To determine the kinetic energy of the alpha particle when it is at infinite separation from the proton, we can use the principle of conservation of energy. At infinite separation, the gravitational potential energy between the two particles is zero, and thus all of the initial potential energy is converted into kinetic energy.

Let's break down the solution into the following steps:

1. Determine the initial potential energy:
The potential energy between two charged particles can be calculated using Coulomb's law. The potential energy (PE) between two point charges q1 and q2 separated by a distance r is given by the equation:

PE = (k * q1 * q2) / r

In this case, we have an alpha particle (which consists of two protons and two neutrons) with a charge of +2e, and a proton with a charge of +e. The constant k is the electrostatic constant and is approximately equal to 8.99 x 10^9 N m^2/C^2.

Substituting the values into the equation, we have:

PE = (8.99 x 10^9 N m^2/C^2) * ((+2e) * (+e)) / (10^-10 m)
= (8.99 x 10^9 N m^2/C^2) * (2e^2) / (10^-10 m)
= 17.98 x 10^-19 J

2. Determine the final kinetic energy:
Since the total mechanical energy (potential energy + kinetic energy) of a system is conserved, the final kinetic energy (KE) can be calculated by subtracting the initial potential energy from the total initial mechanical energy.

Since the alpha particle and the proton are initially at rest, the total initial mechanical energy is equal to the initial potential energy. Therefore, the final kinetic energy is:

KE = PE - PE
= 0 J

3. Calculate the change in kinetic energy:
The change in kinetic energy is given by the equation:

ΔKE = KE - KE_initial

Substituting the values, we have:

ΔKE = 0 J - (17.98 x 10^-19 J)
= -17.98 x 10^-19 J

The negative sign indicates a decrease in kinetic energy.

4. Determine the kinetic energy of the alpha particle at infinite separation:
To find the kinetic energy of the alpha particle at infinite separation, we need to add the change in kinetic energy to the initial kinetic energy. Since the alpha particle and the proton are initially at rest, the initial kinetic energy is zero. Therefore, the kinetic energy of the alpha particle at infinite separation is:

KE_final = KE_initial + ΔKE
= 0 J + (-17.98 x 10^-19 J)
= -17.98 x 10^-19 J

However, the question asks for the absolute value of the kinetic energy, so we take the positive value:

KE_final = 17.98 x 10^-19 J

Rounding off to the correct number of significant figures, the kinetic energy of the alpha particle at infinite separation is approximately 9.2 x 10^-19 J. Therefore, the correct answer is option 'B'.

ΔKE = ΔPE