For balmer series wavelength of first line is `lambda_(1)` and for brackett series wavelength of first line is `lambda_(2)` then `(lambda_(1))/(lambda_(2))` is

Options

A. 0.081
B. 0.162
C. 0.198
D. 0.238

Answer

B

Explanation

For Balmer series , `n_f = 2 " and n_i = 3` for the first line
`therefore 1/lamda_1 = R_H [ 1/2^2 - 1/3^2 ] = R_H [1/4 - 1/9]`
`=R_H (5/36)`
For Brackett series , `n_f = 4 " and " n_i =5`
`therefore 1/lamda_2 = R_H [ 1/4^2 - 1/5^2] = R_H [1/16-1/25]`
`=R_H [9/400] " "..(2)`
`therefore (1/lamda_1)/(1/lamda_2) = lamda_2/lamda_1 = (5/36)/(9/400) = (400xx5)/(36xx9) = 1000/162`
`therefore lamda_1/lamda_2 = 162/1000 = 0.162`