The ratio of the frequency corresponding to the third line in the lyman series of hydrogen atomic spectrum to that of the first line in Balmer series of `Li^(2+)` spectrum is

Options

A. `4/5`
B. `5/4`
C. `4/3`
D. `3/4`

Answer

D

Explanation

For third line in Lyman series,
`n_1 = 1, n_2 = 4`
`v_H = c/(lambda) =c.R_HZ^2(1/(n_1^2) - 1/(n_2^2))`
`= c.R_H(1)^(2)[1/(1^2) - 1/(4^2)] = 15/16 R_Hc`
For first line in Balmer series for `Li^(2+)`
`n_1 = 2, n_2 = 3`
`v_(Li^(2+)) = cR_H(Z)^2[1/(n_1^2) - 1/(n_2^2)]`
`= cR_H(3)^2 [1/(2^2) - 1(3^2)] = c xx R_H xx 9 xx 5/36 = 5/4 cR_H`
`(v_H)/(v_(Li^(2+))) = 15/16 xx 4/5 = 3/4`