Duke University Medical Physics Program
MP200  Radiation Physics
Fall 2010
Assignment 01
Due 09/13/10
( Show your work for each problem. Partial credits are awarded.)
1. Calculate the minimum coefficient of friction necessary to keep a
thin circular ring from sliding as it rolls down a plane inclined at
an angle
θ
with respect to the horizontal plane.
2. Find
< x >
and
< x
2
>
for the first excited state (
n
= 2) in an
infinite squarewell potential.
3. An electron is in a box of length 0
.
1
nm
. Find its minimum kinetic
energy.
4. A particle has the wave function
ψ
(
r
) =
Ne

αr
Where
N
is a normalization factor and
α
is a known real parame
ter.
(a) Calculate the factor
N
.
(b) Calculate the expectation values
< x >
,
< r >
,
< r
2
>
in this
state.
(c) Calculate the uncertainties (Δ
x
)
2
and (Δ
r
)
2
.
(d) Calculate the probability of finding the particle in the region
r >
Δ
r
5. A particle of rest mass 1
MeV/c
2
and kinetic energy 4
MeV
col
lides with a stationary particle of rest mass 3
MeV/c
2
. After the
1
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collision, the two particle stick together. Find (a) the initial mo
mentum of the system (b) the final velocity of the twoparticle
system, and (c) the rest mass of the twoparticle system.
6. Two particles with the same mass
m
are emitted in the same di
rection, with momenta 10
mc
and 20
mc
respectively. As seen from
the slower one what is the velocity of the faster particle, and vice
verse?
7. A particle of rest energy 494
MeV
decays into a
μ
meson of rest
energy 106
MeV
and a neutrino of zero rest energy. Find the ki
netic energies of the
μ
meson and neutrino into which the
K
meson
decays while at rest.
8. How much energy is required to accelerate an electron from rest
to a speed of 0
.
9
c
?
9. A meter stick is observed to be only 0
.
9
m
long to an inertial ob
server.
At what speed, relative to the observer, must the meter
stick be moving?
(a) 0
.
44
×
10
8
m/s
(b)0
.
57
×
10
8
m/s
(c)0
.
95
×
10
8
m/s
(d)
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 Fall '10
 Guna
 Energy, Kinetic Energy, Mass, Momentum, kg, m/s

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