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

Explanation

The rhdberg formula is ` ( hc )/( lamda _(if )) = (M e^4 ) /( 8 epsi_(0)^(2) h^2) ((1)/(n_(f)^(2))-(1)/( n_(i)^(2)))`
The wavelength of the first four lines in the Lyman series correspond to transitions from `n_i =2`
`3,4,5,` to ` n_f=1` we know that ` (me^4 )/( 8 epsi_(0)^(2) h^2)= 13.6 eV =21 .76 xx 10^(-19) J`
therefore ` lamda_(11) = ( hc )/( 21.76 xx 10^(-19) ((1)/(1) - (1)/(n_(i)^(2)))`
=`( 6.625 xx 10^(-34) xx 3 xx 10^8 xx n_(i)^(2) )/( 21.76 xx 10^(-19) xx (n_i ^2 -1))=(0.9134 n_(i)^(2) )/( (n_i ^(2)-1) ) xx 10^(-7) = ( 913 .4 n_(i)^(2 ) Å )/((n_(i)^(2) -1))`
substiting `n_i = 2,3,4,5` we get `lamda_(21) = 1218 Å , lamda_(41) = 1028 ,lamda_(41) = 974.3Å ` and ` lamda_(51) 951 .4 Å `