Question

Spectral line in the Balmer series is usually followed by another line in Lyman series. What is the wavelength of the spectral line in Lyman series?

Answer 1

For the Lyman series in the hydrogen spectrum,

$$\begin{aligned}\Delta E &=13 \cdot 6\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right) eV . \text { Here } n_{1}=1, n_{2}=2 \\&=13 \cdot 6 \times \frac{3}{4} eV =10 \cdot 2 eV \\&=10 \cdot 2 \times 1 \cdot 60 \times 10^{-19} J \\\lambda &=\frac{h c}{\Delta E}=\frac{6 \cdot 626 \times 10^{-34} \times 3 \times 10^{8}}{10 \cdot 2 \times 1 \cdot 60 \times 10^{-19}} m =1 \cdot 218 \times 10^{-7} m =121 \cdot 8 nm .\end{aligned}$$