A uniform magnetic field B is present in a region. An electron is projected perpendicular to the field and moves in a circle. Assuming Bohr's quantization rule for angular momentum, determine the radius of the n th orbit.

Step-by-step solution

When an electron moves in a circular path in a uniform magnetic field, the magnetic force provides the necessary centripetal force. e v B = m v^2 r m v = e B r According to Bohr's quantization rule, the angular momentum of the electron is an integral multiple of h 2 . m v r = n h 2 Substituting m v = e B r into the quantization condition: (e B r) r = n h 2 e B r^2 = n h 2 r = n h 2 e B