Hydrogen atom is bombarded with electrons accelerated through a potential difference of $V$, which causes excitation of hydrogen atoms. If the experiment is being performed at $T = 0\ \text{K}$, the minimum potential difference needed to observe any Balmer series lines in the emission spectra will be $\dfrac{\alpha}{10}\ \text{V}$, where $\alpha =$ ______. (Write the value to the nearest integer)
Numerical value type. Enter your answer.
Answer: 121
At $0\ \text{K}$ all atoms are in the ground state. A Balmer line ($n \to 2$) needs the atom to be excited to at least $n = 3$:
$$\Delta E = 13.6\left(1 - \frac19\right) = 12.09\ \text{eV}$$
So $V = 12.09\ \text{V} = \dfrac{120.9}{10}\ \text{V}$ and $\alpha \approx 121$.
Solution by Sreeraj P, M.Sc Physics