Question

At room temperature, gaseous hydrogen is bombarded with a beam of electrons of 13.6 eV energy. The series to which the emitted spectral line belongs to:

• A. Lyman series
• B. Balmer series
• C. Paschen series
• D. Pfund series

Hint:

The Lyman series corresponds to electronic transitions where the final state is $n = 1$, producing ultraviolet radiation.

Answer 1

The Correct Option is A

The energy of 13.6 eV corresponds to the ionization energy of hydrogen, meaning the electron is excited to the highest possible energy level and then de-excites. The emitted spectral lines belong to the Lyman series when an electron transitions to the $n=1$ energy level: $$\Delta E = h \nu = 13.6 \left( 1 - \frac{1}{n^2} \right) \text{eV}$$ Since all transitions end at $n=1$, the emitted radiation falls in the ultraviolet region, characteristic of the Lyman series.