The ratio of the frequency corresponding to the third line in the 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

Lyman series, `n_(1)` = 1
For third line of Lyman series, `n_(2)` = 4
For hydrogen, Z = 1
`v_(H)=c/lamda=c.R_(H)Z^(2)(1/n_(1)^(2)-1/n_(2)^(2))`
= `c.R_(H)(1)^(2)(1/1-1/(4)^(2))=15/16R_(H).c`
For lithium, Z = 3
For first line of balmer series, `n_(1)=2,n_(2)=3`
`v_(Li^(2+))=c.R_(H)(3)^(2)(1/(2)^(2)-1/(3)^(2))=c.R_(H)xx9xx5/36`
= `5/4c.R_(H)`
`v_(H)/v_(Li^(2+))=((15//16)cR_(H))/((5//4)cR_(H))=15/16xx4/5=3/4`.