Using the Rydberg formula, calculate the wavelength of the first four spectral lines in the Balmer series of the hydrogen spectrum.

Explanation

`(1)/(lamda)=R((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
i) `(1)/(lamda_(32))=R((1)/(2^(2))-(1)/(3^(2)))=Rxx(5)/(36)=(5R)/(36)`
`therefore lamda_(32)=(36)/(5xx1.097xx10^(7))=6575 Å`
ii) `(1)/(lamda_(42))=R((1)/(2^(2))-(1)/(4^(2)))=(3R)/(16)`
`therefore lamda_(42)=(16)/(3xx1.097xx10^(7))=4870 Å`
iii) `(1)/(lamda_(52))=R((1)/(2^(2))-(1)/(5^(2)))=(21R)/(100)`
`therefore lamda_(52)=(100)/(21xx1.097xx10^(7))=4348 Å`.
iv) `(1)/(lamda_(62))=R((1)/(2^(2))-(1)/(6^(2)))=(8R)/(36)`
`therefore lamda_(62)=(36)/(8xx1.097xx10^(7))=4109 Å`.