A proton , a deutron and `alpha )`- particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field . If ` r_(p), r_(d) , and r_(alpha)` denote respectively the radii of the trajectories of these particles , then

Options

A. `r_(alpha)=r_(p) lt r_(d)`
B. `r_(alpha) gt r_(d) lt r_(p)`
C. `r_(alpha)=r_(d) gt r_(p)`
D. `r_(p) = r_(d) = r_(alpha)`

Answer

A

Explanation

Given that `K_(p) - K_(d) = K_(a) = K` (say) We know that `m_(p0 = m, m_(d) = 2m` and `m_(a) = 4m` and `q_(p) = e, q_(d) = 2e`
Further`r = (sqrt(2mK))/(qB) implies r_(p) = (sqrt(2mK))/(eB)`.
`r_(d) = (sqrt(2 (2m) K))/(eB) = sqrt(2) r_(p)`
and `r_(a) = (sqrt(2(4m) K))/((2e) B) = r_(p)`. Hence `r_(alpha) = r_(p) lt r_(d)`