The electron in a hydrogen atom initially in state of quantum number `n_1` makes a transition to a state whose excitation energy with respect to the ground state is 10.2 eV. If the wavelength associated with the photon emitted in this transition is 487.5 nm, find the (i) energy in eV, and (ii) value of the quantum number, `n_1` of the electron in its initial state.

Explanation

To solve the problem step by step, we will follow the instructions given in the video transcript and apply the relevant physics concepts.

### Step 1: Calculate the energy of the emitted photon

We know that the energy of a photon can be calculated using the formula:

\[
E = \frac{hc}{\lambda}
...