Use the nuclide notation _Z^A X

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:

1. _Z – atomic number (protons).
2. ^A – mass number (protons + neutrons).
3. 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:

  1. Measure background for a set time (e.g., 5 min).
  2. Measure sample for the same time.
  3. Net activity = sample count – background count.

5.2.2 Radioactive Decay Types

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: \(N = N0 \left(\frac{1}{2}\right)^{t/t{½}}\) 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)

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

1. 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).

2. Number of neutrons in \$_{92}^{238}\text{U}\$:
   

   \(N = 238 - 92 = 146\) neutrons.

3. Identify element, Z and A for \$_{8}^{15}\text{O}\$:
   

   Element = oxygen (O), Z = 8, A = 15.

4. 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.

5. 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.

6. Balanced α‑decay equation for \$_{84}^{210}\text{Po}\$:
   

   \[

   \,^{210}{84}\text{Po} \;\rightarrow\; \,^{206}{82}\text{Pb} + \,^{4}_{2}\text{He}

   \]

7. 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.

8. 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

1. Write the nuclide notation for an atom that contains 12 protons and 13 neutrons.
2. How many neutrons are present in \$_{92}^{238}\text{U}\$?
3. Identify the element, its atomic number and mass number for the nuclide \$_{8}^{15}\text{O}\$.
4. Two isotopes of iodine are \${53}^{127}\text{I}\$ (stable) and \${53}^{131}\text{I}\$ (radioactive). What is the difference in their neutron numbers?
5. Explain why isotopes of the same element have almost identical chemical properties.
6. Write the balanced nuclear equation for the α‑decay of \$_{84}^{210}\text{Po}\$.
7. State one practical use of each of the following: (a) α‑radiation, (b) β⁻‑radiation, (c) γ‑radiation.
8. 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.)
9. Given a decay‑curve graph (placeholder), determine the half‑life of the sample.
10. 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.