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)/(375) lamda_(1)`

Answer

B

Explanation

`(1)/(lamda_(1))= R ((1)/(2^(2))- (1)/(3^(2)))= R ((1)/(4)- (1)/(9))`
`rArr (1)/(lamda_(1))= R ((5)/(36))` ....(i)
`(1)/(lamda_(2))= R ((1)/(3^(2))- (1)/(5^(2)))= R ((16)/(9 xx 25))` ...(ii)
From (i) and (ii)
`(lamda_(2))/(lamda_(1))= (5)/(36) xx (9 xx 25)/(16) rArr lamda_(2)= (125)/(64) lamda_(1)`