The ratio of the frequencies of the long wavelength limits of the balmer and Lyman series of hydrogen is

Options

A. `27:5`
B. `5:27`
C. `4:1`
D. `1:4`

Answer

A

Explanation

For long wavelength of the lyman series
`n_f " and " n_i =2`
`(1)/(lamda_L) = R [ 1/1^2 - 1/2^2 ] = R[1-1/4] = 3/4 R`
`therefore lamda_L = (4)/(3R)`
for balmer series , `n_f = 2 " and n_i = 3` for longest wavelength
`therefore 1/lamda_B = R [1/2^2 - 1/3^2 ] = R[1/4-1/9] = 5/36 R`
`therefore lamda_B = (36)/(3R)`
`therefore lamda_L/lamda_B = (4)/(3R)xx(5R)/(36) = 5/27`
But `(v_L)/(v_B) = (C ) / lamda_L xx(lamda_B)/(C ) = (lamda_B)/(lamda_L) = 27/5`