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

Key Concept

During α‑decay or β‑decay, the nucleus emits a particle and changes to the nucleus of a different element (i.e. a different atomic number).

🔬 Analogy: Think of the nucleus as a crowded dance floor. When a pair of dancers (an α‑particle) leaves, the crowd’s composition changes – it’s no longer the same group of people. Similarly, when a single dancer (a β‑particle) exits, the crowd changes again.

In α‑decay a nucleus emits a helium nucleus (2 protons + 2 neutrons):

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

Example: Uranium‑238 → Thorium‑234 + α

$$^{238}_{92}\text{U} \;\rightarrow\; ^{234}_{90}\text{Th} \;+\; ^{4}_{2}\text{He}$$

In β‑decay a neutron turns into a proton (or vice‑versa), emitting an electron (β⁻) or a positron (β⁺):

$$^{A}_{Z}\text{X} \;\rightarrow\; ^{A}_{Z\pm1}\text{Y} \;+\; \beta^{\mp} \;+\; \bar{u}_e/u_e$$

Example: Carbon‑14 → Nitrogen‑14 + β⁻ + \(\bar{u}_e\)

$$^{14}_{6}\text{C} \;\rightarrow\; ^{14}_{7}\text{N} \;+\; \beta^- \;+\; \bar{u}_e$$

1. Identify the parent isotope and the type of decay (α or β).
2. Apply the conservation of mass number (A) and atomic number (Z) to find the daughter isotope.
3. Remember: α‑decay reduces A by 4 and Z by 2; β⁻‑decay increases Z by 1 (A unchanged); β⁺‑decay decreases Z by 1.
4. Check that the new element’s symbol matches the calculated Z.