When an alpha particle passes through the center of a hydrogen molecule on a line perpendicular to the internuclear axis, it experiences a force. In this case, we need to find out where on its path the alpha particle experiences the maximum force and what that force is.


The force experienced by the alpha particle can be calculated using Coulomb's law. The electric force between two charged particles is given by:

F = k * q1 * q2 / r^2

Where F is the force, k is the Coulomb's constant, q1 and q2 are the charges on the particles, and r is the distance between them. In this case, the alpha particle has a charge of +2e, where e is the elementary charge. The hydrogen molecule consists of two protons, each with a charge of +e. Therefore, the force experienced by the alpha particle is:

F = k * (2e) * (+e) / (b/2)^2

Where b is the distance between the nuclei of the hydrogen molecule. At the point where the alpha particle is closest to the hydrogen nuclei, its distance from each proton is b/2. Therefore, we use b/2 as the distance between the alpha particle and each proton.


To find the point where the alpha particle experiences the maximum force, we take the derivative of the force with respect to the distance between the nuclei, b. Setting the derivative equal to zero gives us the point of maximum force.

dF/db = -4k * (2e) * (+e) / (b^3) = 0

Solving for b, we get:

b = (8ke^2 / F)^(1/3)

Substituting this value of b into the expression for the force, we get:

F_max = k * (2e) * (+e) / [(8ke^2 / F)^(2/3)]

Simplifying this expression, we get:

F_max = (4 / 3) * (k * e^2 / b^2)

Therefore, the maximum force experienced by the alpha particle is:

F_max = (4 / 3) * (k * e^2 / b^2)

and it occurs at a distance of:

b = (8ke^2 / F)^(1/3)


In conclusion, when an alpha particle passes through the center of a hydrogen molecule on a line perpendicular to the internuclear axis, it experiences a force. The maximum force experienced by the alpha particle is given by:

F_max = (4 / 3) * (k * e^2 / b^2)

and it occurs at a distance of:

b = (8ke^2 / F)^(1/3)