Modern Physics – Spring 2016
Prof. Akhavan
Sharif University of Technology
Physics Department
Problems Set #2.
Due to: 21st of February.
1 Crystal Diffraction of X-Ray.
A certain device for analyzing electromagnetic radiation is based on the Bragg scattering of
the radiation from a crystal. For radiation of wavelength 0.149 nm, the first-order Bragg peak
appears centered at an angle of 15.15◦. The aperture of the analyzer passes radiation in the
angular range of 0.015◦.
What is the corresponding range of wavelengths passing through the analyzer?
2 Crystal Diffraction of X-Ray.
Monochromatic X rays are incident on a crystal in the geometry of Figure 3.5 of the book.
The first-order Bragg peak is observed when the angle of incidence is 34.0◦. The crystal spacing
is known to be 0.347nm.
(a) What is the wavelength of the X rays?
(b) Now consider a set of crystal planes that makes an angle of 45◦ with the surface of the crystal
(as in Figure 3.6). For X rays of the same wavelength, find the angle of incidence measured
from the surface of the crystal that produces the first-order Bragg peak. At what angle from
the surface does the emerging beam appear in this case?
3 The Photoelectric Effect.
A surface of zinc is illuminated and photoelectrons are observed.
(a) What is the largest wavelength that will cause photoelectrons to be emitted?
(b) What is the stopping potential when light of wavelength 220.0 nm is used?
4 The Photoelectric Effect.
Find the momentum of:
(a) a 10.0-MeV gamma ray;
(b) a 25-keV X ray;
(c) a 1.0-μm infrared photon;
(d) a 150-MHz radio-wave photon.
Express the momentum in kg · m/s and eV/c.
5 The Photoelectric Effect.
(a) What is the wavelength of an X-ray photon of energy 10.0 keV?
(b) What is the wavelength of a gamma-ray photon of energy 1.00 MeV?
(c) What is the range of energies of photons of visible light with wavelengths 350 to 700 nm?
6 X-Ray Production.
Suppose an atom of iron at rest emits an X-ray photon of energy 6.4 keV.
Calculate the “recoil” momentum and kinetic energy of the atom. (Hint: Do you expect to need
classical or relativistic kinetic energy for the atom? Is the kinetic energy likely to be much
smaller than the atom’s rest energy?)
7 Studying!
Study sections 2-7 and 2-8 of the book Modern Physics, Krane-3rd edition and see that the
relativistic momentum and energy equal ɣmv and √ m2 c 4 + p 2 c 2 respectfully, where ɣ =
√
1
v 2
1−( )
c
.
8 General Problems.
A photon of wavelength 192 nm strikes an aluminum surface along a line perpendicular to the
surface and releases a photoelectron traveling in the opposite direction. Assume the recoil
momentum is taken up by a single aluminum atom on the surface.
Calculate the recoil kinetic energy of the atom. Would this recoil energy significantly affect the
kinetic energy of the photoelectron?
9 General Problems.
A photon of wavelength 7.52 pm scatters from a free electron at rest. After the interaction, the
electron is observed to be moving in the direction of the original photon.
Find the momentum of the electron.