PH 253 Exam II Solutions
1. The state of a free particle is described by the following wave function
0
(x) = A
0
x < b
b
(1)
2b
x
x > 2b
(a) Determine the normalization constant A.
(b) What is the probability of nding the particle in the interval [0, b]?
PH253 Spring 2015
Exam 2
Name:
This exam covers chapters 5 through 7 of the text. There are 14 questions worth a total of
38 points. You have 75 minutes to complete the exam. Please make sure:
1. Your name is clearly printed on the line above.
2. You have
PH253 Spring 2015
Exam 1
Name:
This exam covers chapters 1 through 4 of the text. There are 16 questions worth a total of
47 points. You have 75 minutes to complete the exam. Please make sure:
1. Your name is clearly printed on the line above.
2. You have
University of Alabama
Department of Physics and Astronomy
PH 253 - Modern Physics
Fall 2011
Exam 1
Instructions
1. Solve six of the eight problems below.
2. Show ALL steps in details. Points will be deducted for not showing the steps clearly, even
if the
University of Alabama
Department of Physics and Astronomy
PH 253 - Modern Physics
Fall 2011
Exam 2
Instructions
1. Solve ALL problems below.
2. Show ALL steps in details. Points will be deducted for not showing the steps clearly, even
if the answer is cor
University of Alabama
Department of Physics and Astronomy
PH 253 - Modern Physics
Fall 2011
Exam 1
Instructions
1. Solve six of the eight problems below.
2. Show ALL steps in details. Points will be deducted for not showing the steps clearly, even
if the
University of Alabama
Department of Physics and Astronomy
PH 253 - Modern Physics
Fall 2011
Exam 2
Instructions
1. Solve ALL problems below.
2. Show ALL steps in details. Points will be deducted for not showing the steps clearly, even
if the answer is cor
PH 253 / LeClair
Fall 2013
Problem Set 1: Solutions
1. Daily problem due 23 Aug 2013: How fast must a rocket travel relative to the earth so
that time in the rocket slows down to half its rate as measured by earth-based observers? Do
present-day jet plane
PH253
Group Exercise 01: Review of Classical Mechanics
Spring 2015
Useful information:
1 u = 931.5 MeV/c2 = 1.661 1027 kg
1 eV = 1.602 1019 J
c = 3.0 108 m/s
1. A particle of mass 1.0 u travels in the positive x direction toward a stationary particle of
m
PH253
Group Exercise 03: Muon Lifetime
Spring 2015
Useful information:
= 1/ 1 2
t = t0
L = L0 /
1. A muon is a unstable sub-atomic particle with a lifetime of 2.2 s. Muons are known to
be produced at the top of the atmosphere when cosmic rays collide wit
PH253
Group Exercise 04: Particle Decay
Spring 2015
Useful information:
p = mc
E = mc2
K = ( 1)mc2
(mc2 )2 = E 2 (pc)2
1. A particle with mass M is moving with speed v in the positive x direction when it decays
into two particles, each of mass 140 MeV/c2
PH253
Group Exercise 03.5: Relativistic Dynamics
Spring 2015
Useful information:
p = mc
E = mc2
K = ( 1)mc2
(mc2 )2 = E 2 (pc)2
1. A pion at rest decays into a muon and a neutrino: + . The pion has a mass
m = 140 MeV/c2 , the muon has a mass m = 106 MeV/c
PH253
Homework 01
Spring 2015
1. An atom of beryllium (m = 8.00 u) splits into two atoms of helium (m = 4.00 u) with
the release of 92.2 keV of energy. If the original beryllium atom is at rest, nd the kinetic
energies and speeds of the two helium atoms.
PH253 Spring 2015
Exam 1
Name:
This exam covers chapters 1 through 4 of the text. There are 16 questions worth a total of
47 points. You have 75 minutes to complete the exam. Please make sure:
1. Your name is clearly printed on the line above.
2. You have
PH253 Spring 2015
Final Exam Formula Sheet
Constants:
Speed of light: c = 2.998 108 m/s
Fundamental charge: e = 1.602 1019 C
Boltzmann constant: k = 8.617 105 eV/K
Stefan-Boltzmann constant: = 5.670 108 W/m2 K4
Wiens Displacement constant: b = 2.898 103 m
PH 253 / LeClair
Fall 2013
Problem Set 7 Solutions
1. The specic heat at constant volume per electron is dened as
cV =
dE
dT
(1)
where E is the average energy of electrons. A classical electron would have an average energy of
3
2 kB T . Presuming the elec
PH 253 / LeClair
Fall 2013
Problem Set 4 Solutions
Daily problem for 27 Sept Consider a particle described by the wave function
(x) =
x2
N
+ a2
(a) What is the probability P (x) dx of nding the particle in the interval [x, x + dx]?
(b) We require that P
PH 253 / LeClair
Fall 2013
Problem Set 5 Solutions
Daily problem for 14 Oct
(a) Show that the speed of an electron in the nth Bohr orbit of hydrogen is c/n, where is the
ne structure constant, equal to e2 /4 o c 1/137.
(b) What would be the speed in a hyd