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Question

A proton and an α-particle enter a uniform magnetic field at right angles to the field with the same speed. The ratio of the periods of α-particle and proton is-

A
2:1
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B
1:1
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C
1:4
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D
1:2
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Solution

The correct option is A 2:1
Proton 1H1 and α-particle 2He4

qp=e ; qHe=2e ; mp=m ; mHe=4m

vB Hence, they will undergo a uniform circular motion.

Fm=Fcentripetal

qvB=mv2r [ v=rω]

Bqrω=mrω2 Bq=mω

Bq=m(2πT)

T=2πmBq Tmq

TαTp=mαmp×qpqα=41×12=21

Tα:Tp=2:1

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (A) is the correct answer.

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