According to Rydberg-Balmer equation ,
`(1)/(lambda)=R[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))] =R [(1)/(1^(2))-(1)/(n_(2)^(2))]`
The Wavelength `(lambda)` will be longest when `n_(2)` is the smallest i.e., `n_(2)=2` and 3 for two longest wavelength lines.
For `n_(2)=2: " "(1)/(lambda)=(1.097 xx 10^(-2)nm^(-1)) [(1)/(1^(2))-(1)/(2^(2))]`
`=(1.097 xx 10^(-2)nm^(-1)) xx(3)/(4) =8.228 xx 10^(-3) nm^(-1) "or" lambda =121.54 nm`
For `n_(2)=3 :" " (1)/(lambda)=(1.097 xx 10^(-2)nm^(-1))[(1)/(1^(2))-(1)/(3^(2))]`
`=(1.097 xx 10^(-2)nm^(-1))xx(8//9) =9.75 xx 10^(-3)nm^(-1) "or" lambda= 102 .56 nm`
