In Bohr's theory the potential of an electron at a position is K r^2 2 , where K is a constant. Then, the quantised energy of the electron in n th orbit is

Step-by-step solution

Given, potential energy of electron, aligned & & U= K r^2 2 & F & = d U d r = d d r K r^2 2 =K r But & F & = m v^2 r K r= m v^2 r & v & =r K m aligned According to Bohr's postulates, aligned L & =m v r= n h 2 m r v & = n h 2 m r r K m & = n h 2 [from Eq. (i)] r^2 K m & = n h 2 r^2 & = n h 2 K m aligned We know that, energy of electron in n th orbit, aligned B_n & =K r^2 & =K n h 2 K m [from Eq. (ii)] & = n h 2 K m aligned