Given,
Ist member of Lyman series of hydrogen spectrum is x. as taken as λ
Rydberg's equation :-
For hydrogen z =1
Ist member of Lyman series = n1 =1 , n2 = 2
λ = 4/3R
Ist member of Balmer series = n1 =2 , n2 = 3
λ = = 36/5R
Now from eqn 1 and 2 we get,
λ/λ' = 27/5
λ' = 27/5 x λ
λ' = 27/5λ