Calculate the mass defect (in g/mol) and the binding energy (in MeV/nucleon) for the following nuclei. Which of the two is more stable? (a) 50Cr (atomic mass = 49.94605)(b) 64Zn (atomic mass = 63.92915)

Verified step by step guidance

1. Identify the number of protons and neutrons in each nucleus. For 50Cr, it has 24 protons and 26 neutrons. For 64Zn, it has 30 protons and 34 neutrons.
2. Calculate the mass of the protons and neutrons separately. Use the mass of a proton (1.00728 u) and the mass of a neutron (1.00866 u).
3. Calculate the total mass of the nucleons for each nucleus by adding the mass of the protons and the mass of the neutrons.
4. Determine the mass defect for each nucleus by subtracting the actual atomic mass from the calculated total mass of the nucleons.
5. Convert the mass defect from atomic mass units (u) to energy using Einstein's equation, E=mc^2, and then to MeV/nucleon. Compare the binding energy per nucleon to determine which nucleus is more stable.

Key Concepts

Mass Defect

Mass defect refers to the difference between the mass of an atomic nucleus and the sum of the masses of its individual protons and neutrons. This discrepancy arises because some mass is converted into binding energy, which holds the nucleus together. The mass defect is crucial for calculating the binding energy and understanding nuclear stability.

Binding Energy

Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It can be calculated using the mass defect and Einstein's equation, E=mc². A higher binding energy per nucleon indicates a more stable nucleus, as it implies that more energy is needed to break the nucleus apart.

Stability of Nuclei

The stability of a nucleus is determined by its binding energy and the ratio of neutrons to protons. Nuclei with higher binding energy per nucleon are generally more stable, as they are less likely to undergo radioactive decay. Comparing the binding energies of different nuclei allows us to assess their relative stability and predict their behavior in nuclear reactions.