A proton of mass m is at rest when it is suddenly struck head-on by an alpha particle (which consists of 2 protons and 2 neutrons)moving at speed v.If the collision is perfectly elastic,what speed will the alpha particle have after the collision? (Assume the neutron's mass is equal to the proton's mass. )
A)zero
B)2v/3
C)3v/5
D)5v/3

Question

Quizplus · Accepted Answer

Since the collision is perfectly elastic, momentum is conserved.
Initial momentum of alpha particle = (2m + 2m)v = 4mv
Initial momentum of stationary proton = 0
Total initial momentum = 4mv

Let the velocity of the alpha particle after collision be V.
Final momentum of alpha particle = (2m)V
Final momentum of proton = (m)V
Total final momentum = (2m + m)V = 3mV

Since momentum is conserved, we have:

Total initial momentum = Total final momentum
4mv = 3mV
V = 4v/3

Therefore, the velocity of the alpha particle after the collision is 4v/3, which is equal to 3v/5 (option C).

A Proton of Mass M Is at Rest When It