A proton and an -particle are projected with the same kinetic energy at right angles to a uniform magnetic field. The ratio of the radii of their paths is

Step-by-step solution

Radius of circular path of a charged particle in uniform magnetic field, when it enters perpendicular direction of magnetic field. r= m v B q ...(i) where, m= mass, v= velocity and q= charge. We know that, kinetic energy, K= 1 2 m v² v= 2 K m ...(ii) From Eqs. (i) and (ii), we get aligned &r= m B q 2 K m &r= 2 K m B q aligned For the same value of kinetic energy, aligned r & m q r_ p r_ &= m_ p m_ q_ q_ p = m_ p 4 m_ p ( 2 q_ p q_ p )= 1 1 or 1: 1 aligned