A 12.5 eV electron beam is used to excite a gaseous hydrogen atom at room temperature. Determine the wavelengths and the corresponding series of the lines emitted.

Explanation

To solve the problem of determining the wavelengths and corresponding series of lines emitted when a 12.5 eV electron beam excites a gaseous hydrogen atom, we can follow these steps:

### Step 1: Calculate the total energy after excitation
The energy of the hydrogen atom in its ground state is given by:
\[ E_1 = -13.6 \text{ eV} \]
When the hydrogen atom is excited by a 12.5 eV electron beam, the total energy becomes:
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