The ratio of angular frequency ( ) of an electron to the total energy ( E) of an electron in the first orbit of hydrogen atom is ( h is the Plank's constant)

Step-by-step solution

The total energy of an electron in an orbit is given by E = - 1 2 m v^2 . The angular frequency is = v r , which gives v = r . Substituting v in the energy expression: E = - 1 2 m ^2 r^2 The ratio of angular frequency to total energy is: E = - 1 2 m ^2 r^2 = -2 m r^2 From Bohr's quantization rule for angular momentum: m v r = nh 2 m r^2 = nh 2 For the first orbit of the hydrogen atom, n = 1 : m r^2 = h 2 Substituting this value in the ratio expression: E = -2 h 2 = - 4 h Answer: - 4 / h