23.1.3Quantum and nuclear physics (A Level)
Mass Defect and Binding Energy
5 min read 11 parts Lesson 16 of 23 1 quiz
Lesson summary
23.1.3 Mass Defect and Binding Energy — AS PHYSICS 9702 notes: Define mass defect, binding energy and binding energy per nucleon and interpret the binding energy per nucleon curve.Mass defect = the difference between the mass of a nucleus and the sum of the individual masses of i…
- Calculation
- Bound system
- Atomic masses
- Not stored energy
- Mass defect usage
- Nuclear reactions
Section 1 of 11Mass defect
Mass defect
Mass defect
Mass defect the difference between the mass of a nucleus and the sum of the individual masses of its protons and neutrons.
Calculation
- Δm = Zmp + (A − Z)mn − mnucleus.
- Z is the proton number, A the nucleon number, and mp, mn the proton and neutron masses.
Bound system
- A system of separated nucleons has more mass than the same nucleons bound together.
Atomic masses
- Tables often give the mass of the whole atom including electrons.
- Subtract the electron masses, or use hydrogen atom masses instead of proton masses so electrons cancel.
Section 2 of 11Binding energy
Binding energy
Binding energy the energy required to break a nucleus into its constituent protons and neutrons,
- which is the minimum energy to separate the nucleons completely.
Equation
- EB = Δmc2.
Formation
- Forming a nucleus from free nucleons releases energy, so it is exothermic.
Unit
- Binding energies are measured in MeV, and 1 u of mass defect corresponds to 931.5 MeV.
Not stored energy
- It is the energy that must be put in to separate all the nucleons, not energy stored in the nucleus.
Mass defect usage
- Use the term only when all the nucleons are separated, not for the mass decrease in radioactive decay.
Section 3 of 11Nuclear and chemical energy
Nuclear reactions
- They involve changes in nuclear binding energy, which is in MeV.
Chemical reactions
- They involve changes in electron binding energy, which is a few eV.
Result
- This is why nuclear reactions release far more energy than chemical reactions.
Section 4 of 11Binding energy per nucleon
Definition
- The binding energy of a nucleus divided by the number of nucleons in it, EB/A.
Stability
- A higher binding energy per nucleon means a more stable nucleus.
Comparison
- Always compare per nucleon, since higher total binding energy does not by itself mean greater stability.
Section 5 of 11Binding energy per nucleon curve
Shape
- A graph of binding energy per nucleon (MeV) against nucleon number A.
Light nuclei
- The curve rises steeply, with hydrogen-2 about 1.1 MeV per nucleon.
- Helium-4 is unusually high at about 7.1 MeV, showing it is particularly stable.
- Carbon-12 and oxygen-16 can be considered as three and four helium nuclei bound together.
Peak
- The broad maximum is about 8.8 MeV per nucleon near A = 56, close to iron-56.
- Iron-56 is the most stable nucleus (nickel-62 is marginally higher).
Heavy nuclei
- The curve falls slowly to about 7.6 MeV per nucleon for uranium-238.
Section 6 of 11Drawing the curve
Start
- Do not start the curve at A = 0, because a single nucleon is not a nucleus.
Anomaly
- Mark helium as a cross above the best-fit curve.
Labels
- Label both axes with units and give numbers, especially at the peak for iron-56.
Section 7 of 11Significance of the curve
Low A
- Attractive nuclear forces dominate repulsion between protons, so nuclei can undergo fusion.
- The gradient is steep, so fusion releases more energy per nucleon than fission.
High A
- Repulsive electrostatic forces between protons begin to dominate, so nuclei can undergo fission.
- The gradient is gentler, so fission releases less energy per nucleon than fusion.
Neutron excess
- Heavier stable nuclei need more neutrons than protons,
- because the electrostatic repulsion has long range but the strong force acts only between near neighbours.
Unstable ratios
- Nuclei with a very high or very low neutron-to-proton ratio decay by beta emission towards the stable region.
Section 8 of 11Calculation method
1
Write the number of protons Z and neutrons A − Z.
2
Find the total mass of the separate nucleons.
3
Subtract the nuclear mass to get Δm.
4
Convert to energy using c2 or 931.5 MeV per u.
5
Divide by A for the binding energy per nucleon.
- Precision
- Keep several significant figures in the subtraction, since Δm is a small difference of two large numbers.
Section 9 of 11More from the specification
More from the specification
Mass-energy equivalence and mass defect
- Mass and energy are equivalent via Einstein's equation delta E = delta m * c2;
- the total mass of separated nucleons always exceeds the mass of the bound nucleus.
Nuclear binding energy per nucleon curve
- Binding energy per nucleon rises steeply from hydrogen to a maximum of ~8.8 MeV per nucleon near iron-56, decreasing gradually for heavier actinides.
Energy release in fission and fusion
- Nuclear fusion of light nuclides or fission of heavy uranium-235 produces daughter nuclei with higher binding energy per nucleon, converting mass defect into kinetic energy.
Daughter nuclei
- The smaller nuclei produced in fission.
Mass-energy equivalence
- The principle that mass and energy are interchangeable, E = mc2.
Section 10 of 11Key terms
| Term | Meaning |
|---|---|
| Mass defect | The difference between the mass of a nucleus and the sum of the individual masses of its protons and neutrons. |
| Binding energy | The energy required to break a nucleus into its constituent protons and neutrons. |
| Binding energy per nucleon | The binding energy of a nucleus divided by the number of nucleons in it. |
| Nucleon | A proton or neutron in a nucleus. |
| Strong nuclear force | The short-range attractive force that binds nucleons together in a nucleus. |
Section 11 of 11Exam technique
1
Using atomic mass as nuclear mass without allowing for electrons — subtract the electron masses or use hydrogen atom masses.
2
Saying binding energy is stored in the nucleus — it is the energy needed to break the nucleus apart.
3
Thinking higher total binding energy always means more stable — compare binding energy per nucleon.
4
Placing the peak of the curve at uranium — the peak is near iron-56.
5
Forgetting the neutron count A − Z when adding the separated nucleons — include all the neutrons.