Q.In a nuclear reactor, moderators slow down the neutrons which come out in a fission process. The moderator used have light nuclei. Heavy nuclei will not serve the purpose because

The key idea is that in an elastic collision, a neutron transfers maximum kinetic energy to a target of comparable mass. A light nucleus (like hydrogen or carbon) has a mass close to that of a neutron, so the neutron loses a large fraction of its energy per collision. A heavy nucleus, being much more massive, recoils very little — the neutron bounces off with nearly its original speed, so it does not slow down effectively.

Step 1: For a head-on elastic collision, the fraction of energy lost by the neutron is $\frac{4m_1 m_2}{(m_1 + m_2)^2}$, where $m_1$ is the neutron mass and $m_2$ the target mass.

Step 2: If $m_2 \gg m_1$, this fraction approaches $4m_1/m_2 \approx 0$ — negligible slowing.

Step 3: Only light nuclei give a significant energy transfer per collision, making them effective moderators.

The question is about moderation — the process of slowing down fast neutrons produced in fission so they can sustain a chain reaction. A moderator must reduce neutron speed efficiently without absorbing them. The physics here is purely about elastic collisions and energy transfer.

Let’s walk through why heavy nuclei fail.

1. The physics of a single elastic collision When a neutron (mass $m$) collides elastically with a stationary nucleus (mass $M$), the fraction of kinetic energy lost by the neutron depends only on the mass ratio. For a head-on collision (maximum energy transfer), the neutron’s final kinetic energy $E_f$ is related to its initial energy $E_i$ by:

The energy transferred to the nucleus is:

2. Why light nuclei are effective

   If $M \approx m$ (e.g., hydrogen, where $M = 1$ u, $m \approx 1$ u), then $\Delta E \approx E_i$ — the neutron can lose almost all its energy in one collision. For deuterium ($M = 2$ u) or carbon ($M = 12$ u), the energy loss per collision is still substantial. This is why light elements like hydrogen (in water), deuterium (in heavy water), and carbon (in graphite) are used as moderators.

3. Why heavy nuclei fail

   If $M \gg m$ (e.g., lead, $M = 207$ u), then:

which is a tiny fraction. For lead, $\Delta E \approx \frac{4}{207} E_i \approx 0.019 E_i$ — less than 2% per collision. To slow a neutron from fission energy (~2 MeV) to thermal energy (~0.025 eV), you would need thousands of collisions, making moderation impractical. The neutron would likely be absorbed or escape before slowing down.

4. The correct reasoning The moderator’s job is to slow neutrons via elastic collisions. Heavy nuclei absorb too little energy per collision to be effective. This is a direct consequence of conservation of momentum and energy in elastic collisions — no other physics is needed.

Method: Analyzing Energy Transfer in an Elastic Collision (Moderator Selection)

Use this whenever a question asks how effectively a moving particle transfers kinetic energy to a stationary target via an elastic collision — the classic "which material makes a good moderator/absorber" type question.

Steps

Step 1: Write the general formula for energy transfer in a head-on elastic collision

For a particle of mass $m$ (here, a neutron) striking a stationary target of mass $M$ head-on, the fraction of kinetic energy transferred to the target is

This single formula governs every "how much energy does the projectile lose" question of this type.

Step 2: Examine the two limiting cases

• If $M \approx m$ (comparable masses), the fraction approaches its maximum value, close to 1 — the projectile can lose almost all its energy in a single collision.
• If $M \gg m$ (target much heavier than projectile), the fraction shrinks to approximately $\dfrac{4m}{M}$, which is small — the projectile barely slows down, bouncing off with nearly its original speed (think of a ball bouncing off a wall).

Step 3: Apply the limiting case to the physical scenario

Decide which regime the problem describes. If the target nuclei are much heavier than the projectile (e.g. heavy nuclei absorbing fast neutrons), very little energy is transferred per collision, so many collisions would be needed to achieve significant slowing — often impractically many before the projectile is absorbed or escapes.

Step 4: Match to the qualitative conclusion

Use the scaling from Step 2 to decide whether the proposed material would be an effective or ineffective moderator/energy-absorber, and select the option that correctly attributes this to the physics of elastic-collision energy transfer (not to unrelated properties like weight, state of matter, or structural breakup).