5.2.3 Radioactive Decay – β‑Emission
Objective: Understand that a β‑particle is a high‑speed electron emitted from the nucleus when a neutron changes into a proton, an electron and an antineutrino, reducing the excess neutrons in the nucleus.
Reaction: n → p + e^- + \bar\nu_e
What is a β‑particle? ⚡️
Think of a neutron as a shy person who wants to become a proton. To do that, it “gives away” a tiny part of itself – an electron (the β‑particle) and an antineutrino. The neutron turns into a proton, and the electron zips out of the nucleus at almost the speed of light. This is called β‑minus decay.
Why does it happen? 🧪
- Neutrons are heavier than protons by about 1.3 MeV.
- Converting a neutron to a proton releases energy.
- The excess energy is carried away by the electron (β‑particle) and an antineutrino.
- The nucleus becomes more stable with one fewer neutron.
Typical Example: Carbon‑14 Decay 📚
| Parent Nucleus | Decay Type | Daughter Nucleus | Emitted Particle |
|---|
| \$^{14}\text{C}\$ | β⁻ | \$^{14}\text{N}\$ | \$e^-\$ + \$\bar\nu_e\$ |
Key Points to Remember
- β‑particles are electrons (β⁻) or positrons (β⁺) depending on the decay.
- They are highly energetic, with kinetic energies up to a few MeV.
- β‑decay reduces the neutron number by one and increases the proton number by one.
- Half‑life of a radioactive isotope tells how quickly the decay occurs.
Exam Tip:
- When given a decay equation, check that the mass number (A) remains unchanged.
- Remember that β⁻ decay changes a neutron into a proton, so the atomic number (Z) increases by 1.
- Use the half‑life to calculate the remaining quantity after a given time using the formula: \$N = N0 \left(\tfrac{1}{2}\right)^{t/t{1/2}}\$.