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Arthur Beiser or Serway? How will the CTMU change modern physics? What are some of the problems facing modern day physics? Light from the sun arrives at the earth, an average of 1. Assume that sunlight is monochromatic with a frequency of 5. Using the result from part a , 4. The maximum wavelength for photoelectric emission in tungsten is nm. What wavelength of light must be used in order for electrons with a maximum energy of 1.
What is the maximum wavelength of light that will cause photoelectrons to be emitted from sodium? What will the maximum kinetic energy of the photoelectrons be if nm light falls on a sodium surface? From Equation 2. A metal surface illuminated by 8. Show that it is impossible for a photon to give up all its energy and momentum to a free electron.
This is the reason why the photoelectric effect can take place only when photons strike bound electrons. An easier alternative is to consider the interaction in the frame where the electron is at rest after absorbing the photon.
In this frame, the final energy is the rest energy of the electron, mec2, but before the interaction, the electron would have been moving to conserve momentum , and hence would have had more energy than after the interaction, and the photon would have had positive energy, so energy could not be conserved.
Electrons are accelerated in television tubes through potential differences of about 10 kV. Find the highest frequency of the electromagnetic waves emitted when these electrons strike the screen of the tube. What kind of waves are these? The distance between adjacent atomic planes in calcite CaCO3 is 0.
Find the smallest angle of Bragg scattering for 0. What is the frequency of an x-ray photon whose momentum is 1. In See. Show that this assumption is reasonable by calculating the Compton wavelength of a Na atom and comparing it with the typical x-ray wavelength of 0. A beam of x-rays is scattered by a target. At 45o from the beam direction the scattered x-rays have a wavelength of 2. What is the wavelength of the x-rays in the direct beam?
An x-ray photon of initial frequency 3. Find its new frequency. At what scattering angle will incident keV x-rays leave a target with an energy of 90 keV? A photon whose energy equals the rest energy of the electron undergoes a Compton collision with an electron. If the electron moves off at an angle of 40o with the original photon direction, what is the energy of the scattered photon?
A positron collides head on with an electron and both are annihilated. Each particle had a kinetic energy of 1.
The wavelength of each photon will be hc 1. Show that, regardless of its initial energy, a photon cannot undergo Compton scattering through an angle of more than 60o and still be able to produce an electron-positron pair. Hint: Start by expressing the Compton wavelength of the electron in terms of the maximum photon wavelength needed for pair production. The linear absorption coefficient for 1-MeV gamma rays in lead is 78 m The linear absorption coefficients for 2.
What thickness of water would give the same shielding for such gamma rays as 10 mm of lead? What thickness of copper is needed to reduce the intensity of the beam in Exercise 48 by half. The sun's mass is 2.
Find the approximate gravitational red shift in light of wavelength nm emitted by the sun. As discussed in Chap. These photons constitute gamma rays. When a nucleus emits a photon, it recoils in the opposite direction.
The mass of a Fe atom is 9. By how much is the photon energy reduced from the full By how much is the photon energy reduced in this situation if the ex- cited Fe nucleus is part of a 1. Such a source was used in the experiment described in See.
What is the original frequency and the change in frequency of a This approximation gives the previous result. Of course, a relativistic calculation is correct here, but it is interesting to see what a classical calculation produces. That is, its total energy must be nonnegative. A photon and a particle have the same wavelength. Can anything be said about how their linear momenta compare? About how the photon's energy compares with the particle's total energy?
Problem Solutions 3. Find the de Broglie wavelength of a 1. By what percentage will a nonrelativistle calculation of the de Broglie wavelength of a keV electron be in error? Problem Solutions keeping extra figures in the intermediate calculations.
The atomic spacing in rock salt, NaCl, is 0. Find the kinetic energy in eV of a neutron with a de Broglie wavelength of 0. Is a relativistic calculation needed? Such neutrons can be used to study crystal structure. This energy is much less than the neutron's rest energy, and so the nonrelativistic calculation is completely valid. Problem Solutions 9. Green light has a wavelength of about nm.
Through what potential difference must an electron be accelerated to have this wavelength? Note that the kinetic energy is very small compared to the electron rest energy, so the nonrelativistic calculation is valid. In the above calculation, multiplication of numerator and denominator by c2 and use of the product he in terms of electronvolts avoided further unit conversion. Show that if the total energy of a moving particle greatly exceeds its rest energy, its de Broglie wavelength is nearly the same as the wavelength of a photon with the same total energy.
Problem Solutions An electron and a proton have the same velocity Compare the wavelengths and the phase and group velocities of their de Broglie waves.
From Equation 3. Verify the statement in the text that, if the phase velocity is the same for all wavelengths of a certain wave phenomenon that is, there is no dispersion , the group and phase velocities are the same.
Find the phase and group velocities of the de Broglie waves of an electron whose kinetic energy is keV. Both will assume the validity of Equation 3. The final result is, or course, the same. What effect on the scattering angle in the Davisson-Germer experiment does increasing the electron energy have? In Sec. Consider a beam of eV electrons directed at a nickel target. The potential energy of an electron that enters the target changes by 26 eV.
Obtain an expression for the energy levels in MeV of a neutron confined to a one-dimensional box 1. What is the neutron's minimum energy? The diameter of an atomic nucleus is of this order of magnitude. A proton in a one-dimensional box has an energy of keV in its first excited state. How wide is the box? Solving for the width L, h2 6. The atoms in a solid possess a certain minimum zero-point energy even at 0 K, while no such restriction holds for the molecules in an ideal gas. Use the uncertainty principle to explain these statements.
The uncertainty in position of each atom is therefore finite, and its momentum and hence energy cannot be zero. The position of an ideal-gas molecule is not restricted, so the uncertainty in its position is effectively infinite and its momentum and hence energy can be zero. The position and momentum of a 1. If its position is located to within 0. A marine radar operating at a frequency of MHz emits groups of electromagnetic waves 0. The time needed for the reflections of these groups to return indicates the distance to a target.
The number of waves in each group is the pulse duration divided by the wave period, which is the pulse duration multiplied by the frequency, 8.
The great majority of alpha particles pass through gases and thin metal foils with no deflections. To what conclusion about atomic structure does this observation lead? Determine the distance of closest approach of 1. In this case, at the point of closest approach the proton will have no kinetic energy, and so the potential energy at closest approach will be the initial kinetic energy, taking the potential energy to be zero in the limit of very large separation.
What is the shortest wavelength present in the Brackett series of spectral lines? In the Bohr model, the electron is in constant motion.
How can such an electron have a negative amount of energy? For the system to be bound, the total energy, the sum of the positive kinetic energy and the total negative potential energy, must be negative. For a classical particle subject to an inverse-square attractive force such as two oppositely charged particles or two uniform spheres subject to gravitational attraction in a circular orbit, the potential energy is twice the negative of the kinetic energy.
This quantity got its name because it first appeared in a theory by the German physicist Arnold Sommerfeld that tried to explain the fine structure in spectral lines multiple lines close together instead of single lines by assuming that elliptical as well as circular orbits are possible in the Bohr model.
Find the quantum number that characterizes the earth's orbit around the sun. The earth's mass is 6. Compare the uncertainty in the momentum of an electron confined to a region of linear dimension ao with the momentum of an electron in a ground-state Bohr orbit. What effect would you expect the rapid random motion of the atoms of an excited gas to have on the spectral lines they produce?
A proton and an electron, both at rest initially, combine to form a hydrogen atom in the ground state. A single photon is emitted in this process. What is its wavelength? The energy of the photon emitted is then -El, and the wavelength is hc 1. In what part of the spectrum is this? A beam of electrons bombards a sample of hydrogen. Through what potential difference must the electrons have been accelerated if the first line of the Balmer series is to be emitted?
A potential difference of The longest wavelength in the Lyman series is Use the figures to find the longest wavelength of light that could ionize hydrogen. When an excited atom emits a photon, the linear momentum of the photon must be balanced by the recoil momentum of the atom. As a result, some of the excitation energy of the atom goes into the kinetic energy of its recoil.
Is the effect a major one?
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