A proton, a deuteron and an `alpha`- particle having the same kinetic energy are moving in circular trajectors 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_pltr_d`
B. `r_(alpha)gtr_dgtr_p`
C. `r_(alpha)=r_dltr_p`
D. `r_p=r_d=r_(alpha)`

Answer

a

Explanation

The centreipetal force is provided by the magnetic force
`(mv^2)/r=qvB implies (mv)/r =qB`
`implies r=(mv)/(qB) =p/(qB) [:' p=mv]`
But `KE=(p^2)/(2m) implies p=sqrt(2mKE)`
Here, KE and B are same for the three particles
`:. Rprop(sqrtm)/q`
`:. r_p:r_d:r_(alpha)=(sqrt1)/1:(sqrt2)/1:(sqrt4)/1=1:sqrt2:1`
`implies r_(alpha)=r_p lt r_d`.