A `12.9 eV` beam of electrons is used to bombard gaseous hydrogen atom at room temperature. Up to which energy level the hydrogen atoms would be excited?
Calculate the wavelength of the first member of Paschen series and first member of Balmer series.

Explanation

To solve the problem step by step, we will first determine the energy level to which the hydrogen atoms would be excited when bombarded by a `12.9 eV` beam of electrons. Then, we will calculate the wavelengths of the first members of the Paschen and Balmer series.

### Step 1: Determine the energy absorbed by the hydrogen atom

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

When the hydrogen atom absorbs energy from the electron beam, the total energy of the atom becomes:
...