A proton, a deuteron and an ( ) - particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energy. The ratio of the radii of the circular paths described by them is

Step-by-step solution

The radius of the circular path described by particle in uniform magnetic field is [ R= m v q B = 2 m E q B ] For proton, ( R_ p = 2 m_ p E q_ p B ) For deuteron, ( R_ d = 2 m_ d E q_ d B ) For a-particle, ( R_ = 2 m_ E q_ B ) Now, ( q_ p =e, q_ d =e, q_ =2 e ) ( m_ p =m, m_ d =2 m, m_ =4 m ) Therefore, ( R_ p = 2 m E e B , R_ d = 4 m E e B , R_ = 8 m E 2 e B = 2 m E e B ) ( R_ p : R_ d ; R_ =1: 2 : 1 )