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 of how a neutron can lose most of its kinetic energy in an elastic collision with a light nucleus like deuterium or carbon, we will go through the following steps:

### Step 1: Define the masses and initial velocities
Let:
- The mass of the neutron be \( m_1 \).
- The mass of deuterium (or carbon) be \( m_2 \) (for deuterium, \( m_2 = 2m_1 \)).
- The initial velocity of the neutron be \( u = 10^7 \, \text{m/s} \).
- The initial velocity of the deuterium nucleus be \( 0 \, \text{m/s} \).
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