Physics - Modern Physics Question with Solution | TestHub

The Lyman series involves transitions to the $n=1$ level.

The shortest wavelength corresponds to the transition from $n=\infty$ to $n=1$, and the longest wavelength corresponds to the transition from $n=2$ to $n=1$.

Using the Rydberg formula, the ratio of the longest to shortest wavelengths is $\frac{{\lambda }_{max}}{{\lambda }_{min}}=\frac{E_{\infty \to 1}}{E_{2\to 1}}=\frac{1}{\frac{1}{4}}\cdot \frac{3}{4}=\frac{4}{3}$. Therefore, the answer is 4/3.