Head-on Collision

When a neutron collides head-on with a deuterium atom at rest, it results in an inelastic collision. In this collision, the neutron transfers a portion of its energy to the deuterium atom. To determine the fraction of energy transferred, we need to analyze the collision using the conservation of momentum and kinetic energy principles.

Conservation of Momentum

The conservation of momentum states that the total momentum of the system before the collision is equal to the total momentum after the collision. Since the deuterium atom is initially at rest, the total momentum before the collision is solely due to the neutron's momentum.

Conservation of Kinetic Energy

The conservation of kinetic energy states that the total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision. In this case, the kinetic energy is shared between the neutron and the deuterium atom.

Fraction of Energy Transferred

To determine the fraction of energy transferred from the neutron to the deuterium, we need to consider the masses and velocities of the particles involved.

1. The neutron's mass (mn) is approximately 1.008665 atomic mass units (u).
2. The deuterium's mass (md) is approximately 2.014102 u.

Since the deuterium atom is initially at rest, its velocity is zero (v = 0).

The fraction of energy transferred can be calculated using the following formula:

Fraction of energy transferred = (Change in kinetic energy of the deuterium) / (Initial kinetic energy of the neutron)

To calculate the initial kinetic energy of the neutron, we need its velocity.

Calculating Initial Kinetic Energy of the Neutron

The neutron's kinetic energy can be calculated using the formula:

Kinetic energy = (1/2) * mass * velocity^2

To find the initial kinetic energy, we need to determine the initial velocity of the neutron. This requires knowledge of the initial conditions, such as the neutron's initial energy or velocity.

Without this information, it is not possible to calculate the fraction of energy transferred accurately. Additional context or data is needed to proceed with the calculation.

Therefore, the fraction of energy transferred from the neutron to the deuterium cannot be determined without further information.

The whole energy of neutron will convert