Find the wave number of the 4^ th line in the Lyman series of H spectrum. (R = Rydberg constant)

Step-by-step solution

For the Lyman series of the hydrogen spectrum, the transitions occur to the ground state, so n₁ = 1 . The 4^ th line corresponds to the transition from n₂ = 5 to n₁ = 1 . The wave number is given by the Rydberg formula: = R ( 1 n₁^2 - 1 n₂^2 ) Substituting n₁ = 1 and n₂ = 5 : = R ( 1 1^2 - 1 5^2 ) = R ( 1 - 1 25 ) = 24R 25 Answer: (24R)/25 cm ⁻¹