The nuclear binding energy for a ⁵⁹Fe nucleus is approximately 4.32×10^−11J.
The nuclear binding energy represents the energy required to disassemble a nucleus into its individual protons and neutrons. It is calculated by determining the mass defect, which is the difference between the actual mass of the nucleus and the sum of the masses of its individual protons and neutrons. Using Einstein's mass-energy equivalence principle (E=mc²), where E is energy, m is mass, and c is the speed of light, the mass defect is then multiplied by the speed of light squared to obtain the binding energy.
For a ⁵⁹Fe nucleus, the mass defect (Δm) is given by the difference between the actual mass of the nucleus and the sum of the masses of its protons and neutrons. The masses of a proton and neutron are provided as 1.673×10^−24g and 1.675×10^−24g, respectively. Multiplying the respective masses by the number of protons and neutrons in a ⁵⁹Fe nucleus (26 protons and 33 neutrons), we get the total mass of the individual particles.
Subtracting the total mass of the individual particles from the actual mass of the ⁵⁹Fe nucleus yields the mass defect. Multiplying the mass defect by c^2 gives the binding energy. The calculated nuclear binding energy for a ⁵⁹Fe nucleus is approximately 4.32×10^−11J, indicating the energy released when the nucleus is formed from its constituent particles.