and c is the speed of light (
8
2.998 × 10 m/s ). Lastly, use the total energy and the energy per photon to determine the number of photons
needed.
Hint 2. Determine the total energy required
How much energy in joules is required to heat 305 mL of coffee from 25.0 ∘ C to 62.0 ∘ C? Assume that the coffee
has the same density, 0.997 g/mL , and specific heat capacity, 4.184 J/(g ⋅ K) , as water over this temperature
range.
Express your answer numerically in joules.
Hint 1. Determine the mass of coffee
What is the mass m of the sample of coffee?
Express your answer numerically in grams.
Hint 1. Conversion factor to use
The density d of a substance expresses the relationship between mass m and volume v as
d=
m
v
ANSWER:
m
= 304 g Hint 2. Determine the temperature change
What is the temperature change in kelvins?
Express your answer numerically in kelvins.
ANSWER:
ΔT
= 37.0 K ANSWER:
q
= 4.71×104 J https://session.masteringchemistry.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=4828294
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Hint 3. Determine the energy of a single photon
What is the energy of a photon with a wavelength of 12.4 cm ?
Express your answer numerically in joules per photon.
Hint 1. Relation between energy and wavelength
The energy of a photon is related to its wavelength by Plank's constant, h, and the speed of light, c, as
E=
hc
λ
where m is the wavelength in meters, h is 6.626 × 10 −34 J ⋅ s, and c is 2.998 × 10 8 m/s.
Hint 2. Determine the wavelength in meters
Convert 12.4 cm to meters? Recall that 1 m
= 100 cm
.
Express your answer numerically in meters.
ANSWER:
= 0.124 m λ
ANSWER:
1.60×10−24 J/photon Hint 4. Identify how to find the number of photons
If x is the total energy in joules, and y is the number of joules per photon, which choice shows how to calculate the
number of photons?
ANSWER:
y/x
xy
x/y
ANSWER:
2.94×1028 photons Correct
Electromagnetic radiation in this region of the spectrum is also used for cellular phones, radar, and wireless Internet.
The Bohr Equation
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Homework 6 Chapter 06
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?
Express your answer with the appropriate units.
Hint 1. Use the Bohr equation
The Bohr equation states that the energy of an electron in a particular orbit is given by
En = −
Rhc
n2
where
R
= 1.10×107 m−1 (the Rydberg constant)
h
= 6.63×10−34 J ⋅ s (Planck's constant)
and
c
= 3.00×108 m/s (the speed of light in a vacuum)
ANSWER:
En
= −1.37×10−19 J
Correct
Part B
What is the change in energy if the electron from Part A now drops to the ground state?
Express your answer with the appropriate units.
Hint 1. How to approach the problem
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You found the energy of n = 4.00 in Part A. Now find the energy of the ground state. Then subtract the two
energies:
ΔE = Ef inal − Einitial
Hint 2. Define the ground state
What is the value of n in the ground state?
Enter your answer numerically.
ANSWER:
= 1
n
ANSWER:
ΔE
= −2.05×10−18 J
Correct
Energy was released in this transition, so we express ΔE 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 ΔE for the remaining calculations.
Part C
What is the wavelength λ of the photon that has been released in Part B?
Express your answer with the appropriate units.
Hint 1. Relationship of energy to wavelength
The energy of the photon emitted by the electron is related to its wavelength by
E =
hc
λ
where λ is the wavelength in meters, 6.63×10−34 J ⋅ s is Planck's constant, and 3.00×108 m/s is the speed of light
in a vacuum.
ANSWER:
= 9.70×10−8 m
λ
Correct
Part D
What might the photon from Part C be useful for?
Hint 1. How to approach the problem
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Homework 6 Chapter 06
Compare the wavelength of the photon calculated in Part C with the electromagnetic spectrum shown in the
introduction.
ANSWER:
Warming up a frozen hot dog
Getting a suntan
Checking for broken bones
Night­vision goggles
Listening to music
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, λ, of a particle of mass m, and moving at velocity v , is given
by the de Broglie relation
λ=
where h
= 6.626 × 10
−34
h
mv
is Planck's constant.
J ⋅ s
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 9.11 × 10 −31 kg. If the de Broglie wavelength for an electron in a hydrogen atom is −10
8
3.31 × 10
m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00 × 10 m/s.
Express your answer numerically as a percent.
Hint 1. How to approach the problem
First, solve the de Broglie equation for velocity:
λ=
h
mv
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, 3.00 × 10 8 m/s.
Hint 2. Calculate the velocity of the electron in meters per second
What is the velocity of the electron?
Express your answer with the appropriate units.
ANSWER:
v
= 2.20×106 m
s
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Homework 6 Chapter 06
ANSWER:
0.732 % Correct
Part B
The mass of a golf ball is 45.9 g . If it leaves the tee with a speed of 80.0 m/s , what is its corresponding wavelength?
Express your answer with the appropriate units.
Hint 1. How to approach the problem
First, convert the mass of the golf ball to kilograms. Then, calculate wavelength using the de Broglie equation
λ=
h
mv
Hint 2. Convert the mass to kilograms
Convert the mass of the golf ball from grams to kilograms.
Express your answer with the appropriate units.
Hint 1. Conversion factor
Recall that 1 kg
= 1000 g
.
ANSWER:
4.59×10−2 kg
ANSWER:
= 1.80×10−34 m
λ
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.
Electron Configurations of Atoms
An atom consists of a small, positively charged nucleus, surrounded by negatively charged electrons. We organize the
electrons in a logical manner. As the atomic number increases, electrons are added to the subshells according to their energy.
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.
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Homework 6 Chapter 06
The periodic table can be used to help you remember the order.
Part A
Give the complete ground­state electron configuration for silicon (Si).
Express the complete electron configuration using superscripts where appropriate. For example, the configuration
for Li would be entered as 1s^22s^1.
Hint 1. How to approach the problem
Determine the number of electrons needed. Fill the lowest energy orbitals first. Proceed to the higher energy
subshells until all the electrons are placed in the correct subshells.
Hint 2. Determine the number of electrons in a neutral atom of Si
The number of electrons in a neutral atom is the same as the atomic number. The atomic number can be read from
the periodic table. How many electrons are in a neutral atom of Si?
Express your answer numerically as an integer.
ANSWER:
14
Hint 3. Build an orbital­filling diagram for Si
Create and fill an orbital­filling diagram for silicon (Si). Be sure to arrange the subshells in order of increasing
energy.
Use the buttons at the top of the tool to add orbitals. Click within the orbital to add electrons.
ANSWER:
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Homework 6 Chapter 06
ANSWER:
1s^22s^22p^63s^23p^2
Correct
Part B
Give the ground­state electron configuration for silicon (Si) using noble­gas shorthand.
Express your answer in condensed form as a series of orbitals. For example, [Ar]4s2 3d 8 would be entered as
[Ar]4s^23d^8.
Hint 1. Determine the noble gas to insert
The complete electron configuration for silicon is 1s2 2s2 2p6 3s2 3p2 . Which noble gas is represented in the
configuration?
ANSWER:
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Homework 6 Chapter 06
Ne
Kr
Ar
He
Xe
ANSWER:
[Ne]3s^23p^2
Correct
Part C
Give the actual ground­state electron configuration for copper (Cu) using the complete form.
Express the electron configuration using superscripts where appropriate. For example, the configuration for Li
would be entered as 1s^22s^1.
Hint 1. How to approach the problem
Determine the number of electrons needed. Fill the lowest energy orbitals first. Proceed to the higher energy
subshells until all the electrons are placed in the correct subshells. This will generate the expected ground­state
electron configuration for copper. Then, consider the stability of a filled d subshell. At least one electron from the
expected configuration will have to be moved from one subshell to another to arrive at the actual configuration.
Hint 2. Determine the number of electrons in a neutral atom of Cu
The number of electrons in a neutral atom is the same as the atomic number. The atomic number can be read from
the periodic table. How many electrons are in a neutral atom of Cu?
Express your answer numerically as an integer.
ANSWER:
29
Hint 3. Build an orbital­filling diagram for Cu
Create and fill an orbital­filling diagram for copper (Cu). Be sure to arrange the subshells in order of increasing
energy.
Use the buttons at the top of the tool to add orbitals. Click within the orbital to add electrons.
ANSWER:
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Homework 6 Chapter 06
ANSWER:
1s^22s^22p^63s^23p^64s^13d^10
Correct
9
The expected ground­state electron configuration of copper is 1s2 2s2 2p6 3s2 3p6 4s2 3d ; however, the actual
10
configuration is 1s2 2s2 2p6 3s2 3p6 4s1 3d because a full d subshell is particularly stable. There are 18 other
anomalous elements for which the actual electron configuration is not what would be expected.
Part D
Give the ground­state electron configuration for copper (Cu) using noble­gas shorthand.
Express your answer in condensed form as a series of orbitals. For example, [Ar]4s2 3d 8 would be entered as
[Ar]4s^23d^8.
Hint 1. Determine the noble gas to insert
The complete electron configuration for silicon is 1s2 2s2 2p6 3s2 3p6 4s1 3d 10 . Which noble gas is represented in
the configuration?
ANSWER:
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Homework 6 Chapter 06
Ne
He
Xe
Kr
Ar
ANSWER:
[Ar]4s^13d^10
Correct
Problem 6.71
What is the maximum number of electrons that can occupy each of the following subshells?
Part A
3p
ANSWER:
6 electrons Correct
Part B
5d
ANSWER:
10 electrons Correct
Part C
2s
ANSWER:
2 electrons https://session.masteringchemistry.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=4828294
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Homework 6 Chapter 06
Correct
Part D
4f
ANSWER:
14 electrons Correct
Problem 6.78
Part A
Identify the group of elements that corresponds to the following generalized electron configuration: [noble gas]ns2 np5
ANSWER:
7A
Correct
Part B
Indicate the number of unpaired electrons for following: [noble gas]ns2 np5
Express your answer as an integer.
ANSWER:
1
Correct
Part C
Identify the group of elements that corresponds to the following generalized electron configuration: 2
[noble gas]ns (n − 1)d
2
ANSWER:
4B
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Homework 6 Chapter 06
Correct
Part D
Indicate the number of unpaired electrons for following: [noble gas]ns2 (n − 1)d
2
Express your answer as an integer.
ANSWER:
2
Correct
Part E
Identify the group of elements that corresponds to the following generalized electron configuration: 2
[noble gas]ns (n − 1)d
10
np
1
ANSWER:
3A
Correct
Part F
Indicate the number of unpaired electrons for following: [noble gas]ns2 (n − 1)d
10
np
1
Express your answer as an integer.
ANSWER:
1
Correct
Part G
Identify the elements that correspond to the following generalized electron configuration: [noble gas]ns2 (n − 2)f 6
Express your answer as the element symbol. If there is more than one answer, separate them by a comma.
ANSWER:
Sm,Pu
Correct
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Homework 6 Chapter 06
Part H
Indicate the number of unpaired electrons for following: [noble gas]ns2 (n − 2)f
6
Express your answer as an integer.
ANSWER:
6
Correct
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