Illinois Institute of Technology
Physics
M.Sc. Comprehensive and Ph.D. Qualifying Examination
PART I
Thursday January 13, 2011
4:00 - 8:00 PM
General Instructions
1. Each problem is to be done on a separate
piece of paper. Label the front of each page with
your identifying code letter, the part number of the exam, and the number of the problem
only; for example: A-I.6. Do not
write your name on any material handed in for grading.
2. Any numerical data not specified in a problem should be found in the table of constants at
the front of the exam.
3.
DON’T PANIC:
It is not expected that each student will solve every problem. Rather, it is
advisable to do a thorough job on those problems that you do solve.
1

Physical Constants
Speed of light in vacuum
c
=
2
.
998
×
10
8
m/s
Planck’s constant
h
=
6
.
626
×
10
−
34
J
·
s
planckover2pi1
=
h/
2
π
=
1
.
055
×
10
−
34
J
·
s
=
6
.
582
×
10
−
16
eV
·
s
Permeability constant
μ
o
=
4
π
×
10
−
7
N/A
2
Permittivity constant
1
4
πǫ
o
=
8
.
988
×
10
9
N
·
m
2
/C
2
Fine structure constant
α
=
e
2
4
πǫ
o
planckover2pi1
c
=
7
.
30
×
10
−
3
=
1
137
Gravitational constant
G
=
6
.
67
×
10
−
11
m
3
/s
2
·
kg
Avogadro’s number
N
A
=
6
.
023
×
10
23
mole
−
1
Boltzmann’s constant
k
=
1
.
381
×
10
−
23
J/K
=
8
.
617
×
10
−
5
eV/K
kT
at room temperature
k
·
300 K
=
0.0258 eV
Universal gas constant
R
=
8
.
314 J/mole
·
K
Stefan-Boltzmann constant
σ
=
5
.
67
×
10
−
8
W/m
2
·
K
4
Electron charge magnitude
e
=
1
.
602
×
10
−
19
C
Electron rest mass
m
e
=
9
.
109
×
10
−
31
kg
=
0.5110 MeV/c
2
Neutron rest mass
m
n
=
1
.
675
×
10
−
27
kg
=
939.6 MeV/c
2
Proton rest mass
m
p
=
1
.
672
×
10
−
27
kg
=
938.3 MeV/c
2
Deuteron rest mass
m
d
=
3
.
343
×
10
−
27
kg
=
1875.6 MeV/c
2
Atomic mass unit (C
12
= 12)
u
=
1
.
661
×
10
−
27
kg
=
931.5 MeV/c
2
Mass of earth
M
E
=
5
.
98
×
10
24
kg
Radius of earth
R
E
=
6
.
37
×
10
6
m
Mass of sun
M
S
=
1
.
99
×
10
30
kg
Radius of sun
R
S
=
6
.
96
×
10
8
m
Gravitational acceleration at
earth’s surface
g
=
9.81 m/s
2
Atmospheric pressure
=
1
.
01
×
10
5
N/m
2
Radius of earth’s orbit
=
1
.
50
×
10
11
m
Radius of moon’s orbit
=
3
.
84
×
10
8
m
Conversion Factors
1 eV
=
1
.
602
×
10
−
19
J
1 J
=
6
.
242
×
10
18
eV
1
˚
A
=
10
−
10
m
1 Fermi
=
10
−
15
m
1 barn (b)
=
10
−
28
m
2
1 in
=
2.54 cm
0
◦
Celsius
=
273.16 K
1 cal
=
4.19 J
2

Problem 1:
CP violation was discovered in the decays of Kaons by Cronin and Fitch in 1964,
where they noticed
K
0
L
could decay to either three or two pions (a different CP eigenstate).
CP violation was observed again in Kaons when is was observed the rate for
K
0
L
→
π
−
e
+
ν
e
and
K
0
L
→
π
+
e
−
¯
ν
e
differ. Given
m
K
0
L
= 500 MeV,
m
π
±
= 140 MeV, and the electron and
neutrino are effectively massless:
(a) What is the maximum energy of the electron when a
K
0
L
decays at rest?

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