Bohr model is applied to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a transverse magnetic field B. The energy of the charged particle in the n^ th level will be (h=Planck's constant)

Step-by-step solution

For a charged particle moving in a transverse magnetic field, the magnetic force provides the necessary centripetal force for circular motion: mv^2 r = qvB v = qBr m According to Bohr's quantization postulate, the angular momentum of the particle is quantized: mvr = nh 2 Substituting the expression for v into the quantization condition, we get: m ( qBr m ) r = nh 2 qBr^2 = nh 2 r^2 = nh 2 qB The total energy of the particle is purely kinetic (since the magnetic force does no work): E = 1 2 mv^2 Substituting v = qBr