Find the quantum number n corresponding to nth excited state of `He^(++)` ion if on transition to the ground state the ion emits two photons in succession with wavelength 108.5 nm and 30.4 nm. The ionization energy of the hydrogen atom is 13.6 eV.

Explanation

To find the quantum number \( n \) corresponding to the nth excited state of the \( \text{He}^{++} \) ion, we will follow these steps:

### Step 1: Calculate the energy of the emitted photons
We will use the formula for the energy of a photon:
\[ E = \frac{hc}{\lambda} \]
where:
...