Calculate the longest wavelength in hydrogen emission spectrum of Lymen series (R_H=109677 ~cm ⁻¹ )

Step-by-step solution

The longest wavelength in the Lyman series of hydrogen corresponds to the smallest energy transition, from n₂ = 2 to n₁ = 1 . Using the Rydberg formula, 1 = R_H ( 1 1^2 - 1 2^2 ) = 109677~ cm ⁻¹ (1 - 1 4 ) = 109677~ cm ⁻¹ 3 4 This simplifies to 1 = 82257.75~ cm ⁻¹ The wavelength is therefore = 1 82257.75 1.2156 10⁻⁵~ cm Among the options, this value is closest to 1.216 10⁻⁵~ cm . The correct choice is B .