60
2 Particle Dynamics
Fig. 2.17a
Fig. 2.17b
2.34 A carbon-14 nucleus which is radioactive decays into a beta particle, a neutrino and N-14 nucleus. In a particular decay, the beta particle has momentum
p and the nitrogen nucleus has momentum of magnitude 4 p/3 at an angle of
90 ◦ to p. In what direction do you expect the neutrino to be emitted and what
would be its momentum?
2.35 If a particle of mass m collides elastically with one of mass m at rest, and
if the former is scattered at an angle θ and the latter recoils at an angle ϕ
with respect to the line of motion of the incident particle, then show that
m
M
=
sin(2ϕ + θ)
sin θ
.
2.36 A body of mass M rests on a smooth table and another of mass m moving
with a velocity u collides with it. Both are perfectly elastic and smooth and
no rotations are set up by this collision. The body M is driven in a direction at
angle ϕ to the initial line of motion of the body m. Show that the velocity of
M is
2m
M + m
u cos ϕ.
2.37 A nucleus A of mass 2 m moving with velocity u collides inelastically with a
stationary nucleus B of mass 10 m. After collision the nucleus A travels at 90 ◦