For balmer series wavelength of first line is `lambda_(1)` and for brackett series wavelength of first line is `lambda_(2)` then `(lambda_(1))/(lambda_(2))` is

Options

A. 0.081
B. 0.162
C. 0.198
D. 0.238

Answer

B

Explanation

For first line of Balmer series `p=2` and `n=3`
`:. 1/lambda_(1)=R[1/p_(2)-1/n^(2)]`
`=R [1/4-1/9]`
`:. lambda _(1)=36/(5R)`
For first line of Brackett series `p=4` and `n=5`
`:. 1/lambda_(2)=R[1/p_(2)-1/n^(2)]`
`=R[1/16-1/25]`
`:. lambda_(2)=(16xx25)/(9R)`
`:. lambda_(1)/lambda_(2)=36/(5R)xx(9R)/(16xx25)=0.162`