The ratio of difference in wavelengths of `1^(st)` and `2^(nd)` lines of Lyman series in H-like atom to difference in wavelength for `2^(nd)` and `3^(rd)` lines of same series is :-

Options

A. 2.5:1
B. 3.5:1
C. 4.5:1
D. 5.5:1

Answer

B

Explanation

`(1)/(\lambda_(1))=R((1)/(1^(2))-(1)/(2^(2)))=(3)/(4)R" "rArr(1)/(lambda)=(4)/(3R)`
`(1)/(\lambda_(2))=R((1)/(1^(2))-(1)/(3^(2)))=(8)/(9)R" "rArrlambda_(2)=(9)/(8R)`
`(1)/(lambda_(1))=R[(1)/(1^(2))=(1)/(4^(2))]=(15)/(16)R" "rArrlambda_(3)=(16)/(15)R`
`(lambda_(1)-lambda_(2))/(lambda_(2)-lambda_(3))=3.5`