A proton and a deuteron with the 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

Step-by-step solution

For a moving charge in a perpendicular magnetic field m v² r =B q v r= m v B q = p B q r_ p r_ d = p_ p p_ d or or Also, momentum p= 2 m E (as q is same for both) p_ p p_ d = m_ p m_ d From Eq. (i) and (ii), we have r_ p r_ d = m_ p m_ d = 1 2 = 1 2