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 = eVs) :
- A.94.1 nm
- B.99.3 nm
- C.974 nm
- D.941 nm
Show answer and solution
Correct option: A
Solution
Energy of transition: E = 13.6(1/1² - 1/4²) = 13.6 × (15/16) = 12.75 eV.
Wavelength: λ = hc/E = (4×10⁻¹⁵ × 3×10⁸) / 12.75 = (1.2×10⁻⁶) / 12.75 ≈ 9.41×10⁻⁸ m = 94.1 nm.
This falls in the Lyman series (UV region), confirming the transition ends at n = 1.
Wavelength: λ = hc/E = (4×10⁻¹⁵ × 3×10⁸) / 12.75 = (1.2×10⁻⁶) / 12.75 ≈ 9.41×10⁻⁸ m = 94.1 nm.
This falls in the Lyman series (UV region), confirming the transition ends at n = 1.
[JEE Main 2023 · 24 Jan · Shift 2]