represent α- and β-decay by a radioactive decay equation of the form UT h92238 90234

Atoms, Nuclei and Radiation

Objective

Represent α‑ and β‑decay by a radioactive decay equation of the form $\,_{Z}^{A}\text{X} \rightarrow \,_{Z'}^{A'}\text{Y} + \text{particle}\,$.

α‑Decay

In α‑decay the nucleus emits an α‑particle, which is a helium‑4 nucleus:

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

• The mass number decreases by 4.
• The atomic number decreases by 2.

β‑Decay

In β‑decay a neutron is transformed into a proton with the emission of an electron (β⁻ particle) and an antineutrino (often omitted in simple equations):

$$ \,_{6}^{14}\text{C} \;\rightarrow\; \,_{7}^{14}\text{N} \;+\; \,_{-1}^{0}\beta $$

• The mass number remains unchanged.
• The atomic number increases by 1.

Comparison of α‑ and β‑Decay

Feature	α‑Decay	β‑Decay
Particle emitted	α‑particle ($\,_{2}^{4}\alpha$)	β⁻ particle ($\,_{-1}^{0}\beta$)
Change in mass number (A)	‑4	0
Change in atomic number (Z)	‑2	+1
Typical energy released	\overline{4}–9 MeV	\overline{0}.5–2 MeV

Practice Questions

1. Write the decay equation for the α‑decay of $\,_{84}^{210}\text{Po}$.
2. Write the decay equation for the β‑decay of $\,_{11}^{22}\text{Na}$.
3. Explain why the mass number does not change in β‑decay.