The wavelength of `H_(alpha)` line of Balmer series is `X Å` what is the `X of H_(beta)`line of Balmer series

Options

A. `X (108)/(80) Å`
B. `X (80)/(108) Å`
C. `(1)/(X) (80)/(108) Å`
D. `(1)/(X) (108)/(80) Å`

Answer

B

Explanation

`H_(alpha)` line of Balmer series means first line of Balmer series
`n_(1) = 2,n_(2) = 3`
`bar v = (1)/(lambda_(alpha)) = R ((1)/(2^(2)) - (1)/(3^(2))) = (5R)/(36)`
`:. Lambda_(alpha)= (36)/(5R) = X`
`H_(beta)` line of Balmer series means second line of Balmer series
`n_(1) = 2,n_(2) = 4`
`bar v = (1)/(lambda_(beta)) = R ((1)/(2^(2)) - (1)/(4^(2))) = (3R)/(16)`
`:. Lambda_(beta)= (16)/(3R) = X`
Then `(16)/(3R) = (X xx 5R xx 16)/(36 xx 3R) = (80)/(108) Å`