A proton, a deuteron and an `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_(d) gt r_(p)`
B. `r_(alpha) = r_(d) = r_(p)`
C. `r_(alpha) lt r_(d) lt r_(p)`
D. `r_(alpha) = r_(p) gt r_(d)`

Answer

A

Explanation

In this case
`R = (mv)/(qB) = (sqrt(2KE.m))/(qB)`
Here `R prop (sqrt(m))/(q) = 1 : sqrt(2) : 1`
So, `r_(alpha) = r_(d) gt r_(p)`