Given weavelength is λ=975Å
By Rydberg's equation for hydrogen atom is
λ1=R(n121−n221)
9751=R(11−n221)
(∵n1=1)for ground state
where R is the Rydberg constant=1.09×107m−1
Solving above equation, we get rounded numerical value n2=4 (highest principal quantum number)
Total number of spectral lines is given in terms of highest principal quantum number as
=2n(n−1)=24(4−1)=6