Question

A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 × 10⁻¹⁵ eVs) :

• A. 99.3 nm
• B. 94.1 nm
• C. 974 nm
• D. 941 nm

Hint:

Use E = 13.6 eV (1/n_f² − 1/n_i²) for the energy of the photon and λ = hc/E with hc = (4 × 10⁻¹⁵ eVs)(3 × 10⁸ m/s).

Answer 1

The Correct Option is B

Step 1: The wavelength of the series limit of the transition to the ground state (Lyman limit) is λ₀ = hc/13.6 eV = 1200 eV nm / 13.6 eV ≈ 88.24 nm.
Step 2: For a transition from n = 4 to n = 1, 1/λ = (1/λ₀)(1 − 1/16) = (15/16)(1/λ₀), so λ = (16/15) λ₀.
Step 3: λ = (16/15) × 88.24 nm ≈ 94.1 nm, which is option (B).