State that during α-decay or β-decay, the nucleus changes to that of a different element

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5.2.3 Radioactive Decay

Learning Objective (AO1)

State that during α‑decay or β‑decay** the atomic number $Z$ of the nucleus changes, so the daughter nucleus is a different chemical element.

Key Point

An element is defined solely by its atomic number $Z$ (the number of protons). Any change in $Z$ therefore means a change of element, irrespective of the mass number $A$.

Cambridge IGCSE Syllabus Requirement (Core)

“Radioactive decay is a change in an unstable nucleus that can result in the emission of α‑particles or β‑particles and/or γ‑radiation; the change is spontaneous and random**.”

Both statements are now explicitly included in the notes.

Decay Types Required by the Syllabus

  • α‑decay: emission of a helium nucleus $^{4}_{2}\text{He}$ (2 p + 2 n).
  • β⁻‑decay: a neutron converts into a proton and an electron (β⁻) is emitted. $$n \;\rightarrow\; p + ^{0}_{-1}\beta + \bar{u}_{e}$$
  • β⁺‑decay / Electron capture (grouped together in the syllabus):
    • β⁺‑decay: a proton converts into a neutron and a positron is emitted. $$p \;\rightarrow\; n + ^{0}_{+1}\beta^{+} + u_{e}$$
    • Electron capture: an inner‑shell electron is captured by a proton, producing a neutron and a neutrino. $$p + e^{-} \;\rightarrow\; n + u_{e}$$
    Both processes reduce $Z$ by 1.

Why the Element Changes – Effect on $Z$ and $A$

DecayChange in $Z$Change in $A$Daughter Nucleus
α‑decay –2 (two protons leave) –4 (two protons + two neutrons leave) $^{A-4}_{Z-2}\text{Y}$
β⁻‑decay +1 (neutron → proton) 0 (mass unchanged) $^{A}_{Z+1}\text{Y}$
β⁺‑decay / Electron capture –1 (proton → neutron) 0 (mass unchanged) $^{A}_{Z-1}\text{Y}$

Step‑by‑Step Guide to Writing a Nuclear Equation (AO2)

  1. Write the parent nuclide in nuclide notation: $^{A}_{Z}\text{X}$.
  2. Identify the decay type and add the emitted particle(s):
    • α‑decay → $^{4}_{2}\text{He}$
    • β⁻‑decay → $^{0}_{-1}\beta$ (electron) + $\bar{u}_{e}$
    • β⁺‑decay → $^{0}_{+1}\beta^{+}$ (positron) + $u_{e}$
    • Electron capture → no external particle; only $u_{e}$ appears on the right‑hand side.
  3. Balance the mass numbers ($A$) on both sides.
  4. Balance the atomic numbers ($Z$) on both sides.
  5. Include the appropriate (anti)neutrino if required.

Worked Examples (Core Syllabus)

Parent NuclideDecay TypeNuclear EquationDaughter Element
$^{238}_{92}\text{U}$ α $^{238}_{92}\text{U} \;\rightarrow\; ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$ U → Th (Z: 92 → 90)
$^{14}_{6}\text{C}$ β⁻ $^{14}_{6}\text{C} \;\rightarrow\; ^{14}_{7}\text{N} + ^{0}_{-1}\beta + \bar{u}_{e}$ C → N (Z: 6 → 7)
$^{22}_{11}\text{Na}$ β⁺ (supplementary) $^{22}_{11}\text{Na} \;\rightarrow\; ^{22}_{10}\text{Ne} + ^{0}_{+1}\beta^{+} + u_{e}$ Na → Ne (Z: 11 → 10)
$^{40}_{19}\text{K}$ β⁻ (primary, with a rare α branch) $^{40}_{19}\text{K} \;\rightarrow\; ^{40}_{20}\text{Ca} + ^{0}_{-1}\beta + \bar{u}_{e}$ K → Ca (Z: 19 → 20)

Additional Points (Beyond the Core Requirement)

  • Stability of the daughter nuclide: Decay occurs because the parent nucleus is energetically unstable. The daughter is usually closer to the band of nuclear stability on the $N$ vs. $Z$ plot.
  • Branching decay: Some isotopes can decay by more than one mode (e.g., $^{40}$K can undergo β⁻ or a very rare α‑decay). The dominant mode is the one most likely to appear in exam questions.

Cross‑Reference

For calculations involving half‑life, decay constant and activity, see Section 5.2.4 – Radioactive Decay Calculations.

Safety Note (linked to Section 5.2.5)

When working with radioactive sources, always apply the three protective principles: time** (minimise exposure), distance** (stay as far as practical), and shielding** (use appropriate material such as lead or concrete).

Quick‑Check Questions

  1. Write the nuclear equation for the α‑decay of $^{226}_{88}\text{Ra}$. Identify the daughter element.
  2. In β⁻‑decay, which particle is emitted and how does the atomic number change?
  3. Explain why $^{238}_{92}\text{U}$ and $^{234}_{90}\text{Th}$ are different elements even though they have the same mass number after the decay.
  4. (Extension) Describe electron capture and state how $Z$ changes.

Summary

Both α‑decay and β‑decay alter the atomic number $Z$ of the nucleus (by –2, +1, or –1). Because $Z$ uniquely defines an element, the daughter nucleus is always a different element from the parent. The accompanying change (or lack of change) in mass number $A$ follows the patterns shown above, enabling students to construct correct nuclear equations, locate the daughter nuclide on the periodic table, and recognise that all decays are spontaneous and random, as required by the Cambridge IGCSE syllabus.

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