A proton and a deuteron with same initial kinetic energy enter a magnetic field in a direction perpendicular to the direction of the field.the ratio of the radii of the circular trajectories described by them is

Radius of trajectory is given by , r= MV / BQ

Similarly , V =

substitute and you will get ,

r= sqrt ( 2MV / Q)B ………………….. (1)

Here, V and B are constants … so we need to look into the mass and charge of each element.

1. Proton mass is 1 a.m.u and charge is +1e
2. For deutron , mass = 2 a.m.u
3. Alpha partical has mass 4 a.m.u and charge 2e

Substituting these values in (1) you get the ratios as 1 : sqrt(2) : sqrt (2)