For Balmer series, wavelength of first line is `lamda_(1)` and for Brackett series, wavelength of first line is `lamda_(2)` then `(lamda_(1))/(lamda_(2))`

Options

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

Answer

B

Explanation

For Balmer series, wavelength of first line `(lamda_(1))` is given by
`(1)/(lamda_(1))=R((1)/(2^(2))-(1)/(3^(2)))=(5R)/(36)`
Where, R is Rydber constant,
For Brackett series, wavelength of first line `(lamda_(2))` is given by
`(1_(1))/(lamda_(2))=R((1)/(4^(2))-(1)/(5^(2)))=(9R)/(400)`
`therefore (lamda_(1))/(lamda_(2))=(1//lamda_(2))/(1//lamda_(1))=(9R//400)/(5R//36)=0.162`