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

Published by Patrick Mutisya · 14 days ago

IGCSE Physics 0625 – Radioactive Decay

5.2.3 Radioactive Decay

Learning Objective

State that during α‑decay or β‑decay the nucleus changes to that of a different element.

Key Concepts

  • The nucleus consists of protons (Z) and neutrons (N). The atomic number Z determines the element.

  • Radioactive decay is a spontaneous process that transforms an unstable nucleus into a more stable one.

  • In α‑decay a helium nucleus \$^{4}_{2}\text{He}\$ (two protons, two neutrons) is emitted.

  • In β‑decay a neutron is converted into a proton with the emission of an electron \$^{0}{-1}\beta\$ (or a positron \$^{0}{+1}\beta^{+}\$ in β⁺ decay).

Why the Element Changes

The element is identified by its atomic number \$Z\$. Any change in \$Z\$ means a different element.

  1. α‑decay: \$Z\$ decreases by 2 because the emitted α‑particle carries two protons.

    \$\$

    ^{A}{Z}\text{X} \;\rightarrow\; ^{A-4}{Z-2}\text{Y} + ^{4}_{2}\text{He}

    \$\$

    The daughter nucleus \$^{A-4}_{Z-2}\text{Y}\$ has atomic number \$Z-2\$, so it is a different element.

  2. β⁻‑decay: \$Z\$ increases by 1 because a neutron becomes a proton.

    \$\$

    ^{A}{Z}\text{X} \;\rightarrow\; ^{A}{Z+1}\text{Y} + ^{0}{-1}\beta + \bar{\nu}{e}

    \$\$

    The daughter nucleus \$^{A}_{Z+1}\text{Y}\$ has atomic number \$Z+1\$, a different element.

  3. β⁺‑decay (positron emission) or electron capture: \$Z\$ decreases by 1.

    \$\$

    ^{A}{Z}\text{X} \;\rightarrow\; ^{A}{Z-1}\text{Y} + ^{0}{+1}\beta^{+} + \nu{e}

    \$\$

    Again the element changes.

Common Examples

Parent NucleusDecay TypeDaughter NucleusChange in Element
\$^{238}_{92}\text{U}\$α\$^{234}_{90}\text{Th}\$U → Th (Z: 92 → 90)
\$^{14}_{6}\text{C}\$β⁻\$^{14}_{7}\text{N}\$C → N (Z: 6 → 7)
\$^{22}_{11}\text{Na}\$β⁺\$^{22}_{10}\text{Ne}\$Na → Ne (Z: 11 → 10)
\$^{40}_{19}\text{K}\$β⁻ (and also α rare)\$^{40}_{20}\text{Ca}\$K → Ca (Z: 19 → 20)

Implications for the Periodic Table

Because the atomic number changes, the daughter nucleus occupies a different position on the periodic table. This is why radioactive decay can be used to produce new elements or isotopes.

Suggested diagram: A schematic showing a parent nucleus emitting an α‑particle or β‑particle and the resulting daughter nucleus, with arrows indicating the change in atomic number.

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, what 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.

Summary

During both α‑decay and β‑decay the atomic number \$Z\$ of the nucleus changes (by –2, +1, or –1). Since \$Z\$ defines the chemical element, the nucleus becomes a different element after the decay.