Proton , deuton and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton , deuteron and alpha particle are respectively `r_(p), r_(d) and r_(alpha)`. Which one of the following relation is correct?

Options

A. `r_alpha=r_p=r_d`
B. `r_alpha=r_p lt r_d`
C. `r_alpha gt r_d gt r_p`
D. `r_alpha=r_d gt r_p`

Answer

B

Explanation

Kinetic energy of a moving particle
`K=1/2mv^2` or `mv=sqrt(2mK)`
As a charged particle is describing a circular path of radius r in the magnetic field B, hence
`Bqv=(mv^2)/(r)` or `r=(mv)/(Bq)=(sqrt(mK))/(Bq)`
`:. rpropsqrtm/q`
Hence `r_p:r_d:r_alpha=sqrtm/e:(sqrt(2m))/(e):(sqrt(4m))/(2e)`
`=1:sqrt2:1`
Thus, `r_p=r_alpha` and `r_dgtr_p` or `r_alpha`.
Thus, option (b) is true.