Question

The wavelength of a spectral line in one of the spectral series of atomic hydrogen is $12825\,\mathring{A}$. What is the wavelength $($ in $\mathring{A})$ of the series limit?

Answer 1

$\Delta E=\frac{1240}{1282.5} eV =0.96\, eV$
This is the difference in levels $5$ and $3$ of atomic hydrogen.
Now series limit means $3 \rightarrow \infty$
$\frac{1}{\lambda}=(912)^{-1}\left(\frac{1}{n_{1}^{2}}\right)$
$\Rightarrow \frac{1}{\lambda}=(912)^{-1}\left(\frac{1}{9}\right)$
$\Rightarrow \lambda=8208\,\mathring{A}$