Name
November 27, 2002
HAPPY THANKSGIVING!
FINAL EXAMINATION OF PHYS3313
Part I (Take Home Test): Chapters 2-9
Due 2:00 pm on Tuesday December 3, 2002
Professor Aihua Xie, Oklahoma State University
h  6.626 10 34 J  s  4.136 10 15 eV  s
e  1.602  10 19 C
a0  0.529  10 10 m ;
me  9.1110 31 kg  0.511MeV / c 2
c  2.998 108 m / s
kB = 1.38110-23 J/K
m p  1.674 10 27 kg = 938.3 MeV/c2
N A  6.022 10 23 mol 1
 0  8.854  10 12 C 2 / N  m 2 .
There are four problems plus a bonus problem of 20 points. Please make sure to have correct units
on all steps of your calculation and explain in words as possible.
1. (20 points) Protons in an accelerator at the Fermi National Laboratory near Chicago are accelerated
to an energy of 400 times their rest energy.
(a) What is the speed of these protons in unit of c?
(b) What is their kinetic energy in MeV?
2. (20 points) A light source of wavelength  illuminates a metal and ejects photoelectrons with a
maximum kinetic energy of 1.00 eV. A second light source with half the wavelength of the first ejects
photoelectrons with a maximum kinetic energy of 4.00 eV.
(a) What is the work function of the metal in unit of eV?
(b) What is the wavelength  of the first light source in unit of nm?
3. (30 points) A proton is confined to moving in a one-dimensional box of width 0.20 nm.
(a) Find the lowest possible energy of the proton (the ground state energy in unit of eV).
(b) What is the lowest possible energy of the electron confined to the same box (in unit of eV)?
(c) Find the de Broglie wavelengths of the proton in (a) and the electron in (b).
(d) How do you account for the large difference in your results for (a) and (b)?
4. (30 points) A hydrogen atom is excited from the ground state to the first-excited state (n=2) and
remains in the first excited-state for 2.0 ns before returning to the ground state by emitting a photon.
(a) What is the wavelength (in unit of nm) of the emitted photon?
(b) What is its approximate uncertainty in energy in the first excited state in unit of eV?
(c) Calculate the most probable distances of the electron from the proton in the hydrogen 2s state
and compare them with the radius of the second Bohr orbit in hydrogen, 4a0.
(d) Calculate the most probable distances of the electron from the proton in the hydrogen 2p state
and compare them with the radius of the second Bohr orbit in hydrogen, 4a0.
Bonus Question:
A proton and a deuteron (a particle with the same charge as a proton, but twice the mass of a
proton) attempt to penetrate a rectangular potential barrier of height 10 MeV and thickness 10-14 m. Each
particle has a kinetic energy of 3 MeV before hitting the barrier.
(a) Use qualitative arguments to predict which particle has the highest probability of succeeding.
(b) Evaluate qualitatively the probability of success for both particles.