Assume a gold nucleus is a sphere of radius 6.9 fermi in which protons and neutrons are distributed. Determine the repulsive force between two protons located at the maximum possible separation. Why do the protons not fly apart under such repulsion?

Step-by-step solution

The maximum possible separation between two protons in the nucleus is its diameter. r = 2R = 2 6.9 fm = 13.8 10⁻¹⁵ m The electrostatic repulsive force between the protons is given by Coulomb's law: F = 1 4 ₀ q^2 r^2 Substituting the values: F = 9 10^9 (1.6 10⁻¹⁹)^2 (13.8 10⁻¹⁵)^2 F = 9 10^9 2.56 10⁻³⁸ 190.44 10⁻³⁰ F 1.2 N The protons do not fly apart because the attractive strong nuclear force between nucleons is much stronger than the electrostatic repulsion at these distances.