In one of the classic nuclear physics experiments at the beginning of the 20th century, an alpha particle was accelerated towards a gold nucleus and its path was substantially deflected by the Coulomb interaction. If the initial kinetic energy of the doubly charged alpha nucleus was 5.28 MeV, how close to the gold nucleus (79 protons) could it come before being turned around

= 4.3 * 10 ⁻¹⁴ m

Explanation:

The alpha particle will be deflected when its kinetic energy is equal to the potential energy

Charge of the alpha particle q₁ = 2 * 1.6 * 10⁻¹⁹ C = 3.2 * 10⁻¹⁹ C

Charge of the gold nucleus q₂ = 79 * 1.6 * 10⁻¹⁹ = 1.264 * 10⁻¹⁷C

Kinetic energy of the alpha particle = 5.28 * 10⁶ * 1.602 * 10⁻¹⁹ J (1 eV)

= 8.459 * 10⁻¹³

k electrostatic force constant = 9 * 10⁹ N. m²/c²

Kinetic energy = potential energy = k q₁q₂ / r where r is the closest distance the alpha particle got to the gold nucleus

r = (9 * 10⁹ N. m²/c² * 3.2 * 10⁻¹⁹ C * 1.264 * 10⁻¹⁷C) / 8.459 * 10⁻¹³

= 4.3 * 10 ⁻¹⁴ m