Calculate the value of Rydberg constant if the wavelength of the first member of Balmer series in the hydrogen spectrum is 6563 Å. Also find the wavelength of the first member of Lyman series in the same spectrum.

Explanation

Given `lamda = 6563 Å = 6563 xx 10^(-10) m`
Using the relation , v` = 1/lamda = R [ (1)/(n_1^2) - (1)/(n_2^2) ]`
For first member in Balmer series , `n_1 = 2` and `n_2 = 3`
`1/lamda = R [1/4 - 1/9]`
`(1)/(6563 xx 10^(-10)) = (5R)/(36)`
` R = 1.097 xx 10^7 m^(-1)`
For first member of lyman series : `n_1 = 1`, and `n_2 = 2`
Using the relation
`(1)/(lamda.) = R [(1)/(n_1^2) - (1)/(n_2^2)]`
`(1)/(lamda.) = 1.097 xx 10^7 [1/1 - 1/4]`
`(1)/(lamda.) = 1.097 xx 10^7 [3/4]`
`lamda. =(4)/(3 xx 1.097 xx 10^7)`
`lamda. = 1.215 xx 10^(-7)`
`lamda. = 1215Å`