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Question

A proton and an αparticle enter in a uniform magnetic field moving with the same speed. If the proton takes 25 μs to make 5 revolutions, then the periodic time for the αparticle would be

A
50 μs
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B
25 μs
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C
10 μs
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D
5 μs
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Solution

The correct option is A 10 μs
Time period of revolution for the charge q and mass m in a circular path: T=2πmqB
Tα=2πmαqαB
Tp=2πmpqpB where p in the subscript is for proton.
TαTp=2πmαqαB2πmpqpB
Tα=Tp×mαmp×qpqα=5×41×12=10μs since mα=4mp and qα=2qp

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