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Question

A proton and an α particle, having kinetic energies Kp and Kα respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of α particle is 2:1. The ratio Kp:Kα will be :

A
1:8
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B
1:4
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C
8:1
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D
4:1
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Solution

The correct option is D 4:1
Given :
rprα=21

We know that,
mαmp=41 and qαqp=21

The radius of trajectory is given by,

r=mvqB=pqB=2mKqB

K=r2q2B22m

So,

KpKα=mα r2p q2pmp r2α q2α=41×(21)2×(12)2=4:1

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