A proton and an `alpha-`particle enter a uniform magnetic field moving with the same speed. If the proton takes `25 mu s` to make 5 revolutions, then the periodic time for the `alpha-` particle would be

Options

A. `50 m sec`
B. `25 m sec`
C. `10 m sec`
D. `5 m sec`

Answer

C

Explanation

Time period `T_(p) = (25)/(5) = 5 mu` sec. By using
`T = (2pi m)/(qB) implies (T_(alpha))/(T_(p)) = (m_(alpha))/(m_(p)) xx (q_(p))/(q_(alpha)) = (4 m_(p))/(m_(p)) xx (q_(p))/(2q_(p))`
`implies T_(alpha) = 2T_(p) = 10 mu` sec.