Question

The lowest energy level for the electron in a hydrogen atom is $-13.6eV$. Calculate the:
(i) Wavelength of the first spectral line of Balmar series.
(ii) Wavelength of the series limit of Balmer series.
(iii) Rydberg constant.

Answer 1

Wavelength in Balmar series is given by $\frac{1}{\lambda }=\frac{13.6}{hc}(\frac{1}{2^2}-\frac{1}{n^2})$ $A^{o^{-1}}$
where $hc=12400eV{A}^o$
(i) : For first spectral line $n=3$
$⟹$ $\frac{1}{{\lambda }_1}=\frac{13.6}{12400}(\frac{1}{2^2}-\frac{1}{3^2})$ $A^{o^{-1}}$
$⟹{\lambda }_1=65.63A^o$
(ii) : For series limit $n=\infty$
$⟹$ $\frac{1}{{\lambda }_l}=\frac{13.6}{12400}(\frac{1}{2^2}-\frac{1}{\infty })$ $A^{o^{-1}}$
$⟹{\lambda }_l=3646A^o$
(iii) : Rydberg constant $R=\frac{13.6}{hc}=\frac{13.6}{12400}{A}^{o^{-1}}$
$⟹R=1.097\times {10}^{-3}\times {10}^{10}{m}^{-1}=1.097\times {10}^7{m}^{-1}$