The wavelength of light emitted from second orbit to first orbit in a hydrogen atom is

Options

(a) 1.215×10⁻⁷ m
(b) 1.215×10⁻⁵ m
(c) 1.215×10⁻⁴ m
(d) 1.215×10⁻³ m

Correct Answer:

1.215×10⁻⁷ m

Explanation:

For hydrogen atom, energy = -(13.6 / n²) eV
Energy radiated = 13.6 [(1/1²) – (1/2²)] = [(13.6 × 3) / 4] eV
Energy = hc / λ = [(6.6 × 10⁻³⁴ × 3 × 10⁸) / λ × 1.6 × 10⁻¹⁹] eV
[(13.6 × 3) / 4] = [(6.6 × 10⁻³⁴ × 3 × 10⁸) / λ × 1.6 × 10⁻¹⁹]
λ = (6.6 × 3 × 4 × 10⁻²⁶) / (13.6 × 3 × 1.6 × 10⁻¹⁹) = 1.215 × 10⁻⁷ m