In Rutherford's famous scattering experiments that led to the planetary model of the atom, alpha particles (having charges of +2e and masses of 6.64 10-27 kg) were fired toward a gold nucleus with charge +79e. An alpha particle, initially very far from the gold nucleus, is fired at 1.6 107 m/s directly toward the nucleus, as in the figure below. How close does the alpha particle get to the gold nucleus before turning around? Assume the gold nucleus remains stationary.

To solve this problem, we can use the principles of conservation of kinetic energy and the electrostatic force between the alpha particle and the gold nucleus.

1. First, let's find the initial kinetic energy of the alpha particle. The kinetic energy (KE) is given by the formula KE = (1/2)mv^2, where m is the mass of the alpha particle and v is its initial speed.
Plugging in the values, we get KE = (1/2)(6.64 * 10^-27 kg)(1.6 * 10^7 m/s)^2.

2. Next, we need to determine the distance at which the alpha particle will turn around. At this point, the kinetic energy of the particle is completely converted into potential energy due to the repulsive electrostatic force between the alpha particle and the gold nucleus.
We can equate the initial kinetic energy to the potential energy at this point: KE = PE. The potential energy (PE) is given by the formula PE = k(q1 * q2) / r, where k is the electrostatic constant (8.99 * 10^9 Nm^2/C^2), q1 and q2 are the charges of the alpha particle and gold nucleus respectively, and r is the distance between them.
Plugging in the values, we get (1/2)(6.64 * 10^-27 kg)(1.6 * 10^7 m/s)^2 = (8.99 * 10^9 Nm^2/C^2)(2e)(79e) / r.

3. We can now solve for r, the distance at which the alpha particle will turn around. Rearranging the equation and solving for r, we get r = (8.99 * 10^9 Nm^2/C^2)(2e)(79e) / [(1/2)(6.64 * 10^-27 kg)(1.6 * 10^7 m/s)^2].

4. Plugging in the values and evaluating the equation, we find r ≈ 0.162 nanometers.

Therefore, the alpha particle will get approximately 0.162 nanometers close to the gold nucleus before turning around.

4.226m