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Q.

A proton, a deuteron and an a-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp, rd and rα denote, respectively, the radii of the trajectories of these particles, then

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a

rα=rp

b

rα>rd>rp

c

rα=rd>rp

d

rp=rd=rα

answer is A.

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Detailed Solution

Given that Kp=Kd=Kα=K (say). We know that mp=m,md=2m and mα=4m and qp=e,qd=e and qα=2e Further, r=2mKqB⇒rp=2mKeBrd=2(2m)KeB=2rp and rα=2(4m)K1(2e)B=rp. Hence, rα=rp
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