The frequency for a series limit of Balmer and paschen serial respectively are `f_1and f_3` if the frequency of the first line of Balmer series is then the relation between `f _1,f_2and f_3` is

Options

A. `v_1 -v_2 = v_3`
B. `v_1 + v_3 = v_2`
C. `v_1 + v_2 = v_3`
D. `v_1 - v_3 = 2v_1`

Answer

A

Explanation

For the various line in the `H_2` spectrum
`1/lamda = R [ (1)/(n_f^2) - (1)/(n_i^2) ] " but " c/lamda`
`therefore v = Rc [ (1)/(n_f^2) - (1)/(n_i^2) ] `
For the series limit n `=oo`
For Balmer series , `n_f = 2 " and " n_i = oo`
`therefore v_1 = Rc[(1)/(2^2) - (1)/(oo) = (Rc)/(4) " "..(1)`
For paschen series , `n_f = 3 " and " n_i =oo`
`therefore v_3 = Rc [ (1)/(3^2) - (1)/(oo)] = (Rc)/(9) " "....(2)`
For the first line in the Balmer series , `n_f = 2, n_i = 3`
`therefore v_2 = Rc [ (1)/(2^2) - (1)/(3^2) ] = Rc [ 1/4 - 1/9] " "...(3)`
`therefore v_1 - v_3 = Rc [ 1/4 - 1/9 ] = v_2`
Thus `v_1 - v_3 = v_2 " or " v_1 - v_2 = v_3 " " ` option (a)