Theoretical Question 3
Part A
Neutrino Mass and Neutron Decay
A free neutron of mass
m
n
decays at rest in the laboratory frame of reference into
three noninteracting particles: a proton, an electron, and an antineutrino. The rest
mass of the proton is
m
p
, while the rest mass of the antineutrino
m
v
is assumed to be
nonzero and much smaller than the rest mass of the electron
m
e
. Denote the speed of
light in vacuum by
c
. The measured values of mass are as follows:
m
n
=
939.56563
MeV/
c
2
,
m
p
=
938.27231
MeV/
c
2
,
m
e
=
0.5109907
MeV/
c
2
In the following, all energies and velocities are referred to the laboratory frame. Let
E
be the total energy of the electron coming out of the decay.
(a) Find the maximum possible value
E
max
of
E
and the speed
v
m
of the antineutrino
when
E
=
E
max
. Both answers must be expressed in terms of the rest masses of the
particles and the speed of light. Given that
m
v
< 7.3
eV/
c
2
, compute
E
max
and the
ratio
v
m
/
c
to 3 significant digits.
[4.0 points]
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Part B
Light Levitation
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 Spring '11
 NA
 Mass, Neutron, Light, Emax, glass hemisphere

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