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. 0.81
B. 0.162
C. 0.198
D. 0.238

Answer

c

Explanation

For balmer series wavelength of first line `(lambda_(1))` is give by
`(1)/(lambda_(1))=R(1)/(2^(12)-(1)/(3^(2))=(5R)/(36)`
where R is Rydberg constant
For brackett series wavelength of first line `(lambda_(2))` is given by
`(1)/(lambda_(2))=R(1)/(4^(2)-(1)/(5^(2))=(9R)/(400)`
`therefore (lambda_(1))/(lambda_(2))=(1//lambda_(2))/(1//lambda_(1))=(9R // 400)/(5R // 36)=0.162`