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: Determine the energy levels of the hydrogen atom
The energy of the electron in the ground state of a hydrogen atom is given as:
\[ E_1 = -13.6 \, \text{eV} \]

### Step 2: Calculate the energy of the excited state
When the electron beam with energy 12.5 eV excites the hydrogen atom, the energy of the electron in the excited state can be calculated as:
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