# Question #f54cb

Dec 1, 2017

The question should have been "WHY does ... ${D}_{2} O$?"...

#### Explanation:

Nuclear fission releases super fast neutrons. To sustain the nuclear chain reaction, these fission released neutrons must induce further fission.

But the fast moving neutrons have a low probability of interacting with other fissile nuclei and will leave the pile without inducing further fission. To avoid this from happening, the fast moving neutrons must be slowed down somehow. This can be done by making the neutrons collide with a target particle. The purpose of a moderator is to slow down the fission released neutrons.

To be a good moderator the target must have the right mass to reduce the kinetic energy of the neutron to the maximum extent possible.

When we consider elastic collisions between two bodies, a projectile particle (neutron) of mass ${m}_{p}$ and a target particle (moderator) of mass ${M}_{t}$, the question we are asking ourselves is - what should be the right ratio of the masses to achieve maximum drop in kinetic energy of the projectile particle?

$X \setminus \equiv {M}_{t} / {m}_{p}$

It can be shown that the percentage loss of the kinetic energy of the projectile nuclei is related to this mass ratio $X$ as :

$\setminus \chi \setminus \equiv \frac{| \setminus \Delta {K}_{p} |}{K} _ \left\{\text{pi}\right\} = | {\left(\setminus \frac{1 - X}{1 + X}\right)}^{2} - 1 |$

The kinetic energy loss is maximum for $X = 1$. This means the projectile and target must have the same mass. So slow moving neutrons are the best moderators. But the very reason for slowing down fission released neutrons is the non-availability of slow moving neutrons. If slow neutrons are available in abundance there is no need of moderation in the first place.

What is the next best option? It would be proton, whose mass is comparable to the neutron's. Nucleus of ordinary hydrogen is made of single proton. So ordinary water would be the second best moderator. In fact it is used in many reactors as moderator. Unfortunately single protons have a tendency to capture neutrons and become a deuterium. We want to only slow down the neutrons, not get captured by the target particle.

So we go for the next best option, which is deuterium. Deuterium is made of one proton and one neutron, giving it a mass that is approximately twice the neutron mass. If it were not for the property of hydrogen to capture neutrons, there would have been no need for heavy water moderators.