Find out the difference of wave number between second and first spectral lines of Lyman series of hydrogen atom's spectrum. `R=1.09xx10^(7)m^(-1)`

Explanation

For second line of Lyman series of hydrogen atom and for first line of Lyman series `(1)/(lambda_(2))=R[(1)/(1^(2))-(1)/(3^(2))]=R[(1)/(1)-(1)/(9)]`
`(1)/(lambda_(2))=(8R)/(9) ....(1)`
and for first line of Lyman series,
`(1)/(lambda_(1))=R[(1)/(1^(2))-(1)/(2^(2))]=R[(1)/(1)-(1)/(4)]`
`(1)/(lambda_(1))=(3R)/(4)" .....(2)`
`rArr` Different of wave number.
`(1)/(lambda_(2))-(1)/(lambda_(1))=(8R)/(9)-(3R)/(4)=R[(8)/(9)-(3)/(4)]`
`=1.09xx10^(7)[(32-27)/(36)]`
`=1.09xx10^(7)xx(5)/(36)` `0.1513xx10^(7)m^(-1)`