OCR Specification focus:
‘Describe mass defect and binding energy; interpret binding energy per nucleon.’
Mass defect and binding energy explain why nuclei have lower mass than their constituent nucleons and reveal how nuclear stability arises from the strong nuclear force.
Understanding Nuclear Mass and Structure
The idea of missing mass
When examining a nucleus, students quickly observe that the total mass of its protons and neutrons when separated is greater than the actual mass of the bound nucleus. This difference is central to the OCR requirement for understanding mass defect and binding energy, and forms the foundation for interpreting binding energy per nucleon as a measure of nuclear stability.
Mass Defect: The difference between the total mass of the separate nucleons and the actual mass of the nucleus once formed.
A nucleus with a larger mass defect has released more energy during its formation, indicating a greater degree of binding and therefore increased stability. This link between mass and energy comes directly from the relativistic connection between mass and energy.
Energy release and nuclear stability
Whenever nucleons combine to form a nucleus, they must lose energy in order to become bound. The strong nuclear force is extremely powerful at short ranges, creating a highly stable configuration that requires energy to overcome or reverse. This lost energy is referred to as the binding energy, and it accounts for the missing mass.
The diagram contrasts a bound nucleus with separated nucleons, illustrating that the bound system has a lower total mass. The difference corresponds to the binding energy required to split the nucleus. This visually reinforces the relationship between mass defect and binding energy. Source.
Binding Energy: The energy released when a nucleus forms from free nucleons, or equivalently, the energy required to completely separate a nucleus into individual nucleons.
This concept is essential for understanding nuclear reactions, as differences in binding energy govern whether processes such as fission or fusion release or absorb energy.
Mass–energy equivalence
The mass–energy equivalence relationship provides the quantitative link between mass defect and binding energy.
EQUATION
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Mass–Energy Equivalence (E) = Δm c²
E = Energy released or absorbed (joules)
Δm = Mass defect (kilograms)
c = Speed of light in vacuum (metres per second)
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This equation emphasises that even a very small mass defect corresponds to a significant amount of energy because the speed of light squared is an extremely large number. It is the mathematical bridge that allows nuclear physicists to calculate the energy changes that occur during nuclear transformations.
A nucleus with a larger binding energy is generally more stable, explaining why nuclei with moderate atomic mass — particularly near iron — tend to be the most strongly bound.
Binding Energy Per Nucleon
Why divide by nucleon number?
While total binding energy is useful, comparing nuclei of different sizes requires a quantity that reflects how tightly each individual nucleon is held. This motivates the definition of binding energy per nucleon, which provides insight into nuclear stability across the periodic table.
Binding Energy per Nucleon: The total binding energy of a nucleus divided by the number of nucleons it contains.
This ratio highlights differences in stability between isotopes and shows characteristic trends across the range of nuclear masses.
A nucleus with a higher binding energy per nucleon is typically more stable. This measure is especially helpful when examining why certain nuclei undergo radioactive decay: less tightly bound nuclei tend to transform into more stable configurations that maximise binding energy per nucleon.
Key features of binding energy per nucleon
Students should recognise the following points when interpreting this important quantity:
Light nuclei generally have lower binding energy per nucleon because the strong force has not yet reached its most effective range across multiple nucleons.
Intermediate-mass nuclei reach maximum stability. Iron-56 is often cited as having one of the highest binding energies per nucleon, illustrating peak nuclear stability.
Very heavy nuclei show a decreasing trend, as repulsive electrostatic forces between many protons reduce overall stability.
These trends underpin why fusion releases energy for light nuclei and fission releases energy for heavy nuclei: both processes move nuclei towards configurations with higher binding energy per nucleon.
This graph plots binding energy per nucleon across different mass numbers, peaking near iron where nuclei are most stable. The curve explains why fusion of light nuclei and fission of heavy nuclei are both energetically favourable. The diagram presents only the essential trends relevant to A-Level study. Source.
Processes and Interpretation
How mass defect and binding energy link to nuclear reactions
Both fusion and fission can be understood through changes in mass defect and binding energy.
Fusion increases binding energy per nucleon by combining light nuclei into a more stable arrangement.
Fission increases binding energy per nucleon by splitting very heavy nuclei into more stable medium-mass nuclei.
Energy released in either case corresponds to the difference in binding energies, directly connected to changes in mass defect.
Although these processes belong to wider nuclear physics topics, understanding mass defect and binding energy is essential for analysing how and why nuclear reactions yield such large amounts of energy.
Why the strong nuclear force matters
The strong nuclear force is responsible for the binding of protons and neutrons, and therefore indirectly determines both mass defect and binding energy. Its short-range strength explains why nucleons are so tightly bound and why significant energy must be supplied to overcome it. Without this force, nuclei would not exist and binding energy would be zero.
Because of its dominance at nuclear scales, the strong force shapes all trends in binding energy per nucleon and is the physical origin of nuclear stability.
Interpreting binding energy per nucleon in real nuclei
Using the concepts above, students can interpret nuclear stability patterns:
Nuclei with high binding energy per nucleon are typically stable and resistant to decay.
Nuclei with low values may undergo alpha, beta, or other decay modes to reach a more favourable configuration.
Observing the relative heights of binding energy per nucleon values is enough to determine whether a reaction should release or absorb energy.
Understanding these relationships completes the OCR requirement for describing mass defect and binding energy and interpreting binding energy per nucleon.
FAQ
Mass defect does tend to increase with nucleon number, but at a diminishing rate. This is because the strong nuclear force is short-range, so adding extra nucleons does not allow each nucleon to form strong additional bonds with all others.
In very heavy nuclei, repulsive electrostatic forces between protons weaken the overall binding effect, meaning the mass defect does not continue increasing proportionally with nucleon number.
A nucleus can be modelled as a deep potential well created by the strong nuclear force. Binding energy represents how far “below” the zero-energy baseline the nucleons sit within this well.
A larger binding energy corresponds to a deeper well, meaning the nucleons require more energy to escape. This visualisation helps explain why stable nuclei resist fission or decay.
Iron-56 lies at the peak of the binding energy per nucleon curve, meaning each nucleon contributes to an exceptionally tight configuration.
Its nucleon arrangement results in an optimal balance between strong-force attraction and proton-proton repulsion.
This is why many nuclear processes tend to move nuclei toward iron-like stability.
Not exactly. Binding energy refers to the energy associated with forming or breaking a specific nucleus, while nuclear reaction energy depends on the difference in total binding energy between reactants and products.
In any nuclear reaction:
• If product nuclei have greater total binding energy, energy is released.
• If they have lower total binding energy, energy must be supplied.
Yes, but only indirectly. High-precision mass spectrometry allows scientists to measure atomic and nuclear masses to many decimal places.
By comparing the measured mass of a nucleus to the combined measured masses of free protons and neutrons, the mass defect can be inferred.
The difference is extremely small but detectable due to the sensitivity of modern equipment.
Practice Questions
Question 1 (2 marks)
Explain what is meant by the term mass defect and state how it is related to the binding energy of a nucleus.
Mark scheme:
• Mass defect is the difference between the total mass of the separate nucleons and the actual mass of the nucleus. (1)
• The missing mass corresponds to the binding energy released when the nucleus is formed, through the relationship E = delta m c squared. (1)
Question 2 (5 marks)
Figure 1 shows a simplified binding energy per nucleon curve (not to scale).
Using the ideas of mass defect and binding energy per nucleon, explain why:
(a) energy is released when two light nuclei undergo fusion, and
(b) energy is released when a very heavy nucleus undergoes fission.
In your answer, refer to changes in nuclear stability and energy considerations.
Mark scheme:
• Binding energy per nucleon indicates how tightly bound a nucleus is. (1)
• Light nuclei have relatively low binding energy per nucleon; fusing them produces a nucleus with a higher binding energy per nucleon. (1)
• The increase in binding energy per nucleon corresponds to an increase in mass defect and therefore an energy release. (1)
• Very heavy nuclei have lower binding energy per nucleon; splitting them produces medium-mass nuclei with higher binding energy per nucleon. (1)
• The increase in total binding energy of the products compared with the original nucleus means energy is released in the fission process. (1)
