The difference between the radii of n th and ( n + 1 ) t h orbits of hydrogen atom is equal to the radius of ( n - 1 ) th orbit of hydrogen. The angular momentum of the electron in the n th orbit is _ _ _ _ _ _ ( h is Planck's constant)

Step-by-step solution

The radius of the hydrogen atom, r n = r 0 n 2 ⇒ r n + 1 = r 0 n + 1 2 ,   r n = r 0 n 2   &   r n - 1 = r 0 n - 1 2 ⇒ r n + 1 - r n = r n - 1 ⇒ r 0 n + 1 2 - r 0 n 2 = r 0 n - 1 2 ⇒ n + 1 2 - n 2 = n - 1 2 ⇒ 2 n + 1 = n 2 + 1 - 2 n ⇒ 4 n = n 2 ⇒ n = 4 now Recall the Bohr's second postulate, m v r = J → = n h 2 π = 4 h 2 π = 2 h π , where J → is known as total angular momentum.