High School

Canadian nuclear reactors use heavy water moderators in which elastic collisions occur between the neutrons and deuterons of mass 2.0u.

Part A:
What is the speed of a neutron, expressed as a fraction of its original speed, after a head-on, elastic collision with a deuteron that is initially at rest?
Express your answer using three decimal places.

Part B:
What is its kinetic energy, expressed as a fraction of its original kinetic energy?
Express your answer using three decimal places.

Answer :

Final answer:

Part A: The speed of the neutron after the head-on, elastic collision with the deuteron is approximately equal to its original speed.

Part B: The fraction of the neutron's original kinetic energy after the collision is 1.000.

Explanation:

In an elastic collision between a neutron and a deuteron, both particles conserve momentum and kinetic energy. Let's solve Part A first.

Part A: To find the speed of the neutron after the collision, we can use the principle of conservation of momentum. Since the deuteron is initially at rest, the momentum before the collision is zero. After the collision, the momentum of the neutron and deuteron together is still zero, as they move in opposite directions. Therefore, the momentum of the neutron after the collision is also zero.

Let's assume the initial speed of the neutron is vi and the final speed of the neutron after the collision is vf. According to the conservation of momentum, we have:

0 = mnvi + mdvf

where mn is the mass of the neutron and md is the mass of the deuteron.

Since the deuteron is much heavier than the neutron, we can approximate its mass as infinite. This means that the final speed of the neutron after the collision is negligible compared to its initial speed. Therefore, the speed of the neutron after the collision is approximately equal to its original speed.

Part B: Since the speed of the neutron after the collision is approximately equal to its original speed, the kinetic energy of the neutron after the collision is also approximately equal to its original kinetic energy. Therefore, the fraction of its original kinetic energy is 1.000.

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