The most stable nucleus in terms of binding energy per nucleon is ⁵⁶Fe. If the atomic mass of ⁵⁶Fe is 55.9349 amu, calculate the binding energy per nucleon for ⁵⁶Fe in Joules. The mass of a hydrogen atom is 1.0078 amu, and the mass of a neutron is 1.0087 amu. Which of the following is the correct binding energy per nucleon for ⁵⁶Fe?

• A. 1.30 x 10^-12 J
• B. 1.42 x 10^-12 J
• C. 1.15 x 10^-12 J
• D. 1.75 x 10^-12 J

Answer: (B)

Verified step by step guidance

1. Calculate the total mass of the protons and neutrons in the nucleus of ⁵⁶Fe. Since ⁵⁶Fe has 26 protons, the mass of the protons is 26 times the mass of a hydrogen atom (1.0078 amu). The number of neutrons is 56 - 26 = 30, so the mass of the neutrons is 30 times the mass of a neutron (1.0087 amu).
2. Add the masses of the protons and neutrons to find the total mass of the nucleons: \( \text{Total mass of nucleons} = 26 \times 1.0078 + 30 \times 1.0087 \) amu.
3. Calculate the mass defect by subtracting the actual atomic mass of ⁵⁶Fe from the total mass of the nucleons: \( \text{Mass defect} = \text{Total mass of nucleons} - 55.9349 \) amu.
4. Convert the mass defect from atomic mass units to kilograms using the conversion factor \( 1 \text{ amu} = 1.660539 \times 10^{-27} \text{ kg} \).
5. Use Einstein's equation \( E = mc^2 \) to calculate the total binding energy, where \( m \) is the mass defect in kilograms and \( c \) is the speed of light \( 3.00 \times 10^8 \text{ m/s} \). Then, divide the total binding energy by the number of nucleons (56) to find the binding energy per nucleon in Joules.