When calculating the nuclear binding energy of an atom, which quantity must be determined first?

• A. The atomic number of the element
• B. The number of valence electrons
• C. The ionization energy of the atom
• D. The mass defect of the nucleus

Answer: (D)

Verified step by step guidance

1. Understand that the nuclear binding energy is the energy required to disassemble a nucleus into its individual protons and neutrons.
2. Recognize that to calculate the nuclear binding energy, you first need to find the mass defect, which is the difference between the total mass of the individual nucleons and the actual mass of the nucleus.
3. Calculate the mass defect by subtracting the measured mass of the nucleus from the sum of the masses of the free protons and neutrons that make up the nucleus.
4. Use the mass defect to find the binding energy by applying Einstein's mass-energy equivalence formula: \(E = \Delta m \times c^{2}\), where \(\Delta m\) is the mass defect and \(c\) is the speed of light.
5. Note that quantities like atomic number, valence electrons, or ionization energy are not directly used in calculating the nuclear binding energy, but the mass defect is essential.