What transition of `Li^(+2)` spectrum will have same wavelength as that of second line of Balmer series in `He^(+)` spectrum ?

Explanation

`(1)/(lambda_("He"^(+)))= (1)/(lambda_(Li^(+)))`
`RZ^(2) [ (1)/(n_(1)^(2) ) - (1)/(n_(2)^(2) ) ] RZ^(2) [ (1)/(n_(1)^(2) )- (1)/(n_(2)^(2))]`
`2^(2)[ (1)/(2^(2) ) - (1)/(4^(2) )] =3^(2) [(1)/(n_(1)^(2) )- (1)/(n_(2)^(2) ) ]`
`4 [ (1)/(4) - (1)/(16)] =9 [ (1)/(n_(1)^(2) )- (1)/(n_(2)^(2) )]\ (4)/(9) xx (3)/(16) = [(1)/(n_(1)^(2) ) - (1)/(n_(2)^(2))]`
`therefore (1)/(n_(1)^(2))- (1)/(n_(2)^(2) ) = (1)/(12)" "n_1=3, n_2 = 6`
`(3 to 6)` will have same wavelength as that of second line of Balmer series in `He^(+)` spectrum.