A
radioactive nucleus moves with a uniform velocity of
0.050c in
the laboratory frame. It
decays by emitting a gamma ray. We
have to find the direction of propagation of the gamma ray in the
laboratory frame. We
may assume that the gamma ray is emitted (a)
parallel to the direction of motion of the
nucleus, as seen in
the frame in which the nucleus is at rest,
(b) at
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Solution: Click For PDF Version Let be
the inertial frame of reference in which the radioactive nucleus is
at rest. It is given that with respect to the laboratory frame of
reference S the frame
is moving with a uniform velocity of 0.050c.
According to the special theory of relativity, if a gamma ray is
emitted in the inertial frame
at an angle
 with
respect to the direction of its relative velocity with respect to S,
the angle of emission of gamma ray
measured by S is
related by the aberration formula
The velocity
of
(a)
For
(b)
For
(c)
For
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to this direction, and
(c) at
to this direction.
.
,
that is when the gamma ray is emitted in the forward direction, the
laboratory frame will also observe that it is moving in the forward
direction,
.
,
the laboratory frame will observe that the gamma ray is moving at
angle given by the equation
,
the laboratory frame will observe that the gamma ray is moving at
angle given by the equation