Theme E — Nuclear and Quantum Physics
E.3.9 Mass Defect and Nuclear Binding Energy — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 26 of 45 1 quiz
Curriculum Equation Key Radioactive Decay & Half-Life FormulasFast Exam Solution
N(t) = N₀ × (1/2)t / t½ | λ = ln(2) / t½ ≈ 0.693 / t½ | E = Δm × c²
Lesson summary
E.3.9 Mass Defect and Nuclear Binding Energy — IB PHYSICS SL notes: Define mass defect and binding energy and use mass-energy equivalence to calculate them.The mass of a nucleus is less than the total mass of its separate protons and neutrons.For example, 6 free protons and 6 fre…
- Use the term mass defect only when all nucleons are separated
- Mass and energy are equivalent
- What the symbols mean
- A bound system has less mass than separated nucleons
- It is not energy stored in the nucleus
- Binding energy per nucleon
Part 1 of 7Mass defect
1
The mass of a nucleus is less than the total mass of its separate protons and neutrons.
- For example, 6 free protons and 6 free neutrons have more mass than a carbon-12 nucleus.
2Mass defect
Mass defect the difference between the sum of the masses of the separate nucleons and the measured mass of the nucleus.
3Δm
Zmp + (A − Z)mn − mnucleus
- Z is the proton number and A the nucleon number.
- mp and mn are the masses of a proton and a neutron; mnucleus is the measured nuclear mass.
4Use the term mass defect only when all nucleons are separated
- Use the term mass defect only when all nucleons are separated not for the mass lost in a radioactive decay.
Part 2 of 7Mass-energy equivalence
Mass-energy equivalence
Mass and energy are equivalent
- Mass and energy are equivalent mass can be converted into energy and energy into mass.
E
E mc2
What the symbols mean: E = energy (J) · m or Δm = mass (change) (kg) · c = 3.00 × 108 m s−1
- E is energy in J, m is mass in kg and c is the speed of light in m s-1.
Examples
- Examples fusion in the Sun, fission in reactors, nuclear weapons and high-energy collisions in accelerators.
A bound system has less mass than separated nucleons
- A bound system has less mass than separated nucleons so energy is released when a nucleus forms.
Part 3 of 7Binding energy
1Binding energy
Binding energy the energy required to separate a nucleus completely into its protons and neutrons.
- It is also the energy released when the nucleus forms from free nucleons.
2EB
Δm c2
- Δm is in kg and EB is in joules.
3It is not energy stored in the nucleus
- It is not energy stored in the nucleus it is the energy that must be put in to pull all the nucleons apart.
4Binding energy per nucleon
EB / A.
- A higher value means the nucleons are more tightly bound and the nucleus is more stable.
- Free nucleons have zero binding energy.
Part 4 of 7Atomic mass unit and conversions
1Unified atomic mass unit u
Unified atomic mass unit u exactly one twelfth of the mass of a neutral carbon-12 atom.
- 1 u = 1.661 × 10-27 kg, roughly the mass of one proton or neutron.
21 u is equivalent to 931.5 MeV c-2
- 1 u is equivalent to 931.5 MeV c-2 so EB(MeV) = Δm(u) × 931.5.
31 MeV
1.60 × 10-13 J.
4
Typical values for proton mass 1.00728 u and neutron mass 1.00866 u.
Part 5 of 7Calculating binding energy
1
Count the protons Z and neutrons N = A − Z.
2
Find Δm = Z mp + N mn − mnucleus in u.
3
Multiply Δm in u by 931.5 to get EB in MeV (or use 1.661 × 10-27 kg per u and then c2 for joules).
4
Divide by A to get the binding energy per nucleon.
1Keep enough significant figures
- Keep enough significant figures because Δm is a small difference between large numbers.
2The mass defect is below 1% of the nuclear mass
- The mass defect is below 1% of the nuclear mass so rounding the masses early ruins the result.
Part 6 of 7Atomic masses and scale of energies
1
Tables may give neutral atom masses, which include Z electrons.
- Use hydrogen-atom masses in place of proton masses: Δm = ZmH + Nmn − matom.
- The electron masses then cancel, giving the same result as the nuclear method.
2Binding energies are millions of eV per nucleon
- Binding energies are millions of eV per nucleon compared with a few eV for chemical bonds.
- A nuclear reaction therefore releases about a million times more energy per atom than a chemical one.
Part 7 of 7More from the specification
1
Nuclear binding and stellar years
- Nuclear binding and stellar years huge binding energy released per nuclear nucleon sustains core thermonuclear fusion in stars over billions of years.
2
Nuclear Mass Defect and Binding Energy
- The total mass of an assembled nucleus is always less than the sum of its individual constituent nucleons;
- this mass defect Δm is converted into nuclear binding energy according to Einstein's equation E = Δm c2.
3
Binding Energy per Nucleon Curve
- Nuclear stability peaks at iron-56;
- light nuclei release energy via nuclear fusion as binding energy per nucleon increases,
- while heavy nuclei release energy through nuclear fission.
4
Characteristics of Alpha, Beta, and Gamma Radiation
- Unstable nuclei decay by emitting alpha particles, beta particles (electrons or positrons),
- (helium-4 nuclei)
- or gamma rays (photons), governed by the strong, weak,
- and electromagnetic fundamental forces.
5
Radioactive Decay Law and Sample Activity
- The activity of a radioactive isotope sample is the rate of nuclear disintegrations (A = λ N),
- which halves after each successive half-life period.
6
Nuclear Mass Defect and Binding Energy
- The total mass of an assembled nucleus is always less than the sum of its individual constituent nucleons;
- this mass defect Δm is converted into nuclear binding energy according to Einstein's equation E = Δm c2.
7
Binding Energy per Nucleon Curve
- Nuclear stability peaks at iron-56;
- light nuclei release energy via nuclear fusion as binding energy per nucleon increases,
- while heavy nuclei release energy through nuclear fission.
8
Characteristics of Alpha, Beta, and Gamma Radiation
- Unstable nuclei decay by emitting alpha particles, beta particles (electrons or positrons),
- (helium-4 nuclei)
- or gamma rays (photons), governed by the strong, weak,
- and electromagnetic fundamental forces.
9
Radioactive Decay Law and Sample Activity
- The activity of a radioactive isotope sample is the rate of nuclear disintegrations (A = λ N),What the symbols mean: A = activity (Bq = decays per second) · λ = decay constant (s−1) · N = number of undecayed nuclei
- which halves after each successive half-life period.
10
Ionising radiation
- Radiation with enough energy to remove electrons from atoms
11
Penetrating power
- How far radiation travels through a material.
12
Nuclear notation
- Symbol showing mass number and atomic number.
13
Beta-plus decay
- Proton changes to a neutron with emission of a positron and a neutrino.
14
Decay equation
- An equation in nuclide notation with balanced nucleon and proton numbers.
15
Radiation
- Transfer by electromagnetic waves, requiring no medium
16
Half-life
- Time for half the nuclei of an isotope to decay.
17
Isotope
- Atom of the same element with a different number of neutrons.
18
Isotopes
- Nuclei with the same proton number but different neutron numbers.
19
Source
- Reservoir at TH providing heat QH
20
Background radiation
- Radiation that is always present in the environment.
21
Alpha particle
- Helium nucleus, charge +2.
22
Alpha decay
- Loss of 2 protons and 2 neutrons.
Key terms
| Term | Meaning |
|---|---|
| Mass defect | Sum of the separate nucleon masses minus the mass of the nucleus. |
| Binding energy | Energy needed to separate a nucleus into free protons and neutrons. |
| Unified atomic mass unit | One twelfth of the mass of a carbon-12 atom; 1 u = 931.5 MeV c-2. |
| Mass-energy equivalence | The relation E = mc2. |
| Binding energy per nucleon | Binding energy divided by nucleon number; a measure of stability. |
| Nucleon | A proton or a neutron in the nucleus. |
Avoid these mistakes
1
Subtracting the wrong way and getting a negative mass defect — the nucleus is lighter than its parts.
2
Forgetting to multiply by 931.5 to convert u to MeV.
3
Using binding energy as the energy of one nucleon rather than of the whole nucleus.
4
Describing binding energy as energy stored in the nucleus — it is the energy needed to separate all the nucleons.
5
Mixing atomic and nuclear masses without adjusting for electrons.
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