if the wavelength of the first line of the balmer series of hydrogen is `6561 Å`, the wavelength of the second line of the series should be

Options

A. `(27)/(20) xx 4861 Å`
B. `(20)/(27) xx 4861 Å`
C. `20 xx 4861 Å`
D. ` 4861 Å`

Answer

A

Explanation

`(1)/(lambda_(2)) = R [(1)/(2^(2)) - (1)/(2^(2))]`
`(1)/(lambda_(2)) = R [(1)/(4) - (1)/(16)]`
`(1)/(lambda_(2)) = R [(3)/(16)] or lambda_(2) =(16)/(3 R)`
Again `(1)/(lambda_(1)) = R [(1)/(2^(2)) - (1)/(3^(2))]`
`(1)/(lambda_(1)) = R [(1)/(4) - (1)/(9)]`
`(1)/(lambda_(1)) = R (5 R)/(36) or - lambda_(1) = (36)/(3 R)`
`(lambda_(1))/(lambda_(2)) = (36)/(3 R) xx (3 R)/(16) = (27)/(20)`
or `lambda_(1) = (27)/(20) xx 4861 Å`