Neutron-Atom Collision: Energy Transfer

[bgil1989]

1. A neutron in a reactor makes an elastic head-
on collision with the nucleus of an atom ini-
tially at rest.
Assume: The mass of the atomic nucleus is
about 13.2 the mass of the neutron.
What fraction of the neutron’s kinetic en-
ergy is transferred to the atomic nucleus?

 

[LowlyPion]

1. A neutron in a reactor makes an elastic head-
on collision with the nucleus of an atom ini-
tially at rest.
Assume: The mass of the atomic nucleus is
about 13.2 the mass of the neutron.
What fraction of the neutron’s kinetic en-
ergy is transferred to the atomic nucleus?

Welcome to PF.

What do you know about elastic collisions?

What gets conserved?

 

[baba89]

In this scenario, the neutron's kinetic energy is transferred to the atomic nucleus through an elastic head-on collision. The amount of energy transferred will depend on the mass of the nucleus compared to the mass of the neutron. Since the mass of the nucleus is about 13.2 times greater than the mass of the neutron, the transfer of energy will be significant.

To calculate the exact fraction of energy transferred, we can use the formula for elastic collisions, which states that the initial kinetic energy of the system is equal to the final kinetic energy. In this case, the initial kinetic energy is solely from the neutron and the final kinetic energy is shared between the neutron and the nucleus.

We can express this as:

(1/2)mv^2 = (1/2)(mv^2) + (1/2)(Mv^2)

Where m is the mass of the neutron, v is its initial velocity, and M is the mass of the nucleus.

Solving for the fraction of energy transferred (E) we get:

E = [(1/2)(m/M)] / [(1/2)(m/M) + 1]

Plugging in the values given, we get:

E = [(1/2)(1/13.2)] / [(1/2)(1/13.2) + 1]

E = 0.038 or approximately 3.8% of the neutron's kinetic energy is transferred to the atomic nucleus in an elastic head-on collision.

This transfer of energy is important in understanding the behavior of particles in nuclear reactions and can have significant implications in fields such as nuclear energy and particle physics. Further studies and experiments can help us better understand and utilize the energy transfer in neutron-atom collisions.