A neutron with an energy of `4.6 MeV` collides elastically with proton and is retarded. Assuming that upon each collision the neutron is deflected by `45^(@)`, find the number of collisions which will reduce its energy to `0.23 eV`.

Explanation

To solve the problem step by step, we will follow the principles of conservation of momentum and energy in elastic collisions.

### Step 1: Understand the Problem
We have a neutron with an initial energy of \(4.6 \, \text{MeV}\) colliding elastically with a proton. After each collision, the neutron is deflected by \(45^\circ\). We need to find out how many collisions it takes for the neutron's energy to be reduced to \(0.23 \, \text{eV}\).

### Step 2: Convert Energies
Before proceeding, let's convert the energies into the same units.
- Initial energy of neutron:
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