Final answer:
The task is to calculate the voltage needed to accelerate an alpha particle so that it gains enough kinetic energy to approach a gold nucleus to a certain distance without being stopped by the electric potential energy. This involves equating the kinetic energy gained from acceleration to the electric potential energy between the alpha particle and the gold nucleus at the given distance.
Step-by-step explanation:
The question is asking to determine the voltage needed to accelerate an alpha particle so that it has just enough kinetic energy to overcome the electric potential energy due to the Coulomb force of a gold nucleus, at a specified distance. To find this, we can use the concept of electrical potential energy and kinetic energy equivalence. The electrical potential energy U between two point charges is given by U = k * q1 * q2 / r, where k is Coulomb's constant, q1 and q2 are the charges, and r is the separation between the charges. For the alpha particle, we can say that the kinetic energy gained from being accelerated through a voltage V is equal to the electric potential energy at that distance from the nucleus, which gives us e * V = k * (79e) *(2e) / r. We can solve for V using the given numbers.