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

Explanation

The Rydberg formula is `"hc"//lambda_("if")=(me^(4))/(8epsilon_(0)^(2)h^(2))((1)/(n_(f)^(2))-(1)/(n_(t)^(2)))`
The wavelengths 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
`lambda_(il)=(hc)/(21.76xx10^(-19)((1)/(1)-(1)/(n_(t)^(2)))m`
`=(6.625xx10^(-34)xx3xx10^(8)xxn_(i)^(2))/(21.76xx10^(-19)xx(n_(i)^(2)-1))m=(0.9134n_(i)^(2))/((n_(i)^(2)-1))xx10^(7)m`
`=9134.4n_(i)^(2)//(n_(i)^(2)-1)A`
Substituting `n_(i)=2,3,4,5` we get `lambda_(21)=1218overset(0)A`,
`lambda_(31)=1028overset(0)A,lambda_(41)=974.3overset(A)` and `lambda_(51)=951.4overset(0)A`.