A light of energy 12 . 75   eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is x π × 10 - 17   eVs . The value of x is ______ (use h = 4 . 14 × 10 – 15   eVs ,   c = 3   × 10 8   m   s – 1 )

Step-by-step solution

Let the electron jumped to n t h excited state. In the ground state, energy E = - 13 . 6   eV So, using relation 12 . 75 = 13 . 6 1 1 2 - 1 n 2 ⇒ 0 . 9375 = 1 - 1 n 2 ⇒ n 2 = 16 ⇒ n = 16 = 4 Now, angular momentum, L = n h 2 π = 4 h 2 π = 2 h π = 2 π × 4 . 14 × 10 - 15 = 828 × 10 - 17 π   eVs Hence, the value of x = 828 .