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 middle point of a radius.

Step-by-step solution

Given Z = 79 , the total charge of the nucleus is Q = Ze = 79 1.6 10⁻¹⁹ C . The radius of the nucleus is R = 7.0 10⁻¹⁵ m . The electric field inside a uniformly charged solid sphere at a distance r from the center is given by: E = 1 4 ₀ Q r R^3 At the middle point of a radius, r = R 2 . Substituting this into the formula gives: E = 1 4 ₀ Q ( R 2 ) R^3 = 1 4 ₀ Q 2 R^2 Substituting the known values: E = 9 10^9 79 1.6 10⁻¹⁹ 2 (7.0 10⁻¹⁵)^2 E = 9 126.4 10⁻¹⁰ 2 49.0 10⁻³⁰ E = 1137.6 10⁻¹⁰ 98.0 10⁻³⁰ E = 11.608 10²⁰ N C