Question

A proton and an alpha particle moves perpendicular to a magnetic field find the ratio of the radii of circular path described by them when both having equal kinetic energies

Answer 1

Answer:

Rp : Ra = 1:1

Explanation:

For a particle moving in a circular path, R=sqr rt(2M*KE)/BQ

For an alpha particle: R=Ra, Ma=4Mp , Qa=2Qp

For proton:R=Rp, M=Mp, Q=Qp

then, Ra= sqr rt (2*4 Mp * KE) / B*2 Qp = [2*sqr rt (2 Mp*KE)] / [2*B*Qp]                               = sqr rt(2Mp*KE)/BQp

Rp = sqr rt(2Mp*KE)/BQp

Now Rp / Ra = [sqr rt(2Mp*KE)/BQp] / [sqr rt(2Mp*KE)/BQp] = 1:1