The mass defect is the difference between the mass of a nucleus and the sum of the masses of its individual nucleons (protons and neutrons). Here's how to calculate it:
1. Understand the Concept
- The mass defect arises because energy is released when nucleons bind together to form a nucleus. This energy, known as the binding energy, is equivalent to a small amount of mass according to Einstein's mass-energy equivalence (E=mc²).
2. Identify the Given Information
You will need the following information:
- Atomic number (Z): The number of protons in the nucleus.
- Mass number (A): The total number of protons and neutrons in the nucleus.
- Mass of a proton (mp): Approximately 1.00728 atomic mass units (u) or 1.67262 × 10-27 kg.
- Mass of a neutron (mn): Approximately 1.00866 atomic mass units (u) or 1.67493 × 10-27 kg.
- Actual mass of the nucleus (mtotal): This is typically given in the problem or can be found in a data table. Make sure this is the mass of the nucleus and not the neutral atom (you may need to subtract the mass of the electrons if given the neutral atom mass). Expressed in atomic mass units (u) or kg.
3. Calculate the Total Mass of the Individual Nucleons
This is the sum of the masses of all the protons and neutrons if they were separate entities.
- Total mass of protons = Z × mp
- Total mass of neutrons = (A - Z) × mn
- Total mass of individual nucleons = (Z × mp) + ((A - Z) × mn)
4. Calculate the Mass Defect (Δm)
The mass defect is the difference between the total mass of the individual nucleons and the actual mass of the nucleus.
- Δm = (Z × mp) + ((A - Z) × mn) - mtotal
5. Units
- Ensure all masses are in the same units (either atomic mass units (u) or kilograms (kg)). If the masses are in atomic mass units (u), the mass defect will also be in atomic mass units (u). If the masses are in kilograms (kg), the mass defect will also be in kilograms (kg).
- If you need to calculate binding energy, and the mass defect is in atomic mass units (u), you can use the conversion factor 1 u = 931.5 MeV/c².
Example
Let's say we want to calculate the mass defect of Helium-4 (4He).
- Z = 2 (2 protons)
- A = 4 (4 nucleons total)
- mp = 1.00728 u
- mn = 1.00866 u
- mtotal = 4.00150 u
- Total mass of protons: 2 × 1.00728 u = 2.01456 u
- Total mass of neutrons: (4 - 2) × 1.00866 u = 2 × 1.00866 u = 2.01732 u
- Total mass of individual nucleons: 2.01456 u + 2.01732 u = 4.03188 u
- Mass defect: 4.03188 u - 4.00150 u = 0.03038 u
Summary
To calculate the mass defect, find the total mass of individual protons and neutrons, then subtract the actual mass of the nucleus. Make sure all masses are in the same units. This mass difference corresponds to the binding energy holding the nucleus together.
