Building nuclei
Section: Particle Physics | Syllabus: Cambridge AS Level Physics (9702)
Nucleons and Nuclear Composition
Nucleons The particles found in the nucleus of an atom: protons and neutrons.The nucleus of an atom is composed of protons and neutrons. The table below gives the precise charge and mass of each constituent particle of the atom:
| Particle | Symbol | Charge / C | Mass / kg |
|---|---|---|---|
| Proton | p or ^1_1p | +1.60 × 10^-19 | 1.67 × 10^-27 |
| Neutron | n or ^1_0n | 0 | 1.67 × 10^-27 |
| Electron | e or ^\;\;0_-1e | -1.60 × 10^-19 | 9.11 × 10^-31 |
In exams, you will look up values such as the elementary charge (e) and rest masses from the data and formulae sheet provided at the start of the paper.
Describing Nuclear Composition
Proton Number (Z) The number of protons in the nucleus. Also called the atomic number. This determines the element. Neutron Number (N) The number of neutrons in the nucleus. Nucleon Number (A) The total number of protons and neutrons in the nucleus. Also called the mass number.These are related by:
A = Z + NNuclide Notation
The nuclear composition of any nuclide can be represented using the standard notation:
^A_Z Xwhere X is the chemical symbol of the element.
FIG 11.6: Hydrogen Atom with Nuclide NotationA simple hydrogen atom showing one proton in the nucleus and one electron orbiting, alongside its nuclide notation ¹₁H. The proton and electron are clearly labelled. This illustrates the simplest atom.
Practice: Writing Nuclide Notation| Element | Symbol | Protons (Z) | Neutrons (N) | Nuclide Notation |
|---|---|---|---|---|
| Lithium | Li | 3 | 4 | ^7_3Li |
| Iron | Fe | 26 | 30 | ^56_26Fe |
| Lead | Pb | 82 | 122 | ^204_82Pb |
| Uranium | U | 92 | 146 | ^238_92U |
Isotopes
Isotopes Nuclei of the same element with the same number of protons but different numbers of neutrons. They have the same proton number (Z) but different nucleon numbers (A).Key points about isotopes:
- Same number of protons → same chemical properties
- Different number of neutrons → different mass
- The additional neutrons do not affect the element's chemical behaviour
Three atoms side by side: (1) Protium (¹₁H): one proton, one electron, no neutrons; (2) Deuterium (²₁H): one proton, one neutron, one electron; (3) Tritium (³₁H): one proton, two neutrons, one electron. All have the same proton number but different neutron numbers.
| Isotope Name | Notation | Protons | Neutrons | Nucleons |
|---|---|---|---|---|
| Hydrogen (Protium) | ^1_1H | 1 | 0 | 1 |
| Deuterium | ^2_1H | 1 | 1 | 2 |
| Tritium | ^3_1H | 1 | 2 | 3 |
To identify isotopes, check that the proton numbers are the same but the nucleon numbers are different. If the proton numbers differ, they are different elements, not isotopes.
The Unified Atomic Mass Unit
Unified Atomic Mass Unit (u) Defined as one twelfth ((1/12)) of the mass of a carbon-12 atom. 1 u = 1.66 × 10^-27 kg (to 3 s.f.)The nucleon number of any isotope is always an integer because it counts the number of particles. The atomic mass in unified atomic mass units approximately equals the nucleon number:
| Element | Nucleon Number (A) | Atomic Mass / u |
|---|---|---|
| Hydrogen | 1 | 1.0078 |
| Helium | 4 | 4.0026 |
| Lithium | 7 | 7.0160 |
| Oxygen | 16 | 15.995 |
| Iron | 56 | 55.934 |
| Uranium | 238 | 238.05 |
The values of atomic mass and nucleon number are not identical because neutrons are slightly heavier than protons, and there is also a mass defect due to binding energy.
Conservation Laws in Nuclear Reactions
In all nuclear reactions and radioactive decays, two quantities must be conserved:
Conservation of Nucleon Number
Conservation of Nucleon Number The total number of nucleons before a nuclear reaction equals the total number of nucleons after the reaction. Σ A_before = Σ A_afterConservation of Charge
Conservation of Charge The total charge before a nuclear reaction equals the total charge after the reaction. Σ Z_before = Σ Z_after Essential Exam Statement"In all nuclear reactions, total charge and total nucleon number are conserved."
This statement should be memorised - it is frequently required in examination answers.
Nuclear Stability
Nuclear stability depends on the ratio of neutrons to protons within the nucleus. Some nuclei are stable and do not change over time. Many isotopes are unstable and undergo nuclear decay to form a different, more stable nucleus.
FIG 11.8: Nuclear Stability Band (N-Z Graph)Graph plotting neutron number (N) against proton number (Z) showing a "band of stability" where stable nuclei lie. For light nuclei, N ≈ Z (45° line). For heavier nuclei, the band curves upward (N > Z). Regions above the band: neutron-rich nuclei undergo β⁻ decay. Regions below: proton-rich nuclei undergo β⁺ decay. Heavy nuclei undergo α decay.
Key points about stability:
- For light nuclei (low Z): stable nuclei have N ≈ Z
- For heavier nuclei (high Z): stable nuclei require N > Z to provide additional strong force to overcome increased electrostatic repulsion
- Unstable nuclei undergo radioactive decay to reach a more stable configuration
At AS Level, you need only a qualitative understanding of nuclear stability. You should know that the neutron-to-proton ratio affects stability and that unstable nuclei decay to become more stable.
Applying Conservation Laws
When analysing any nuclear reaction, always verify that both conservation laws are satisfied:
Example: Verifying ConservationConsider uranium-238 decaying by alpha emission:
^238_92U arrow \;^234_90Th + \;^4_2HeCheck nucleon number: 238 = 234 + 4 ✓
Check charge: 92 = 90 + 2 ✓
Both quantities are conserved, so this is a valid nuclear equation.
Exam TipWhen asked to write or balance nuclear equations, always verify that both the top numbers (nucleon numbers) and bottom numbers (proton numbers/charges) balance on both sides.
Interactive revision notes, videos and practice questions load below.