Kuwait University
Faculty of Science
Physics Department
Modern Physics 209
Final Exam
Time: 2 Hours
Date: May 30, 2004
Instructors: Drs. K.S. Bhatia & Abdulmuhsen Ali
Name……………………………….. Student No. …………
1. Solve all problems.
2. Show detailed solution for each problem
Prob.
Marks
1
2
3
4
5
6
7
8
9
10
Fundamental Constants
k
1
 9.0  10 9 N  m 2 / C 2
4  o
(Coulomb constant)
o = 8.85  10-12 C2 / (N·m2)
(Permittivity of free space)
o = 4  10-7 T.m/A
(Permeability of free space)
e = +1.6  10-19 C
(Elementary unit of charge)
NA = 6.022 1023
(Avogadro’s number)
g = 9.8 m/s2
(Acceleration due to gravity)
me= 9.11  10-31 kg
(Electron mass)
mp = 1.67  10-27 kg
(Proton mass)
Prefixes of units
m = 10-3
k = 103
 = 10-6
M = 106
n = 10-9
G = 109
p = 10-12
T = 1012
Total
1. Calculate speed of an object which appears to be contracted by 50% of its
original length as observed by a stationary observer.
2. Rocket A moving with speed of 0.9 C is followed by rocket B with a speed
of 0.75 C. What is the speed of A as measured by observer in the
reference frame of B?
3. Calculate the energy and momentum of a photon of blue colour  = 450
nm. If a star appears blue in colour what is the approximate temperature
of the star.
4. Incident X-ray photons of energy 10.39 KeV are Compton scattered at 45
to the incident direction. Calculate the energy and momentum of the
scattered electrons.
5. Calculate % energy uncertainty for the following particles:
a) -meson E = 140 MeV and lifetime  = 26 ns
b) -meson E = 765 MeV and  = 4.4  10-24 s.
6. An electron is accelerated through a potential difference of 50 billion volts.
Calculate the corresponding de-Broglie wavelength.
7. Show that the average value of < x2 > in one dimensional well of width L is
given by:

L2 1  1 2 2
3
2 n

8. An electron beam of current 1 mA moving with speed of 2  106 m/s is
incident on a potential barrier of height V at x  0. Energy of the electrons
reduces to 50% of the incident electron speed.
Calculate the
corresponding current transmitted through the barrier. What is the height
of the potential well.
9. An -particle of kinetic energy 5 MeV are scattered by 90 when projected
on a gold foil (z = 79). Calculate the impact parameter and the minimum
distance of approach.
10. A singly ionized He atom 21 He or He  in n = 4 state emits a photon of
 = 470 nm. Calculate the energy and n value of the lower state.