If a polonium-210 (Po-210) atom has just decayed, how close can the ejected

alpha particle get to a neighboring Po-210 nucleus?
Hint: W = F*r
F=kq1q2/r

To determine how close the ejected alpha particle can get to a neighboring Po-210 nucleus, we can use Coulomb's law and the concept of potential energy.

Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

F = k * q1 * q2 / r^2

Where:
F is the electrical force between the charges,
k is the electrostatic constant (9 x 10^9 N*m^2/C^2),
q1 and q2 are the charges of the two objects, and
r is the distance between the charges.

In this case, the alpha particle has a charge of +2e (twice the charge of an electron) and the Po-210 nucleus has a charge of +84e (84 times the charge of an electron).

Given that information, we can calculate the force between the alpha particle and the Po-210 nucleus.

Now, potential energy (U) is defined as the work (W) done to move a charged object from one point to another against an electric field.

W = U = -ΔPE (potential energy change)

Using the equation W = F * r, we can calculate the potential energy change for the alpha particle.

Since the alpha particle is being ejected, it starts at a distance far away from the nucleus. At this distance, the potential energy is zero.
Therefore, the potential energy change will be the negative of the potential energy at the nearest approach of the alpha particle to the Po-210 nucleus.

Setting the potential energy change equal to zero, we can solve for the closest distance (r) between the particles at which the potential energy is not zero.

0 = (k * q1 * q2) / r

Rearranging the equation, we find:

r = (k * q1 * q2) / 0

Now, we can substitute the values for the charges of the alpha particle (q1) and the Po-210 nucleus (q2) and the value for the electrostatic constant (k) into the equation and solve for r.

r = (9 x 10^9 N*m^2/C^2) * (2e) * (84e) / 0

Keep in mind that dividing by zero is undefined, indicating that the particles will never make contact.

Therefore, the ejected alpha particle cannot get arbitrarily close to the neighboring Po-210 nucleus because the equation breaks down at very small distances.