Download Modern physics 2330

Modern physics 2330
Incomplete Exam.
Time: Two Hours
The Islamic University of Gaza
Department of Physics
.........................................:‫ الرقم الجامعي‬....................................................................:‫االسم‬
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Q1 Indicate (√ ) for true statement and (× ) for false statement.
1- ( ) According to the special theory of relativity, interaction between objects in
nature propagates with infinite speed.
2- ( ) An event is determined by the location where, and by the time at which
occurs.
3- ( ) According to classical mechanics, a moving clock runs slower than one at
rest.
4- ( ) The number, strength, and exact position of the lines in the spectrum of an
element depend only upon temperature.
5- ( ) According to de Broglie, the electron of the Bohr atom forms a standing
h
wave around the nucleus with   .
p
6- ( ) Davisson-Germer experiment (1927) is a direct experimental proof that the
electron charge is, e=1.6x10-19C.
7- ( ) Classical mechanics is a special (limiting) case of relativistic mechanics.
8- ( ) The Heisenberg uncertainty principle states that, position and conjugate
momentum can not be measured simultaneously with any degree of accuracy.
9- ( ) A wave packet is a superposition of many plane waves.
10- ( ) In classical mechanics the state of a particle is fully determined by its
wavefunction x  .
Q2 Explain in details the Davisson-Germer experiment.
Q3 Discuss both Rutherford and Bohr atomic models.
Q4 Show that the group velocity of the matter wave particle v g is the same as the
particle speed v.
E
(Hint: you may need the relations, v p    , E  p 2 c 2  m 2 c 4 , and the
p
relativistic energy and momentum respectively are, E  mc 2 , p  mv )
Q5 Consider a 200 gram object in a box 10 m on a side, moving with a speed of 3 m/s
along x-axis. Show that the spread of velocities caused by the uncertainty principle
does not have measurable consequences for macroscopic object.
Q6 A particle is described by the wave function

L
L
 x 
, for   x 
 A cos
 x   
2
2
 L 
0,
otherwise.

a) Determine the normalization constant A.
b) What is the probability that the particle will be found between
L
x  0 and x  if a measure of its position is made.
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