A light of energy 12.75 eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches one of its excited states. The angular momentum of the atom in the excited state is (x/π) × 10⁻¹⁷ eV s. The value of x i s ______. [Use h = 4.14 × 10⁻¹⁵ eV s]
Physics · Atomic Structure and X-rays · Atomic Structure & Bohr's Atomic Model
JEE Mains 1 February 2023 Shift 1 Morning Shift

Question

A light of energy 12.75 eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches one of its excited states. The angular momentum of the atom in the excited state is (x/π) × 10⁻¹⁷ eV s. The value of x i s ______. [Use h = 4.14 × 10⁻¹⁵ eV s]

Physics · Atomic Structure and X-rays · Atomic Structure & Bohr's Atomic Model

JEE Mains 1 February 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

Final energy = -13.6 + 12.75 = -0.85 eV. Using Eₙ = -13.6/n² gives n²=16 and n=4. Angular momentum L = nh/(2π) = 4h/(2π)=2h/π = [2×4.14×10⁻¹⁵]/π = (828/π)×10⁻¹⁷ eV s. Hence x=828.