In a nuclear reactor, a neutron of high speed `(~~10^(7)ms^(-1))` must be slowed down to `10^(3)ms^(-1)` so that it can have a high probality of interacting with isotipe `_92U^(235)` and causing it to fission. Show that a neutron can lose most of its K.E. in an elastic collision with a light nuclei like deuterium or carbon which has a mass of only a fewe times the neutron mass. The material making up the light nuclei usually heavy water `(D_(2)O)` or graphite is called modertaor.

Explanation

To solve the problem, we will analyze the elastic collision between a neutron and a light nucleus (like deuterium) to determine how much kinetic energy the neutron can lose during the collision.

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( m_1 \) be the mass of the neutron.
- Let \( m_2 \) be the mass of the deuterium nucleus (which is approximately \( 2m_1 \)).
- Let the initial velocity of the neutron be \( v \) (approximately \( 10^7 \, \text{m/s} \)).
...