The wavelength of the first balmer line caused by a transition from the `n = 3` level to the n = 2 level in hydrogen is `lamda_(1)`. The wavelength of the line caused by an electronic transition from `n =5` to `n =3` is

Options

A. `(375)/(128) lamda_(1)`
B. `(125)/(64) lamda_(1)`
C. `(64)/(125) lamda_(1)`
D. `(128)/(378) lamda_(1)`

Answer

B

Explanation

`(lamda_(1))/(lamda_(2))=((1)/(2^(2))-(1)/(3^(2)))/((1)/(3^(2))-(1)/(5^(2)))=((1)/(4)-(1)/(9))/((1)/(9)-(1)/(25))=(125)/(64)`
`lamda_(2)=(125)/(64)lamda_(1)`.