A proton traps a free electron to form the hydrogen atom of lowest energy level. If photon is emitted in this process then what will be its wavelength. Assume initial kinetic energy of the electron to be zero.

Explanation

To solve the problem of finding the wavelength of the photon emitted when a proton traps a free electron to form a hydrogen atom at its lowest energy level, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial and Final Energy States**:
- Initially, the free electron has zero kinetic energy and no potential energy. Thus, the initial energy \( E_1 \) is:
\[
E_1 = 0 \, \text{eV}
...