What is the kinetic energy of the electron in the nth level, moving in a plane under the influence of a magnetic field 'B'? [ m-mass of electron; h- Planck's constant; e- electronic charge]

Step-by-step solution

The electron moves in a circular orbit under the influence of a magnetic field B . The magnetic force provides the necessary centripetal force for circular motion: evB = mv^2 r This simplifies to evB = mv^2 r r = mv eB According to Bohr's quantization condition for angular momentum: mvr = nh 2 Substituting the expression for r into the quantization condition: mv ( mv eB ) = nh 2 m^2 v^2 eB = nh 2 m^2 v^2 = nheB 2 v^2 = nheB 2 m^2 The kinetic energy K is given by: K = 1 2 mv^2 = 1 2 m ( nheB 2 m^2 ) K = nheB 4 m Ans