Physics - Modern Physics Question with Solution | TestHub

$$\begin{array}{rl}& \mathrm{E}=\frac{\mathrm{hc}}{\lambda }\Rightarrow \lambda =\frac{\mathrm{hc}}{\mathrm{E}}=\frac{6.62\times 10^{-34}\times 3\times 10^8}{12.5\times 1.6\times 10^{-19}}\\ & =993{\mathrm{A}}^{\circ }\\ & \frac{1}{\lambda }=\mathrm{R}\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)\\ & \end{array}$$ (where Rydberg constant , $\mathrm{R}=1.097\times 10^7$ ) or, $\frac{1}{993\times 10^{-10}}=1.097\times 10^7\left(\frac{1}{1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$ Solving we get ${\mathrm{n}}_2=3$ Spectral lines Total number of spectral lines $=3$ Two lines in Lyman series for ${\mathrm{n}}_1=1,{\mathrm{n}}_2=2$ and ${\mathrm{n}}_1=1,{\mathrm{n}}_2=3$ and one in Balmer series for ${\mathrm{n}}_1=2,{\mathrm{n}}_2=3$