Introduction
An understanding of the composition of matter and the organization of the atom is necessary, not
only to explain natural phenomena, but to control natural phenomena and to develop new
technologies. The physical sciences did showed little progress using Aristotle’s theories of matter.
7.1 Early Atomic Models
Since atoms cannot be directly observed scientists develop atomic models to help visualize and
understand the atom. A model relates something we are familiar with to something that is otherwise
unfamiliar and not tangible. As new experimental evidence is obtained the models become more
sophisticated.
Notes:
Billiard Ball model of the atom
___________________________
This model suggests that atoms are very small, indivisible particles.
___________________________
Raisin Bun (Plum Pudding) Model of the Atom
Developed by J. J. Thomson
___________________________
Experimental Evidence:
Cathode rays are beams of electrons produced at the cathode.
They are produced using a high voltage and a cathode and
anode inside a glass tube.
___________________________
Cathode Ray Tubes (CRT)
___________________________
___________________________
___________________________
___________________________
anode
Cathode
rays
Properties of cathode rays:
• travel in straight lines.
• deflected by electric and magnetic fields.
• produce chemical reactions similar to that of light.
Copyright © Kennedy/Oswald
Cathode
Rays
7.1.1
Chapter 7 - 283
Notes:
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___________________________
___________________________
___________________________
___________________________
___________________________
Interpretation of Evidence:
Since the cathode rays are deflected by electric fields and
magnetic fields, they must be discrete (i.e., individual)
charged particles.
Thomson determined the charge-to-mass ratio (q/m) for
these cathode rays. The ratio was the same no matter what
material was used for the cathode. Thomson interpreted this
as meaning that all substances contained the same small
discretely charged particles. These are now called electrons.
- - - - -
___________________________
___________________________
___________________________
electrons embedded in a
positive fluid
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Planetary (Nuclear) Model of the Atom
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___________________________
___________________________
Developed by Rutherford
Experimental Evidence:
A thin gold foil scattered a beam of alpha particles. Most
alpha particles went directly through, a few scattered at small
angles, very few scattered at large angles.
Alpha-particle Scattering
___________________________
few
very few
2+
most
α
Interpretation of Evidence:
gold
foil
Rutherford interpreted this as meaning the atom is mostly empty space with an extremely small
positive nucleus with electrons orbiting it.
Electrons are interpreted as circling the nucleus which means they
are undergoing a centripetal acceleration. Therefore the model
must be invalid, as accelerating charges should be emitting EMR.
As the electrons emit EMR they are losing energy and should
spiral into the nucleus.
Copyright © Kennedy/Oswald, 2008
e
e
-
-
++
Chapter 7 - 284
Examples
1.
A stream of charged particles having an initial speed of 5.7 x 106 m/s enters a magnetic field
of 0.264 T. As they enter the magnetic field they deflect into a circular path with radius of 7.5
cm. Determine the charge-to-mass ratio of the charged particles.
The charge to mass ratio is 2.9 x 108 C/kg.
2.
An electron beam enters a 10000 N/C electric field and a 15.5 mT magnetic field in a CRT
and passes through un-deflected as shown in the diagram.
a. Use arrows to draw the electric field between the charged plates.
b. Determine the speed of the electrons.
e-
|E|
B
b. The electrons’ speed is 6.45 x 104 m/s.
3.
Explain why Rutherford suggested that the electron orbit the nucleus.
Just as a satellite must orbit the Earth to maintain its altitude, Rutherford thought an
electron should do the same.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 285
Problems
Use the following information to answer questions 1 & 2.
A basic cathode ray tube consists of a thin filament carrying an electrical current. When the filament
gets hot, electrons “boil” off the surface of the metal in a process called thermionic emission. They
are then accelerated across a potential difference – from the cathode to the anode.
1.
Use the rest mass of an electron and the elementary charge to determine the charge-to-mass
ratio of an electron. [1.76 x 1011 C/kg]
The charge-to-mass ratio for an electron is 1.76 x 1011 C/kg.
2.
A beam of charged particles travelling at 7.5 x 106 m/s enter a 0.651 T magnetic field
perpendicular to the direction the electrons are moving. As they enter the magnetic field they
deflect into a circular beam with radius of 5.5 cm. Determine the charge-to-mass ratio of the
charged particles. [2.1 x 108 C/kg]
The charge-to-mass ratio is 2.1 x 108 C/kg.
3.
J. J. Thomson performed an experiment to measure the charge-to-mass ratio of a hydrogen
ion (p+) and compared it with the charge-to-mass (q/m ) ratio for an electron in order to
determine how much more massive a proton was in comparison to an electron. Determine the
a. charge-to-mass ratio (q/m) for a hydrogen ion. [9.58 x 107 C/kg]
b. mass of a proton relative to an electron (the charge-to-mass ratio for an electron is
1.756 x 1011 C/kg). [1833]
a. The charge-to-mass ratio is 9.58 x 107 C/kg.
b. The proton is 1833 times larger than the electron.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 286
4.
An electron enters a magnetic field of 75.0 mT and deflects in to a circular arc with a radius of
0.0075 m. Determine the kinetic energy of the electrons in electron volts. [28 keV]
The electron’s kinetic energy is 28 keV.
Use the following information to answer question 5.
An electric field can be used to balance the magnetic field so that beams of charged particles go undeflected in CRT experiments. To do this the electric field must be perpendicular relative to the
magnetic field.
5.
A stream of electrons enters a 7200 N/C electric field and a 6.5 mT magnetic field in a CRT
and is not deflected as it passes through the two fields.
a. Draw a free-body diagram for the electron. [Appendix A]
b. Determine the speed of the undeflected electrons. [1.1 x 106 m/s]
b. The electrons’ speed is 1.1 x 106 m/s.
6.
Unidentified ions enter a magnetic field of 0.800 T at 3.40 x 105 m/s and deflected with a
radius of 8.50 cm. Determine the charge-to-mass ratio of the ions. [5.00 x 106 C/kg]
The charge-to-mass ratio is 5.00 x 106 C/kg.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 287
7.
Electrons are accelerated from rest across a potential difference of 1200 V in a
CRT. This beam of electrons then enter a magnetic field of 0.0450 T. Determine
the radius of the beam’s curvature (assume the beam and the magnetic field are
perpendicular to each other). [2.60 mm]
?
7.1a
The beam’s radius would be 2.60 mm.
8.
The gold foil, in Rutherford’s experiment gradually accumulated a positive charge. Explain
why this happened and how it helped Rutherford determine atomic structure. [Appendix A]
The alpha particles are knocking off electrons.
9.
Describe the major problem with Rutherford’s Planetary Model. [Appendix A]
Maxwell’s theory of electromagnetism predicts the failure of the planetary model because a
moving charge should emit energy. If the electron is emitting energy, it should gradually
undergo orbital decay and the atomic structure should collapse.
10.
Determine the centripetal acceleration of an electron circling a proton if they are separated by
a distance of 5.29 x 10-11 m. [9.03 x 1022 m/s2]
The centripetal acceleration is 9.03 x 1022 m/s2.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 288
7.2 Summary Notes – Atomic Spectra & the Quantized Model
Notes:
The Bohr Atom
Developed by Bohr
___________________________
___________________________
Experimental Evidence:
___________________________
The light produced (spectra) by various substances was
used to develop this model. The light is analyzed using a
prism or diffraction grating. There are three types of
spectra:
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Continuous Spectra
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When a solid is heated it will produce a continuous
spectra (blackbody radiation).
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ROYGBIV
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Line-emission Spectra
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When a gas absorbs energy a bright line spectra is
observed. Each element has its own characteristic lineemission spectrum which may be used to identify the
elements.
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Line-absorption Spectra
White light (a continuous spectra) is passed through a gas at low temperature. A spectrum with lines
of missing wavelengths (dark lines) is produced.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 289
Interpretation of Evidence:
Notes:
___________________________
According to Bohr, only certain electron energies are
allowed as an electron orbits a nucleus – the energy is
quantized. At these energy levels Maxwell’s law stating
that accelerating charges must emit EMR does not apply.
___________________________
___________________________
___________________________
When an electron absorbs energy (through the collision
with a passing electron or a photon) it moves to higher
energy levels. When an electron moves to lower energy
levels it releases energy as a photon.
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___________________________
___________________________
• A line-emission spectrum is produced when the
electron in an atom releases energy as a photon.
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• A line-absorption spectrum is produced when the
electron in an atom absorbs photon energy.
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___________________________
Therefore, only light with certain frequencies and
wavelengths can be emitted or absorbed by an atom.
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Examples
1.
Two atomic spectra are provided below. Explain why they appear to be produced from the
same substance.
Visible line-emission spectrum
red
green
blue
violet
Visible line-absorption spectrum
red
(missing)
green
(missing)
blue
violet
(missing) (missing)
They are most likely from the same substance because the bright line spectrum has lines where
the absorption spectrum does not.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 290
Use the information below to answer questions 2 – 4.
The energies of an electron within an atom are most often given relative to ionization as shown
below.
Ionization
D
-2.0 eV
C
-7.0 eV
B
-10.0 eV
A
2.
0 eV
-14.0 eV
Ground state
Determine the energy of a photon released as an electron makes a transition from D to B.
The photon released has an energy of 8.0 eV.
3.
Determine the number of photons of different wavelengths that could possibly be produced
due to an electron at level C moving back to ground state.
Three transitions are possible; therefore, three different photons may possibly be released.
4.
An electron at ground state in the atom is struck by a passing electron having an energy of
9.0 eV and the atom’s electron absorbs as much of the energy as possible. Determine the
a. kinetic energy of the passing electron after it collides with the electron in the atom.
b. minimum possible wavelength of light that could be released from the atom.
a. The kinetic energy of the passing electron after the collision is 2.0 eV.
b. The minimum possible wavelength released is 1.8 x 10-7 m.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 291
Problems
Use the information below to answer questions 1 & 2.
The energy levels for an atom are drawn below. The energy at each level is given relative to ground
state and levels are labelled alphabetically.
Ionization
D
9.0 eV
C
6.0 eV
B
4.0 eV
A
1.
14.0 eV
0
Ground state
A passing electron having a kinetic energy of 7.0 eV collides with an electron in the ground
state of the atom. Determine the
a. highest energy level the electron in the atom could obtain. [C]
b. kinetic energy of the passing electron after the collision. [1.0 eV]
a. Since energy may only be absorbed in quantized amounts, level C is the highest achievable
level.
2.
Determine the energy of the photon released as an electron makes a transition from
a. D to A. [9.0 eV]
b. C to B. [2.0 eV]
a. The energy of the photon released is 9.0 eV.
b. The energy of the photon released is 2.0 eV.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 292
Use the information below to answer questions 3 – 6.
The energies of an electron within an
atom are most often given relative to
ionization as shown to the right.
Ionization
D
-3.0 eV
C
-8.0 eV
B
-11.0 eV
A
3.
0 eV
-15.0 eV
Ground state
Determine the energy of the photon released as an electron makes a transition from
a. D to A. [12.0 eV]
b. C to B. [3.0 eV]
a. The energy of the photon released when an electron moves from D to A is 12.0 eV.
b. The energy of the photon released when an electron moves from C to B is 3.0 eV.
4.
Determine the energy required to ionize the atom if its electron is originally in the ground
state. [15.0 eV]
An energy of 15 eV is required to ionize the atom.
5.
Determine the number of photons of different wavelengths that could possibly be produced
due to an electron at level D moving back towards ground state. [Appendix A]
A total of six different transitions are
possible.
6.
An electron at ground state in the atom is struck by a passing electron having an energy of
8.0 eV and the atom’s electron absorbs as much of the energy as possible. Determine the
a. kinetic energy of the passing electron after it collides with the electron in the atom. [1.0 eV]
b. minimum possible wavelength of light that could be released from the atom. [1.8 x 10-7 m]
a. The kinetic energy of the passing electron after the collision is 1.0 eV.
b. The minimum possible wavelength of light is 1.8 x 10-7 m.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 293
Use the information below to answer questions 7 – 9.
Mercury gas is used in fluorescent lights and many street lamps. Some
of the possible transitions for an electron in a mercury atom are given
in the energy level diagram.
7.
The electron in a mercury atom drops (de-excites) from energy
level E to energy level B. Determine the
a. energy of the photon emitted. [3.06 eV]
b. frequency of the photon emitted. [7.39 x 1014 Hz]
c. wavelength of the photon emitted. [406 nm]
d. region of the EMR spectrum where the photon is classified.
[Appendix A]
ionization
0 eV
F
E
-2.48 eV
-2.68 eV
D
-3.71 eV
C
B
-5.52 eV
-5.74 eV
A
-10.38 eV
The light is visible - violet.
8.
Determine the quantity of energy would be required to ionize a mercury atom if its electron is
already excited to energy level E. [2.68 eV]
0 – -2.68 eV = 2.68 eV
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 294
9.
10.
An electron with 5.00 eV of energy collides with an electron in the ground state of the
mercury atom. Complete the chart below as the electron moves towards ground.
[Appendix A]
a.
Transition
C-A
∆E (eV)
4.86
Wavelength (m)
2.56 x 10-7
Spectral region
UV
b.
C-B
0.22
5.65 x 10-6
IR
c.
B-A
4.64
2.68 x 10-7
UV
A gas is used to produce a bright line spectra and then is also used to produce a dark line
spectra. Explain why the bright line and dark line spectra have lines at the same wavelengths.
Use energy level diagrams as part of your explanations. [Appendix A]
The energy that the gas atoms can emit to produce a bright line spectra are identical to the
energies that can be absorbed to produce the dark line spectra because of the quantized energy
levels
11.
photon will be absorbed if a transition exists that is exactly the same amount of energy as the
photon - the photon must be completely absorbed. Consider an excited mercury atom that
absorbs a photon with 0.22 eV of energy. Identify the initial energy level of the mercury atom
before being struck by the photon. [Appendix A]
An energy difference of 0.22 eV occurs for the transition from n = 2 to n = 3.
12.
A coin machine that requires exact change and a store that requires at least the cost of the item
and can give change back may be analogous to an atom that can accept energy from a photon
or an electron to excite the atom. Using this analogy, explain how the photon is analogous to
money in a vending machine and how the electron is analogous to the coins used for the
machine. [Appendix A]
Photons will be absorbed if they are the exact amount of energy – no more and no less. This is
like coins in a vending machine. Electrons can transfer energy to an atom as long as they have
enough energy; they keep the extra energy. This is like getting change at a store after a
purchase.
13.
A line absorption spectrum is shown below. Are any photons of light emitted at the locations
of the dark lines in the spectrum? Explain. [Appendix A]
Yes. Photons are emitted at all the wavelengths. However, there are fewer photons at the
locations of the dark lines.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 295
7.3 Summary Notes – Matter Waves
Notes:
___________________________
___________________________
DeBroglie suggested that since waves can act as particles,
perhaps particles could act like waves. This wave-particle
duality allowed wavelength to be related to momentum:
___________________________
___________________________
p=
h
λ
and p = mv to give
λ=
h
mv
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___________________________
___________________________
___________________________
Small masses travelling at high speeds have noticeable
wavelengths. Electrons were demonstrated to behave like
waves in diffraction experiments using crystals as a
diffraction grating.
Example
1.
Use deBroglie’s formula to determine the wavelength of a positron that has 6.56 x 10-19 J of
kinetic energy.
The positron’s wavelength is 6.06 x 10-10 m.
Problems
1.
Determine the deBroglie wavelength of an electron moving at 4.51 x 107 m/s. [1.61 x 10-11 m]
The electron’s deBroglie wavelength is 1.61 x 10-11 m.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 296
2.
Determine the speed of an electron which has a deBroglie wavelength of 2.10 x 10-11 m.
[3.47 x 107 m/s]
The electron is travelling at a speed of 3.47 x 107 m/s.
3.
Compare the de Broglie wavelength of an electron moving at 4.0 x 106 m/s and a 50 kg
physics student moving at 5.0 m/s. Would it be possible to diffract the physics student in an
experiment like Young’s double slit experiment? Explain. [Appendix A]
No. It would not be possible to diffract the student. The wavelength is too small.
Use the following information to answer question 4.
The electron microscope uses electrons which have a wavelength much shorter than visible light in
order to distinguish (i.e., resolve) and observe detailed features.
4.
Determine the deBroglie wavelength of an electron accelerated from rest across a potential
difference of 600 V. [5.01 x 10-11 m]
The de Broglie wavelength of the electron is 5.01 x 10-11 m.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 297
5.
Determine the kinetic energy of an electron whose matter wavelength is 3.50 x 10-11 m.
[1.97 x 10-16 J]
The electron’s kinetic energy is 1.97 x 10-16 J.
6.
Calculate the potential difference that an electron would be accelerated across so that its
deBroglie wavelength is 2.00 x 10-11 m. [3.77 kV]
The electron would have to be accelerated across a potential difference of 3.77 kV.
7.
Determine the deBroglie frequency of an electron after it is accelerated across a potential
difference of 20.0 kV. [9.65 x 1018 Hz]
The electron’s de Broglie frequency is 9.65 x 1018 Hz.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 298
7.4 Summary Notes – Wave Mechanical Model
Classical physics does not adequately explain the behavior
of atomic or sub-atomic particles due to their significant
wave nature.
Notes:
___________________________
___________________________
___________________________
___________________________
Experimental Evidence:
___________________________
Moving electrons were observed to have wave properties.
___________________________
___________________________
Interpretation of Evidence:
___________________________
DeBrogle explained that electrons were circular standing
waves around a nucleus. An electron can exist where there
is constructive interference and cannot exist where there is
destructive interference. This explained Bohr’s quantized
orbits.
___________________________
A probability interpretation was given – the electron is
found in regions of constructive interference producing a
probability cloud.
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___________________________
___________________________
___________________________
___________________________
Example
1.
In order to constructively interference, the wavelength of the electron must fit evenly into the
circumference of the orbit where the circumference is equal to the wavelength (C = λ). An
electron in an atom may be interpreted as being a wave that surrounds the nucleus. Draw the
electron standing wave for the 2nd energy level around an atom’s nucleus.
n=1
Copyright © Kennedy/Oswald, 2008
n=2
Chapter 7 - 299
Problems
1.
An electron orbits a proton at a distance of 1.06 x 10-10 m. Use the planetary model of the
atom to determine the
a. speed of the electron in circular motion. [1.54 x 106 m/s]
b. deBroglie wavelength of the electron as it moves around the nucleus. [4.71 x 10-10 m]
a. The speed of the electron is 1.54 x 106 m/s.
b. The deBroglie wavelength of the electron is 4.71 x 10-10 m.
2.
An anaolgy can be made between standing waves on a rope and electron standing waves
around a nucleus. The diagrams below show a rope between two fixed points. Select the
diagram of the rope producing waves of the highest energy if it analogous to an electron
standing wave. [Appendix A]
a
b
c
Standing wave c has the greatest frequency and therefore has the greatest energy.
3.
The diagram to the right represents an electron as a standing
wave circling the nucleus of an atom. Determine the number
of complete wavelengths the electron is producing around the
nucleus. [Appendix A]
Four complete wavelengths surround the nucleus.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 300
4.
Fill in the blank. The amplitude of an electron wave surrounding the nucleus of an atom may
probability of finding the electron at that location. [Appendix A]
be interpreted as the ___________
5.
The two diagrams below represent identical atoms with their electrons at different energy
states. Identify the atom having the electron at the higher energy state. Explain. [Appendix A]
a
b
Atom a has the higher energy since it shows a wavelength with the greater frequency.
6.
Explain the diagrams from the previous question in terms of constructive and destructive
interference to explain how an energy level is “quantized”. [Appendix A]
Constructive and destructive interference occurs between the allowed energy levels. Therefore,
the wave cannot exist between orbits. This explains why electrons are allowed only certain
orbits.
Use the following formula to answer questions 7 & 8.
When an electron is treated as a matter wave it may be interpreted as acting as a standing wave
around the nucleus of an atom. The relationship of its radius of orbit, quantum number and
deBroglie wavelength is given by:
2πr = nλ
Where:
2πr is the circumference of the orbit (m)
n is the quantum number (always a whole number)
λ is the de Broglie wavelength (m)
7.
Determine the wavelength of an electron orbiting a hydrogen atom at a distance of 5.29 x 10-11 m
from the nucleus when the electron is in its first energy state. [3.23 x 10-10 m]
The wavelength is 3.23 x 10-10 m.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 301
8.
If an electron moves around a nucleus with a velocity of 3.8 x 106 m/s determine
a. its deBroglie wavelength. [1.92 x 10-10 m]
b. the orbital radius if it is at its 3rd energy level. [9.14 x 10-11 m]
a. The wavelength is 1.92 x 10-10 m.
b. the orbital radius is 9.14 x 10-11 m.
9.
Describe how the diffraction and interference of electrons in a double slit experiment may be
interpreted as meaning that electrons may be thought of as waves. [Appendix A]
Depending on the circumstances or the experiment observed a photon must be thought of as
being a particle or must be treated as a wave. This is also true for electrons. When electrons
are sent one at a time through double slits, an interference pattern is produced. Therefore the
electron is showing its wave nature.
10.
The Bohr model of the atom was unable to explain why only certain electrons orbits around a
nucleus are allowed. Explain how the wave interpretation of an electron helps explain
quantized energy levels for the electrons in orbit about a nucleus. [Appendix A]
Only certain proportions of a wave are allowed to produce standing waves. When the electron
acts as a waves surrounding a nucleus it sets up a standing wave of only certain allowed
proportions.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 302
7.5 Extensions
Use the information below to answer question 1.
James Franck and Gustav Hertz provided more evidence for the quantized structure of the atom.
They supplied energy to the atom through collision with a fast moving electron.
The following diagrams show the collision between a fast moving electron and a mercury atom. The
collisions are shown on an atomic level and again on a subatomic level. The electron’s kinetic energy
is measured before and after the collision. As the initial kinetic energy of the electron increased the
following happened:
i.
4.5 eV
e4.5 eV
ii.
0.1 eV
e-
Hg
5.0 eV
e-
4.5 eV
1.1 eV
eHg
4.5 eV
e-
iii.
6.0 eV
Hg
0.1 eV
e-
e-
5.0 eV
1.1 eV
e-
e-
6.0 eV
The Hg atom could only absorb 4.9 eV; no more, no less.
As the electron’s velocity was increased, it was found that other energies could also be absorbed.
1.
A certain atom can absorb energies of 4.90 eV, 6.81 eV, and 10.38 eV. If an incoming electron
with kinetic energy of 5.97 eV is used to bombard this atom, determine the
a. energy of the incoming electron after the collision. [1.07 eV]
b. wavelength of light emitted. [1.16 x 10-6 m]
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 303
7.6 Review
1.
To determine the speed of charged particles in a cathode ray tube, J. J. Thomson balanced the
force produced by a(n)
a. electromagnetic field and a gravitational field
b. magnetic field and a gravitational field
c. electric and a gravitational field
d. electric field and a magnetic field
2.
The charge and the approximate diameter of a nucleus can be estimated from
a. alpha particle scattering experiments
b. X-ray diffraction experiments
c. photoelectron experiments
d. cathode ray experiments
3.
An absorption spectrum is produced when white light is passed through a cool gas and then
the light is viewed through a diffraction grating. The EMR for an absorption spectrum of an
element is produced by
a. centripetal acceleration of the electrons within the element
b. electrons within the element dropping down from the excited state as they absorb energy
c. electrons within the element moving up to an excited state as they absorb energy
d. the nucleus of an atom moving from a low energy to a high energy state as it absorbs
energy
4.
An electron moving with a kinetic energy of 5.2 eV strikes an atom and rebounds with a
kinetic energy of 3.1 eV. The atom then releases a photon of light. The most likely frequency
of the emitted light is
a. 1.25 x 1015 Hz
b. 2.00 x 1015 Hz
c. 5.07 x 1014 Hz
d. 7.07 x 1014 Hz
5.
Constructive and destructive interference of electrons help support the
a. nuclear model
b. Bohr model
c. wave mechanical model
d. billiard ball model
6.
Use the mass and charge of an alpha particle to determine its charge-to-mass ratio.
[4.82 x 107 C/kg]
7.
Calculate the charge-to-mass ratio of a particle travelling at 3.60 x 105 m/s that is deflected
with a radius of 7.40 cm as it travels through a perpendicular magnetic field of 0.420 T.
[1.16 x 107 C/kg]
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 304
Use the information below to answer questions 8 – 10.
Consider the following energy level diagram for an element under
investigation.
8.
When the element de-excites from energy level D to energy level
A. Determine the
a. energy of the photon emitted. [6.72 eV]
b. frequency of the photon emitted. [1.62 x 1015 Hz]
c. wavelength of the photon emitted. [185 nm]
d. region of the EMR spectrum where the photon is classified.
[Appendix A]
ionization
0 eV
F
E
-2.44 eV
-2.59 eV
D
-3.73 eV
C
B
-5.67 eV
-5.81 eV
A
-10.45 eV
9.
Determine the quantity of energy that would be required to ionize the element if its electrons
are already excited to energy level C. [5.67 eV]
10.
An electron with 5.50 eV of kinetic energy collides with an electron in the ground state of the
investigated element. Complete the chart below that includes the possible transitions.
[Appendix A]
a.
Transitions
C-A
∆E (eV)
4.78
Wavelength (m)
260
Spectral region
UV
b.
C-B
0.14
8879
IR
c.
B-A
4.64
268
UV
11.
Calculate the wavelength of a photon that has the same momentum as a proton travelling at
9.55 x 106 m/s. [4.16 x 10-14 m]
12.
If an electron moves around a nucleus with a velocity of 5.87 x 106 m/s determine its
deBroglie wavelength. [1.24 x 10-10 m]
7.7 Review Assignment
1.
An electron enters a magnetic field of 85.0 mT and deflects in to a circular arc with a radius of
7.8 mm. Determine the kinetic energy of the electrons in electron volts.
2.
The charge-to-mass ratio for potassium ion is 2.54 x 106 C/kg. If a potassium ion was
accelerated to a speed of 4.72 x 105 m/s and then deflected into a circular beam with a radius
of 8.1 cm, determine the magnetic field causing the deflection.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 305
Use the information below to answer questions 3 – 7.
Consider an incident electron with 14.2 eV
of energy. It collides with an electron of an
unexcited gas atom (described by the
following energy levels in the diagram to the
right).
Ionization
0 eV
D
-1.5 eV
C
-8.4 eV
B
-11.4 eV
A
-14.9 eV
Ground state
3.
Determine the maximum level the atom’s electron could be excited to.
4.
Determine the number of photons of different wavelengths that could possibly be produced
due to an electron at level D moving back towards ground state.
5.
If the electron only exited this gas atom to energy level C, determine the
a. kinetic energy of the incident electron left over.
b. Is there enough energy left over to excite another gas atom? If so, to what level?
6.
If the above gas atom absorbs the maximum possible energy of the incoming electron,
determine all the possible wavelengths of light that could be emitted by the excited atom and
indicate where their spectral lines would be observed on the spectrum ruler below.
Transition
D-A
∆E (eV)
13.4
Wavelength (nm)
92.8
Spectral region
uv
D-C
6.9
180
uv
C-B
3.0
414
visible
C-A
6.5
191
uv
D-B
9.9
126
uv
100 nm
200 nm
300 nm
400 nm
7.
If a dark line absorption spectra for this same gas were being analyzed instead of a bright line
(as above) where would the dark lines appear? Explain.
8.
Describe the five main atomic models studied in this unit. Include the names of those who
developed the model, strengths and weakness of the model, and a diagram. Organize in a
chart.
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 306
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 307
Copyright © Kennedy/Oswald, 2008
Chapter 7 - 308