A gold nucleus ( Z = 79 ) has a radius of approximately 7.0 10⁻¹⁵ m . Assuming its positive charge is uniformly distributed throughout the nuclear volume, determine the strength of the electric field at the surface of the nucleus.

Step-by-step solution

The charge of the gold nucleus is given by q = Ze , where Z = 79 and e = 1.6 10⁻¹⁹ C . q = 79 1.6 10⁻¹⁹ C The electric field at the surface of a uniformly charged sphere of radius R is given by: E = 1 4 ₀ q R^2 Substituting the given values: E = 9 10^9 79 1.6 10⁻¹⁹ (7.0 10⁻¹⁵)^2 E = 1137.6 10⁻¹⁰ 49 10⁻³⁰ E = 23.216 10²⁰ N C ⁻¹ E 2.32 10²¹ N C ⁻¹