Question

 A beam of electrons bombards a sample of hydrogen. Through what potential difference must the electrons have been accelerated if the first line of the Balmer series is to be emitted?

Answer 1

The first line of the Balmer series is the transition 3→1 with the energy of

$$E=E_3-E_1=-E_1\bigg(1-\frac1{3^2}\bigg)=12.1\text{ eV}.$$

The potential difference that would accelerate the electrons to the energy of this transition:

$$V=E/e=12.1\text{ V}.$$