Nuclear Energy

In a cyclotron, the kinetic energy gained by a particle is given by the relation: Where:
is the charge of the particle,
is the magnetic field strength,
is the radius of the circular path,
is the mass of the particle.

For a given magnetic field strength and radius, the kinetic energy gained by the particle depends on its mass. Since the proton, deuteron, and -particle have different masses, they will experience different accelerations. The proton has the least mass, followed by the deuteron and then the -particle. The minimum kinetic energy is gained by the particle with the smallest mass because it requires the least force to accelerate to a given velocity.

Thus, the minimum K.E. is gained by the deuteron, as it has a mass between the proton and -particle.

• Inefficient neutron slowing: Elastic collisions between neutrons and heavy nuclei (like uranium or lead) transfer minimal kinetic energy, failing to thermalize neutrons effectively.
• Physics principle: Momentum conservation dictates that light nuclei (e.g., hydrogen, carbon) slow neutrons best, as they absorb more energy per collision.

Why other options are incorrect:

• A: Heavy nuclei do not inherently "break up" due to neutron collisions.
• C: Weight is a practical concern but not the primary physics reason.
• D: State of matter (liquid/gas) is irrelevant; moderators like graphite (solid) are commonly used.