What is the ratio of shortest wavelength of the Balmer series ot the shortest waelength of the Lyman series?

Options

A. `4:1`
B. `4:3`
C. `4:9`
D. `5:9`

Answer

A

Explanation

For a Balmer series
`(1)/(lambda_(B))=R[(1)/(2^(2))-(1)/(n^(2))] " "...(i)`
where, `n=3,4.....`
The shortest wavelength of the4 Balmer series cab calculated by putting
`n= oo`
in Eq (i)
`:. (lambda _(s))_(s),=(4)/(R) " "...(ii)`
For a Lyman series,
`(1)/(lambda_(L))=R[(1)/(1^(2))-(1)/(n^(2))] " "...(iii)`
where `n=2,3,4...`
By puttng `n=oo` in Eq. (iii) , we obtain the series limit of the Lyman series, the shortest wavelength of the Lyman series can be calculated by putting `n=oo` in Eq. (ii)
or `(lambda_(L))_(s)=(1)/(R)" "...(iv)`
On dividding Eq. (ii) by Eq. (iv) , we get
`((lambda_(s))_(s))/((lamda_(L))_(s))=(4)/(1)`