The ratio of the frequency corresponding to the thrid line in Lyman series of hydrogen atomic spectrum to that of the first line in Balmer series of `Li^(2+)` spectrum is

Options

A. `(4)/(5)`
B. `(5)/(4)`
C. `(4)/(3)`
D. `(3)/(4)`

Answer

D

Explanation

For Lyman series, `n_(1)=1`
and for third line, `n_(2)=4`
`barv_(1)=R_(H)Z^(2)((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
`=R_(H)(1)^(2)((1)/(1)-(1)/(16))=(15)/(16)R_(H)` (`because` For H atom Z = 1)
For Balmer series, `n_(1)=2` and for first line, `n_(2)=3`
`barv_(2)=R_(H)Z^(2)((1)/((2)^(2))-(1)/((3)^(2)))["For "Li^(2+),Z=3]`
`=R_(H)(3)^(2)((1)/(4)-(1)/(9))=9R_(H)((5)/(36))`
`(v_(1))/(v_(2))=(15R_(H)xx36)/(16xx9xx5R_(H))=(3)/(4)`