Final answer:
In a classic nuclear physics experiment, an alpha particle was accelerated towards a gold nucleus and its path was deflected by the Coulomb interaction. The question asks how close the alpha particle could come to the gold nucleus before being deflected. The answer explains that the alpha particle will be deflected at a distance where the Coulomb force is equal to the centripetal force.
Step-by-step explanation:
In one of the classic nuclear physics experiments, an alpha particle was accelerated towards a gold nucleus, and its path was substantially deflected by the Coulomb interaction. The energy of the doubly charged alpha nucleus was given as 5.00 MeV. The question asks how close to the gold nucleus could the alpha particle come before being deflected?
To answer this question, we need to understand the concept of the Coulomb interaction. The Coulomb interaction is the electrostatic force between two charged particles. The force is given by Coulomb's Law: F = k * (q1 * q2) / r^2, where F is the force, k is a constant, q1 and q2 are the charges of the particles, and r is the distance between the particles.
In the case of an alpha particle (which has a charge of +2) and a gold nucleus (which has a charge of +79), the Coulomb force will be repulsive. As the alpha particle approaches the gold nucleus, the Coulomb force will increase, causing the alpha particle to be deflected. The alpha particle will be deflected at the point where the Coulomb force is equal to the centripetal force, which is given by F = m * v^2 / r, where m is the mass of the alpha particle, v is its velocity, and r is the distance between the particles.
To calculate the distance at which the alpha particle will be deflected, we can equate the Coulomb force and the centripetal force. Solving for r, we get r = k * (q1 * q2) / (m * v^2). Plugging in the values for the charges of the alpha particle and gold nucleus, as well as the mass and velocity of the alpha particle, we can calculate the distance. However, since the question does not provide values for the mass and velocity, we cannot give an exact numerical answer. Nevertheless, we can conclude that the alpha particle will be deflected at a distance that is greater than zero but less than infinity.