When a hydrogen atom in the ground state absorbs 10.2 eV of energy, the orbital angular momentum of the electron increases by

Step-by-step solution

The energy of an electron in the n^ th orbit of a hydrogen atom is given by E_n = - 13.6 n^2 eV . For the ground state ( n=1 ), E₁ = -13.6 eV . When the electron absorbs 10.2 eV of energy, its new energy becomes: E_n = -13.6 + 10.2 = -3.4 eV Equating this to the energy expression for the n^ th orbit: - 13.6 n^2 = -3.4 n^2 = 13.6 3.4 = 4 n = 2 According to Bohr's model, the orbital angular momentum of an electron in the n^ th orbit is L = nh 2 . The increase in orbital angular momentum is: L = L₂ - L₁ = 2h 2 - h 2 =