The first emission of hydrogen atomic spectrum in Lyman series appears at a wavelength of

Step-by-step solution

The Rydberg formula for the hydrogen spectrum is given by 1 = R ( 1 n₁^2 - 1 n₂^2 ) , where R is the Rydberg constant. For the Lyman series, the transition occurs to the ground state, so n₁ = 1 . The first emission line corresponds to the transition from the first excited state, n₂ = 2 . Substituting these values into the formula: 1 = R ( 1 1^2 - 1 2^2 ) = R ( 1 - 1 4 ) = R ( 3 4 ) Therefore, the wavelength is given by: = 4 3R cm Answer: 4 3 R ~cm