Download Honors Chemistry Worksheet – Electronic Structure of the Atom

Honors Chemistry Worksheet – Electronic Structure of the Atom
NEATLY provide the best complete responses to the following questions and problems.
For problems, show all equations, work, units, significant figures, and labels.
Radiant Energy
1. The mean distance of the moon from earth is 239,000 mi. How long did it take for the
TV pictures from the Apollo mission to reach earth from the moon?
2. The equipment designed to search for evidence of biological life on Mars is expected
to transmit its findings to earth from as far away as 420 million mi. How long will it take
for these transmissions to reach earth? Suppose they are received at a station in
California, and then immediately relayed to New York 3400 mi away. How much later
will they be received in New York than in California?
3. A particular AM radio station broadcasts at a frequency of 1120 kHz. Its sister FM
radio station casts at a frequency of 98.8 MHz. What are the wavelengths of the
radiations from each station?
4. Giant radio telescopes listening for radiation from outer space have detected strong
radio signals from a wavelength of 21 cm. What is the frequency of this radiation?
5. The red color of blood is due to a strong absorption of light centered at about 450 nm
in the visible region of the spectrum. What is the frequency of light which matches this
absorption?
6. Which of the following types of electromagnetic radiation is highest in energy? Which
is lowest? (a) sunlight through a green filter; (b) radiation from an FM station; (c)
radiation from an infrared heat lamp; (d) radiation from a hot oven.
Quantum Theory
7. The yellow lamps that illuminate highway intersections and city streets are filled with
sodium vapor that is electrically excited and then emits light. The strongest line emitted
by the sodium is at a wavelength of 589.2 nm. What is the magnitude of a quantum of
energy at this wavelength?
8. In the photoelectric effect experiment, why would no current flow when the light
sending waves to strike the emitter plate is off? What causes current to flow when the
light is on?
9. The energy required to move an electron from the metal by a photon is called the
photoelectric work function. For cesium metal the photoelectric work function is 3.05 x
10-19 J. What is the maximum wavelength of light that will cause electrons to be emitted
from cesium metal?
Honors Chemistry Worksheet – Electronic Structure of the Atom
Page 2
10. Photocells that are used in “electric eye” door openers and burglar alarms operate on
the principle of photoelectric emission. If the lamp used as the source of light has an
effective wavelength of 540 nm, would it be satisfactory to use copper as the metal in the
photocell? The photoelectric work function (that is, the energy required to remove an
electron from copper metal) is 6.69 x 10-19 J.
11. Calculate the energy required for the ionization of an electron from the ground state
of the hydrogen atom. What wavelength of light would ionize a hydrogen atom?
12. Explain how it is possible to tell from study of the light from a distant star that
hydrogen is present in the outer atmosphere of the star.
13. When the light from a neon lamp is dispersed in a prism to form a spectrum, it is
found that the spectrum is not continuous, that is, it does not consist of a broad range of
wavelengths of light. Rather, it consists of several sharp lines. Explain in general terms
why the emissions form a line spectrum rather than a continuous spectrum.
Bohr’s Theory
14. In Bohr’s theory of the hydrogen atom, under what conditions does the atom absorb
or emit radiant energy?
15. What is the energy of the electron, in Joules, when it is in the n = 6 state of the
hydrogen atom? When the electron moves from this state to the one in which n = 4, is
energy emitted or absorbed by the atom? Explain.
16. At what frequency would you expect to find the lowest frequency line in the series of
hydrogen absorption lines for which n1 = 3? What is the wavelength of this line? In what
region of the spectrum does it appear?
17. The He+ ion is isoelectronic with H; that is, it has the identical electronic structure.
Would you expect the ionization potential for He+ to be larger or smaller than for H?
Explain.
18. Atoms of He differ from H in having two electrons moving about the central nucleus.
How does this complicate the task of calculating the energies of these electrons? Is
Bohr’s theory suitable for He atoms? Explain.
Matter Waves
19. According to the de Broglie relationship, what requirement must the characteristic
wavelength of the electron have in order for it to be in an allowed orbit?
20. Cite one or more pieces of experimental evidence that show that it is possible for
particles of matter to possess wave properties.
Honors Chemistry Worksheet – Electronic Structure of the Atom
Page 3
21. Neutrons from an atomic reactor can be selected according to velocity and made into
beams of neutrons with the same velocity. What is the characteristic wavelength of a
neutron moving with a velocity of 3.22 x 103 m/sec?
22. What is the characteristic wavelength of a golf ball of mass 82 g, moving with a
speed of 265 km per hour?
Additional
23. How did Bohr’s model of the atom differ from that of Rutherford’s planetary model?
24. What are six regions of the electromagnetic spectrum?
a) Arrange them in increasing wavelength
b) Arrange them in increasing frequency
c) Arrange them in increasing energy
25. What are the colors of the visible spectrum?
a) Arrange them in order of increasing energy
26. Distinguish between the terms ground state and excited state.
27. Define the terms quantum and photon. How are these concepts similar? How are they
different?
28. Describe the photoelectric effect. How did Einstein utilize quantum theory to explain
the observations.
29. Who proposed the idea of quantization of light (quantum theory)? What does it really
mean?
30. Why did Heisenberg believe that one could never identify the exact location ands
momentum of the electron at the same time?
Honors Chemistry Worksheet – Electronic Structure of the Atom ANSWER KEY
NEATLY provide the best complete responses to the following questions and problems.
For problems, show all equations, work, units, significant figures, and labels.
Radiant Energy
1. The mean distance of the moon from earth is 239,000 mi. How long did it take for the
TV pictures from the Apollo mission to reach earth from the moon?
t = dxs
x 12 inch x 2.54 cm x 10-2 m x
1s
= 1.28 s
8
1 foot
1 inch
1 cm
3.00 x 10 m
239,000 mi. x 5,280 ft.
1 mile
2. The equipment designed to search for evidence of biological life on Mars is expected
to transmit its findings to earth from as far away as 420 million mi. How long will it take
for these transmissions to reach earth? Suppose they are received at a station in
California, and then immediately relayed to New York 3400 mi away. How much later
will they be received in New York than in California?
t = dxs
420,000,000 mi. x 5,280 ft.
1 mile
x
12 inch x 2.54 cm x 10-2 m x
1s
x
8
1 foot
1 inch
1 cm
3.00 x 10 m
1 min. = 14.784 min. = 15 min.
60 s
3,400 mi. x 5,280 ft.
1 mile
x 12 inch x 2.54 cm x 10-2 m x
1s
= 0.018 s
8
1 foot
1 inch
1 cm
3.00 x 10 m
3. A particular AM radio station broadcasts at a frequency of 1120 kHz. Its sister FM
radio station casts at a frequency of 98.8 MHz. What are the wavelengths of the
radiations from each station?
λ = c/υ
=
3.00 x 108 m/s
1,120 kHz
x 1kHz x
103 Hz
3.00 x 108 m/s
98.8 MHz
x 1MHz x
106 Hz
1 Hz = 268 m
/s
λ = c/υ
=
1 Hz = 3.04 m
/s
4. Giant radio telescopes listening for radiation from outer space have detected strong
radio signals from a wavelength of 21 cm. What is the frequency of this radiation?
ν = c/λ
=
3.00 x 108 m/s
21 cm
x
1 cm = 1.4 x 109 s-1
10-2 m
5. The red color of blood is due to a strong absorption of light centered at about 450 nm
in the visible region of the spectrum. What is the frequency of light which matches this
absorption?
ν = c/λ
=
3.00 x 108 m/s
450 nm
x
1 nm = 6.7 x 1014 s-1
10-9 m
6. Which of the following types of electromagnetic radiation is highest in energy? Which
is lowest? (a) sunlight through a green filter; (b) radiation from an FM station; (c)
radiation from an infrared heat lamp; (d) radiation from a hot oven.
Highest - (a) sunlight through a green filter
Lowest - (b) radiation from an FM station
Quantum Theory
7. The yellow lamps that illuminate highway intersections and city streets are filled with
sodium vapor that is electrically excited and then emits light. The strongest line emitted
by the sodium is at a wavelength of 589.2 nm. What is the magnitude of a quantum of
energy at this wavelength?
ν = c/λ
=
3.00 x 108 m/s
589.2 nm
x
1 nm = 5.09 x 1014 s-1
10-9 m
E = hν
= 6.6262 x 10-34 J-s x 5.09 x 1014 s-1
Answer: 3.37 x 10-19 J
8. In the photoelectric effect experiment, why would no current flow when the light
sending waves to strike the emitter plate is off? What causes current to flow when the
light is on?
In order for the electrons to be released from the emitter plate creating a
current, the plate must be struck by sufficient energy to overcome the binding
energy or meet the work function of the metal. If the switch is off, no radiant energy
is striking the emitter plate’s surface causing electron release.
9. The energy required to move an electron from the metal by a photon is called the
photoelectric work function. For cesium metal the photoelectric work function is 3.05 x
10-19 J. What is the maximum wavelength of light that will cause electrons to be emitted
from cesium metal?
ν = E/h
=
3.05 x 10-19 J
= 4.60 x 1014 s-1
6.6262 x 10-34 J-s
λ = c/υ
=
3.00 x 108 m/s
4.60 x 1014 /s
= 6.52 x 10-7 m
Honors Chemistry Worksheet – Electronic Structure of the Atom
Page 2
10. Photocells that are used in “electric eye” door openers and burglar alarms operate on
the principle of photoelectric emission. If the lamp used as the source of light has an
effective wavelength of 540 nm, would it be satisfactory to use copper as the metal in the
photocell? The photoelectric work function (that is, the energy required to remove an
electron from copper metal) is 6.69 x 10-19 J.
ν = c/λ
=
3.00 x 108 m/s
540 nm
x
1 nm = 5.56 x 1014 s-1
10-9 m
E = hν
= 6.6262 x 10-34 J-s x 5.56 x 1014 s-1
Answer: 3.68 x 10-19 J
Answer: No, because the energy of the photons of light would not cause release of
any electrons from copper in order to create an electrical current.
11. Calculate the energy required for the ionization of an electron from the ground state
of the hydrogen atom. What wavelength of light would ionize a hydrogen atom?
E = RH (1/ni2 - 1/nf2)
= 2.179 x 10-18 J (1/12 - 1/∞2)
= 2.179 x 10-18 J
ν = E/h
=
2.179 x 10-18 J
6.6262 x 10-34 J-s
= 3.288 x 1015 s-1
λ = c/υ
=
3.00 x 108 m/s = 9.12 x 10-8 m
3.288 x 1015 /s
12. Explain how it is possible to tell from study of the light from a distant star that
hydrogen is present in the outer atmosphere of the star.
Emission and absorption lines can tell us a great deal about a distant celestial
source, but they only occur under certain conditions.
Emission lines from an element will appear if:
1) there are atoms of the element present
2) the atoms are present as a low-density gas
3) the atoms are excited into a particular high energy level by some external
source
Absorption lines from an element will appear if
1) there are atoms of the element present
2) the atoms are present as a low-density gas
3) the atoms spend most of their time in a particular low-energy level
4) the gas lies between us and a source of continuous light (of all
wavelengths)
13. When the light from a neon lamp is dispersed in a prism to form a spectrum, it is
found that the spectrum is not continuous, that is, it does not consist of a broad range of
wavelengths of light. Rather, it consists of several sharp lines. Explain in general terms
why the emissions form a line spectrum rather than a continuous spectrum.
The atom is energetically quantized. The electrons are only permitted certain
energies, not an infinite range of energies. Therefore energy transitions made
by the electrons are limited and neither smooth nor continuous. The limited
shifts from one energy level to another result in the emission of only certain
wavelengths or frequencies which are needed to carry that precise amount of
energy.
Bohr’s Theory
14. In Bohr’s theory of the hydrogen atom, under what conditions does the atom absorb
or emit radiant energy?
The hydrogen atom may absorb or emit specific amounts of energy
corresponding to some hν. The “particle” of energy must correspond to an
electron absorption or emission which represents some ΔE between two
allowed orbits.
15. What is the energy of the electron, in Joules, when it is in the n = 6 state of the
hydrogen atom? When the electron moves from this state to the one in which n = 4, is
energy emitted or absorbed by the atom? Explain.
E = - RH (1/n2)
= - 2.179 x 110-18 J (1/62)
= - 6.053 x 10-20 J
E = RH (1/ni2 - 1/nf2)
= 2.179 x 10-18 J (1/62 - 1/42)
= - 7.566 x 10-18 J
When the electron moves closer to the nucleus, it becomes more stable as its
potential energy decreases. Therefore, a shift from n = 6 to n = 4 would be
accompanied by a release of energy as seen in the above calculation where the
resulting energy value was negative.
16. At what frequency would you expect to find the lowest frequency line in the series of
hydrogen absorption lines for which n1 = 3? What is the wavelength of this line? In what
region of the spectrum does it appear?
ΔE = hν = RH (1/ni2 - 1/nf2)
ν = RH/h (1/ni2 - 1/nf2)
=
2.179 x 10-18 J
(1/32 - 1/42)
6.6262 x 10-34 J-s
= 1.599 x 1014 s-1
λ = c/υ
=
3.00 x 108 m/s = 1.88 x 10-6 m
1.599 x 1014 /s
This line falls in the infrared region of the electromagnetic region.
17. The He+ ion is isoelectronic with H; that is, it has the identical electronic structure.
Would you expect the ionization potential for He+ to be larger or smaller than for H?
Explain.
The ionization potential (energy) of helium would be greater as the helium
nucleus contains two protons whereas, hydrogen only contains one. The
helium nucleus would have a greater coulombic attraction for the lone
electron than hydrogen due to this additional proton. f el = k Q1Q2 / r2
18. Atoms of He differ from H in having two electrons moving about the central nucleus.
How does this complicate the task of calculating the energies of these electrons? Is
Bohr’s theory suitable for He atoms? Explain.
Bohr’s theory is not suitable. This is because the mathematics he generated
was based on only one interaction within the atom, that between the electron
and proton (nucleus). When another electron is introduced the movement
and energy of the electrons are impacted by the presence of each other as
they coulombically repel.
Matter Waves
19. According to the de Broglie relationship, what requirement must the characteristic
wavelength of the electron have in order for it to be in an allowed orbit?
An integral number of wavelengths must fit inside the allowed orbit. It
cannot destructively interfere.
20. Cite one or more pieces of experimental evidence that show that it is possible for
particles of matter to possess wave properties.
Electron diffraction and interference.
Honors Chemistry Worksheet – Electronic Structure of the Atom
Page 3
21. Neutrons from an atomic reactor can be selected according to velocity and made into
beams of neutrons with the same velocity. What is the characteristic wavelength of a
neutron moving with a velocity of 3.22 x 103 m/sec?
λ = h / mv
=
6.6262 x 10-34 J-s
x
-24
3
1.675 x 10 g x 3.22 x 10 m/s
= 1.23 x 10-10 m
103 g
1 kg
x 1 kg m2/s2
1J
22. What is the characteristic wavelength of a golf ball of mass 82 g, moving with a
speed of 265 km per hour?
λ = h / mv
=
6.6262 x 10-34 J-s x 103 g
82 g x 265 km/hr 1 kg
x 1 kg m2/s2 x 1 km
1J
103 m x 1 hr x 1 min.
60 min
60 s
= 1.1 x 10-34 m
Additional
23. How did Bohr’s model of the atom differ from that of Rutherford’s planetary model?
The main difference was the electrons were quantized by traveling in only
certain allowed orbits or pathways about the nucleus.
24. What are six regions of the electromagnetic spectrum?
Radio, microwave, infrared, visible, ultraviolet, x-ray, gamma
a) Arrange them in increasing wavelength
Gamma, x-ray, ultraviolet, visible, infrared, microwave, radio
b) Arrange them in increasing frequency
Radio, microwave, infrared, visible, ultraviolet, x-ray, gamma
c) Arrange them in increasing energy
Radio, microwave, infrared, visible, ultraviolet, x-ray, gamma
25. What are the colors of the visible spectrum?
Red, orange, yellow, green, blue, violet (ROYGBV)
a) Arrange them in order of increasing energy
Red, orange, yellow, green, blue, violet
26. Distinguish between the terms ground state and excited state.
Ground state refers to an atom existing in its lowest energy state. All
electrons occupy positions of least energy.
The atom enters an excited state when it absorbs external energy resulting in
one or more electrons occupying positions of energy greater than the lowest
available.
27. Define the terms quantum and photon. How are these concepts similar? How are they
different?
Similarity – The each represent a particle of electromagnetic energy.
Difference – The term quantum is used for all forms of electromagnetic
radiation. The term photon is usually tied to visible energy.
28. Describe the photoelectric effect. How did Einstein utilize quantum theory to explain
the observations.
Electrons are emitted from the clean surface of a metal when struck by
radiant energy.
29. Who proposed the idea of quantization of light (quantum theory)? What does it really
mean?
Max Planck proposed the quantum theory. He attempted to draw
conclusions from the radiation to the radiating atom. On basis of empirical
data, he developed a new formula which later showed remarkable agreement
with accurate measurements of the spectrum of heat radiation. The result of
this formula was so that energy is always emitted or absorbed in discrete
units, which he called quanta.
30. Why did Heisenberg believe that one could never identify the exact location ands
momentum of the electron at the same time?
As an example, Heisenberg considered the measurement of the position of an
electron by a microscope. The accuracy of such a measurement is limited by
the wave length of the light illuminating the electron. Thus, it is possible, in
principle, to make such a position measurement as accurate as one wishes, by
using light of a very short wave length, e.g., γ-rays. But for γ-rays, the
Compton effect cannot be ignored: the interaction of the electron and the
illuminating light should then be considered as a collision of at least one
photon with the electron. In such a collision, the electron suffers a recoil
which disturbs its momentum. Moreover, the shorter the wave length, the
larger is this change in momentum. Thus, at the moment when the position of
the particle is accurately known, Heisenberg argued, its momentum cannot
be accurately known: