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 lt r_d`

Answer

D

Explanation

Radius of the circular path of charged particle in a magnetic field is given by :
`r=(mv)/(Bq)=sqrt(2mK)/(Bq)` ( `because` Kinetic energy , `K=1/2mv^2` )
For the same value of K and B ,
`r prop sqrtm/q`
`therefore r_p : r_d : r_alpha =sqrtm_p/q_p : sqrtm_d/q_d :sqrtm_alpha/q_alpha`
`=sqrtm/e :sqrt(2m)/e : sqrt(4m)/(2e)=1:sqrt2:1`
or `r_alpha = r_p lt r_d`