5.1 The Atom and the Nucleus
Learning Objectives
- Describe the structure of an atom (nucleus, electrons, ion formation).
- Write and interpret nuclide notation
$_Z^{A}\text{X}$.
- Identify the atomic number (Z), mass number (A) and number of neutrons (N) for any nuclide.
- Explain isotopes, stable isotopes and radioactive isotopes.
- Understand how radioactivity is detected, measured and protected against.
- Calculate half‑lives, decay‑curves and nuclear‑reaction energies.
- Describe the two main nuclear reactions (fission and fusion) and the three common types of radioactive decay (α, β, γ).
5.1.1 The Atom
- Nucleus – contains protons (p⁺) and neutrons (n⁰). The total positive charge is +Ze where Z is the atomic number.
- Electron cloud – electrons (e⁻) occupy shells around the nucleus. The number of electrons equals the number of protons in a neutral atom.
- Ion formation – loss of electrons → positive ion (cation); gain of electrons → negative ion (anion). The charge on an ion is the difference between the numbers of protons and electrons.
5.1.2 The Nucleus
- Protons: positively charged, determine the element (Z).
- Neutrons: neutral, together with protons give the total number of nucleons.
- Net charge of the nucleus = +Ze.
Atomic Number, Mass Number and Neutrons
\[
Z = \text{number of protons}
\qquad
A = \text{mass number} = Z + N
\qquad
N = A - Z
\]
Nuclide Notation $_Z^{A}\text{X}$
Read from left to right:
- Z – atomic number (protons).
- A – mass number (protons + neutrons).
- X – chemical symbol of the element.
Example: $_6^{12}\text{C}$ means 6 protons, 12 – 6 = 6 neutrons.
5.2 Radioactivity
5.2.1 Detection of Radioactivity
- Geiger–Müller (GM) counter – detects ionising particles; gives counts per minute (cpm) or counts per second (cps).
- Scintillation detector – uses a phosphor that flashes when struck by radiation; often coupled to a photomultiplier.
- Background radiation – natural radiation that must be measured and subtracted from experimental counts.
- Typical procedure:
- Measure background for a set time (e.g., 5 min).
- Measure sample for the same time.
- Net activity = sample count – background count.
5.2.2 Radioactive Decay Types
| Decay |
Particle emitted |
Change in nucleus |
Penetration |
Ionisation |
| α (alpha) |
Helium‑2 nucleus, $_2^{4}\text{He}$ (2p + 2n) |
A − 4, Z − 2 |
Low – stopped by a sheet of paper |
High – heavy, doubly charged |
| β⁻ (beta minus) |
Electron, e⁻ |
n → p + e⁻ + \(\baru\); A unchanged, Z + 1 |
Medium – stopped by a few mm of aluminium |
Moderate |
| β⁺ (beta plus, positron) |
Positron, e⁺ |
p → n + e⁺ + ν; A unchanged, Z − 1 |
Medium |
Moderate |
| γ (gamma) |
High‑energy photon |
No change in A or Z (usually follows α or β decay) |
High – requires several cm of lead |
Low |
5.2.3 Half‑Life and Decay Curves
- Half‑life (t½) – the time required for half of a given number of radioactive nuclei to decay.
- Mathematical form: \(N = N_0 \left(\frac{1}{2}\right)^{t/t_{½}}\) where \(N_0\) is the initial number of nuclei.
- Activity \(A = \lambda N\) where \(\lambda = \frac{\ln 2}{t_{½}}\) is the decay constant.
Example calculation: A sample of $_6^{14}\text{C} (t½ = 5 730 y) contains \(1.0\times10^{12}\) nuclei. After 11 460 y the remaining nuclei are:
\[
N = 1.0\times10^{12}\left(\frac{1}{2}\right)^{11\,460/5\,730}=2.5\times10^{11}
\]
A typical decay‑curve graph (placeholder) should show a smooth exponential decline; the point where the curve reaches half the initial activity marks the half‑life.
5.2.4 Safety Precautions (ALARA)
- Time – minimise exposure time.
- Distance – increase distance from the source (inverse‑square law).
- Shielding – use appropriate material: paper for α, aluminium for β, lead or concrete for γ.
- ALARA principle – keep radiation “As Low As Reasonably Achievable”.
5.3 Isotopes
- Atoms of the same element (Z identical) but with different mass numbers (A) are isotopes.
- Isotopes may be stable (no decay) or radioactive (spontaneous transformation).
Isotope Table (selected examples)
| Element |
Nuclide |
Protons (Z) |
Neutrons (N) |
Mass number (A) |
Stability |
| Carbon |
$_6^{12}\text{C}$ |
6 |
6 |
12 |
Stable |
| Carbon |
$_6^{13}\text{C}$ |
6 |
7 |
13 |
Stable |
| Carbon |
$_6^{14}\text{C}$ |
6 |
8 |
14 |
Radioactive (β⁻, t½ = 5 730 y) |
| Uranium |
$_{92}^{235}\text{U}$ |
92 |
143 |
235 |
Radioactive (fissionable) |
5.4 Nuclear Reactions
5.4.1 Fission
- Heavy nucleus splits into two (or more) lighter nuclei, releasing several neutrons and ≈200 MeV of energy per fission.
- Typical reactor equation (U‑235 fission):
\[
\,^{235}_{92}\text{U} + \,^{1}_{0}n \;\rightarrow\; \,^{94}_{36}\text{Kr} + \,^{141}_{56}\text{Ba} + 3\,^{1}_{0}n + \approx 200\;\text{MeV}
\]
- Chain reaction: the neutrons emitted can cause further fissions.
- Energy calculation (example):
Mass of reactants = 235.0439 u + 1.0087 u = 236.0526 u
Mass of products = 93.9344 u + 140.9144 u + 3 × 1.0087 u = 236.0 u (≈0.0526 u loss)
Energy released = Δm c² = 0.0526 u × 931.5 MeV u⁻¹ ≈ 49 MeV (illustrative; actual fission releases ≈200 MeV due to kinetic energy of fragments).
5.4.2 Fusion
- Two light nuclei combine to form a heavier nucleus, releasing energy because the binding energy per nucleon of the product is larger.
- Deuterium‑tritium reaction (the Sun’s primary fusion process):
\[
\,^{2}_{1}\text{H} + \,^{3}_{1}\text{H} \;\rightarrow\; \,^{4}_{2}\text{He} + \,^{1}_{0}n + \approx 17\;\text{MeV}
\]
- Requires temperatures >10⁷ K to overcome Coulomb repulsion.
- Energy example (mass defect):
\[
\Delta m = (2.0141 + 3.0160) - (4.0026 + 1.0087) = 0.0188\;\text{u}
\]
\[
E = 0.0188\;\text{u}\times 931.5\;\text{MeV u}^{-1} \approx 17.5\;\text{MeV}
\]
5.5 Example Calculations
- Write the nuclide notation for an atom with 12 protons and 13 neutrons.
\(Z = 12,\; N = 13,\; A = Z+N = 25\)
$_{12}^{25}\text{Mg}$ (magnesium‑25).
- Number of neutrons in
$_{92}^{238}\text{U}$:
\(N = 238 - 92 = 146\) neutrons.
- Identify element, Z and A for
$_{8}^{15}\text{O}$:
Element = oxygen (O), Z = 8, A = 15.
- Neutron difference between chlorine isotopes
$_{17}^{35}\text{Cl}$ and $_{17}^{37}\text{Cl}$:
N₁ = 35 − 17 = 18, N₂ = 37 − 17 = 20 → difference = 2 neutrons.
- Why isotopes of the same element have almost identical chemical properties:
Chemical behaviour depends on electron configuration, which is determined by the number of protons (Z). Neutrons do not affect the electron cloud, so isotopes share the same chemistry.
- Balanced α‑decay equation for
$_{84}^{210}\text{Po}$:
\[
\,^{210}_{84}\text{Po} \;\rightarrow\; \,^{206}_{82}\text{Pb} + \,^{4}_{2}\text{He}
\]
- Practical uses:
- α‑radiation – smoke detectors (americium‑241 source).
- β⁻‑radiation – medical imaging (PET scanners use β⁺, but β⁻ is used in radiotherapy for cancer).
- γ‑radiation – sterilisation of medical equipment and food; also used in radiography.
- Why fusion releases more energy per nucleon than fission:
The binding energy per nucleon curve peaks around iron (A ≈ 56). Light nuclei (A < 56) gain binding energy when they combine (fusion), while heavy nuclei (A > 56) gain binding energy when they split (fission). The increase in binding energy per nucleon is larger for fusion of very light nuclei than for fission of very heavy nuclei, giving a greater energy release per nucleon.
5.6 Practice Questions
- Write the nuclide notation for an atom that contains 12 protons and 13 neutrons.
- How many neutrons are present in
$_{92}^{238}\text{U}$?
- Identify the element, its atomic number and mass number for the nuclide
$_{8}^{15}\text{O}$.
- Two isotopes of iodine are
$_{53}^{127}\text{I}$ (stable) and $_{53}^{131}\text{I}$ (radioactive). What is the difference in their neutron numbers?
- Explain why isotopes of the same element have almost identical chemical properties.
- Write the balanced nuclear equation for the α‑decay of
$_{84}^{210}\text{Po}$.
- State one practical use of each of the following: (a) α‑radiation, (b) β⁻‑radiation, (c) γ‑radiation.
- Calculate the energy released when
$_{2}^{4}\text{He}$ (α‑particle) is emitted from $_{92}^{238}\text{U}$ to form $_{90}^{234}\text{Th}$. (Atomic masses: U‑238 = 238.0508 u, Th‑234 = 234.0436 u, He‑4 = 4.0026 u.)
- Given a decay‑curve graph (placeholder), determine the half‑life of the sample.
- Describe three safety measures you would adopt when working with a strong γ‑source.
5.7 Suggested Diagrams
- Hand‑drawn or computer‑generated schematic of a nucleus showing protons, neutrons, and labelled Z, N and A.
- Decay‑curve graph (activity vs. time) with the half‑life point marked.
- Energy‑level diagram illustrating the mass‑defect calculation for a fission or fusion reaction.
- Illustration of shielding: paper for α, aluminium for β, lead for γ.