Name: ______________________
CPO: ___________
MODERN PHYSICS
PHY 320
FINAL EXAM
(May 21, 2003)
(Answer all questions from Part I and 5 questions from Part 2. To get partial
credits show all the steps of your calculation clearly. Good luck.)
h = 6.626 x 10-34 J.s
1 eV = 1.602 x 10-19 J
me = 9.109 x 10-31 kg = 0.5110 MeV/c2
c = 3.0 x 108 m/s
1. Briefly and clearly answer all the following questions:
(a) Define an inertial reference frame. What are the laws of special theory of
relativity?
(5 pts)
(b) Define proper time and proper length. What is time dilation in special
theory of relativity? Give an example of time dilation.
(4+3+3=10 pts)
(c) What is a “black body”? State Stefan’s law for the blackbody radiation.
(5 pts)
(d) An x-ray photon is scattered by an electron. What happens to the
frequency of the scattered photon relative to that of the incident photon?
Explain your answer.
(5 pts)
(e) Which has more energy, a photon of ultraviolet radiation or a photon of
yellow light? Explain your answer.
(5 pts)
(f) On the basis of Bohr’s theory of the atom briefly explain the origin of
spectral lines.
(5 pts)
(g) State de Broglie’s hypothesis on wave-particle duality of matter waves.
(5 pts)
(h) State Heisenberg’s uncertainty principle.
(5 pts)
(i) Why do lithium, potassium, and sodium exhibit similar chemical
properties?
(5 pts)
Problems: (Answer only five problems out of six. Points will be taken off for
not showing the steps of your calculation and for not getting the right
numbers.)
1. (a) The period of a pendulum is measured to be 3.0 s in the rest frame of the
pendulum. What is the period of the pendulum when measured by an observer
moving at a speed of 0.95c with respect to the pendulum?
(5 pts)
Sol:
(b) Two spaceships A and B are moving in opposite directions. An observer on
Earth measures the speed of A to be 0.750c and the speed of B to be 0.850c.
Find the velocity of B with respect to A.
(5 pts)
Sol:
2. An electron has a speed u=0.850 c. Find its total energy and kinetic energy in
electron volts.
(10 pts)
Sol:
3. X-rays with energy of 300 keV undergo Compton scattering from a target. If
the scattered rays are detected at 30o relative to the incident rays, find (a) the
Compton shift at this angle, (b) the energy of the scattered x-ray, and (c) the
energy of the recoiling electron.
(10 pts)
Sol:
4. Consider a particle moving in a one-dimensional box with walls at x=-L/2 and
x=L/2. (a) Write down the time independent Schrodinger equation for the particle.
(b) What are the boundary conditions? (c) Using the boundary conditions solve
the Schrodinger equation to obtain the normalized wave functions of the particle.
(d) What are the allowed energy values?
(10 pts)
Sol:
5. Consider a particle moving in a two-dimensional box of length L on each side.
(a) Write down the time independent Schrodinger equation for the particle. (b)
What are the boundary conditions? (c) Using the boundary conditions solve the
Schrodinger equation to obtain the normalized wave functions of the particle. (d)
What are the allowed energy values?
(10 pts)
Sol:
6. Calculate all the possible values of the total angular momentum J and the zcomponent of total angular momentum Jz for an electron in the 6f state of
hydrogen.
(10 pts)
Sol: