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SSM
THE PHOTOELECTRIC EFFECT
• The work function for tungsten is 4.58 eV. (a) Find the
threshold frequency and wavelength for the photoelectric effect to
occur when monochromatic electromagnetic radiation is incident
on the surface of a sample of tungsten. Find the maximum kinetic
energy of the electrons if the wavelength of the incident light is
(b) 200 nm and (c) 250 nm.
21
• When monochromatic ultraviolet light that has a wavelength equal to 300 nm is incident on a sample of potassium, the
emitted electrons have maximum kinetic energy of 2.03 eV.
(a) What is the energy of an incident photon? (b) What is the work
function for potassium? (c) What would be the maximum kinetic
energy of the electrons if the incident electromagnetic radiation had
a wavelength of 430 nm? (d) What is the maximum wavelength of
incident electromagnetic radiation that will result in the photoelectric emission of electrons by a sample of potassium?
22
• The maximum wavelength of electromagnetic radiation
that will result in the photoelectric emission of electrons from a
sample of silver is 262 nm. (a) Find the work function for silver.
(b) Find the maximum kinetic energy of the electrons if the incident
radiation has a wavelength of 175 nm.
23
• The work function for cesium is 1.90 eV. (a) Find the minimum frequency and maximum wavelength of electromagnetic
radiation that will result in the photoelectric emission of electrons
from a sample of cesium. Find the maximum kinetic energy of the
electrons if the wavelength of the incident radiation is (b) 250 nm
and (c) 350 nm.
24
•• When a surface is illuminated with electromagnetic radiation of wavelength 780 nm, the maximum kinetic energy of the
emitted electrons is 0.37 eV. What is the maximum kinetic energy if
the surface is illuminated using radiation of wavelength 410 nm?
20
COMPTON SCATTERING
• Find the shift in wavelength of photons scattered by free
stationary electrons at u " 60°. (Assume that the electrons are initially moving with negligible speed and are virtually free of (unattached to) any atoms or molecules.)
26
• When photons are scattered by electrons in a carbon sample, the shift in wavelength is 0.33 pm. Find the scattering angle.
(Assume that the electrons are initially moving with negligible speed
and are virtually free of (unattached to) any atoms or molecules.)
25
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•• When a surface is illuminated with electromagnetic radiation of wavelength 780 nm, the maximum kinetic energy of the
emitted electrons is 0.37 eV. What is the maximum kinetic energy if
the surface is illuminated using radiation of wavelength 410 nm?
24
COMPTON SCATTERING
• Find the shift in wavelength of photons scattered by free
stationary electrons at u " 60°. (Assume that the electrons are initially moving with negligible speed and are virtually free of (unattached to) any atoms or molecules.)
26
• When photons are scattered by electrons in a carbon sample, the shift in wavelength is 0.33 pm. Find the scattering angle.
(Assume that the electrons are initially moving with negligible speed
and are virtually free of (unattached to) any atoms or molecules.)
27
• The photons in a monochromatic beam are scattered by
electrons. The wavelength of the photons that are scattered at
an angle of 135° with the direction of the incident photon beam is
2.3 percent less than the wavelength of the incident photons. What
is the wavelength of the incident photons?
28
• Compton used photons of wavelength 0.0711 nm.
(a) What is the energy of one of those photons? (b) What is the
wavelength of the photons scattered in the direction opposite to the
direction of the incident photons? (c) What is the energy of the photon scattered in that direction?
25
• For the photons used by Compton (see Problem 28), find
the momentum of the incident photon and the momentum of the
photon scattered in the direction opposite to the direction of the incident photons. Use the conservation of momentum to find the momentum of the recoil electron in this case.
29
•• A beam of photons that have a wavelength equal to
6.00 pm is scattered by electrons initially at rest. A photon in the
beam is scattered in a direction perpendicular to the direction of
the incident beam. (a) What is the change in wavelength of the
photon? (b) What is the kinetic energy of the electron?
30
ELECTRONS AND MATTER WAVES
• An electron is moving at 2.5 & 105 m>s. Find the electron’s
wavelength.
31
• An electron has a wavelength of 200 nm. Find (a) the
magnitude of its momentum and (b) its kinetic energy.
32
•• An electron, a proton, and an alpha particle each have a
kinetic energy of 150 keV. Find (a) the magnitudes of their momenta and (b) their de Broglie wavelengths.
33
• A neutron in a reactor has a kinetic energy of approximately 0.020 eV. Calculate the wavelength of the neutron.
34
• Find the wavelength of a proton that has a kinetic energy
of 2.00 MeV.
35
• What is the kinetic energy of a proton whose wavelength
is (a) 1.00 nm and (b) 1.00 fm?
36
• The kinetic energy of the electrons in the electron beam
in a run of Davisson and Germer’s experiment was 54 eV. Calculate
the wavelength of the electrons in the beam.
37
• The distance between Li ' and Cl# ions in a LiCl crystal
is 0.257 nm. Find the energy of electrons that have a wavelength
equal to that spacing.
38
• An electron microscope uses electrons that have energies
equal to 70 keV. Find the wavelength of the electrons. SSM
39
• What is the wavelength of a neutron that has a speed of
1.00 & 106 m>s?
40
A PARTICLE IN A BOX
•• (a) Find the energy of the ground state (n ! 1) and the
first two excited states of a neutron in a one-dimensional box of
length L ! 1.00 & 10#15 m ! 1.00 fm (about the diameter of an
atomic nucleus). Make an energy-level diagram for the system.
Calculate the wavelength of electromagnetic radiation emitted
when the neutron makes a transition from (b) n ! 2 to n ! 1,
(c) n ! 3 to n ! 2, and (d) n ! 3 to n ! 1.
41
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47
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••
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Problem
cooling transition of the atoms is l ! 780.24 nm. Estimate the number of photons needed to slow down an 85 Rb atom from a typical
thermal velocity of 300 m>s to a stop. SSM
THE BOHR MODEL OF
THE HYDROGEN ATOM
• The first Bohr radius is given by a0 ! U2>1mke22 !
0.0529 nm (Equation 36-12). Use the known values of the constants
in the equation to show that a0 is equal to 0.0529 nm.
22
• The longest wavelength in the Lyman series for the
hydrogen atom was calculated in Example 36-2. Find the wavelengths
for the transitions (a) ni ! 3 to nf ! 1 and (b) ni ! 4 to nf ! 1.
23
• Find the photon energies for the three longest wavelengths in the Balmer series for the hydrogen atom, and calculate
the three wavelengths.
24
•• Find the photon energy and wavelength for the series
limit (shortest wavelength) in the Paschen series (nf ! 3) for the
hydrogen atom. (b) Calculate the wavelength for the three longest
wavelengths in Paschen series.
25
•• (a) Find the photon energy and wavelength for the series
limit (shortest wavelength) in the Brackett series (nf ! 4) for the
hydrogen atom. (b) Calculate the wavelength for the three longest
wavelengths in Brackett series.
26
••• In the center-of-mass reference frame of a hydrogen atom,
the electron and nucleus have momenta that have equal magnitudes
p and opposite directions. (a) Using the Bohr model, show that the
total kinetic energy of the electron and nucleus can be written
K ! p2>(2m) where m ! meM>(M " me) is called the reduced mass,
me is the mass of the electron, and M is the mass of the nucleus.
(b) For the equations for the Bohr model of the atom, the motion of
the nucleus can be taken into account by replacing the mass of the
electron with the reduced mass. Use Equation 36-14 to calculate
the Rydberg constant for a hydrogen atom that has a nucleus of
mass M ! mp. Find the approximate value of the Rydberg constant
by letting M go to infinity in the reduced mass formula. To how
many figures does this approximate value agree with the actual
value? (c) Find the percentage correction for the ground-state energy
of the hydrogen atom by using the reduced mass in Equation 36-16.
27
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