Know that a β-particle is a high-speed electron emitted from the nucleus, formed when a neutron changes into a proton and an electron and a reduction in the number of excess neutrons; the following change in the nucleus occurs during β-emission neutr

5.2.3 Radioactive Decay – β‑Particle Emission

What is β‑decay?

• Spontaneous, random nuclear transformation that changes one element into another.
• One of the three decay modes required by the Cambridge IGCSE syllabus (α, β, γ).
• In β‑decay a neutron in the nucleus is converted into a proton, a high‑speed electron (the β‑particle) and an antineutrino.

The nuclear reaction

The fundamental change can be written as

\$n \;\rightarrow\; p^{+} + e^{-} + \bar{\nu}_e\$

where n = neutron, p⁺ = proton, e⁻ = β‑particle, \(\bar{\nu}_e\) = antineutrino (carries away excess energy and momentum).

Changes in the nucleus

• Atomic number (Z) increases by 1.
• Mass number (A) remains unchanged.

For a generic nucleus ⁽ᴬ⁾₍ᶻ₎X the decay is

\$^{A}{Z}\!X \;\rightarrow\; ^{A}{Z+1}\!Y + e^{-} + \bar{\nu}_e\$

Numeric example

Potassium‑39 decays by β‑emission:

\$^{39}{19}\!K \;\rightarrow\; ^{39}{20}\!Ca + e^{-} + \bar{\nu}_e\$

• Before decay: Z = 19, A = 39 (potassium).
• After decay: Z = 20, A = 39 (calcium). The element changes, but the mass number does not.

Summary of nuclear changes

Comparison of the three types of radiation

Detection of β‑particles

• β‑particles are recorded as electrical pulses in a Geiger‑Müller tube, scintillation counter or semiconductor detector.
• The instrument shows a count‑rate (counts s⁻¹). To obtain the net rate, subtract the background count‑rate measured with no source present (see 5.2.1).
• Because β‑particles are charged, they ionise air; the ionisation current is the basis of most detection methods.

Half‑life – definition and simple calculation

• Half‑life (T½): the time required for half of a given number of radioactive nuclei to decay.
• For IGCSE the decay law can be written as

  \$N = N0\left(\frac{1}{2}\right)^{t/T{½}}\$

  where N₀ is the initial number of nuclei, N the number remaining after time t.

• Example: ⁹⁰₃₈Sr has T½ = 28.8 years. After 57.6 years (2 × T½) the activity is \(\frac{1}{4}\) of the original.

Safety precautions for β‑radiation

• β‑particles are stopped by a few millimetres of aluminium or Plexiglas; use these as shields when handling sources.
• Wear gloves and use forceps or tongs to avoid direct skin contact.
• Store sources in lead containers (lead also stops any accompanying γ‑radiation) and keep them out of the laboratory when not in use.
• Apply the three‑principle rule: minimise time, maximise distance, and use appropriate shielding.

Common β‑emitters and their applications

• ¹⁴₆C – carbon dating (archaeology, geology).
• ³²₁₅P – medical tracer in blood‑pool studies.
• ⁹⁰₃₈Sr – industrial gauges and thickness monitors.
• ³H (tritium) – self‑luminous exit signs and nuclear‑fusion research.
• ⁴⁰K – natural background radiation; used in geological dating.

Key points to remember

• β‑decay converts a neutron into a proton, an electron (β‑particle) and an antineutrino.
• Atomic number increases by 1; mass number remains unchanged.
• β‑particles have medium penetrating power; a few mm of aluminium stops them.
• The decay is spontaneous and random; the half‑life characterises the rate of decay.
• Detection is usually by a Geiger‑Müller tube, scintillation counter or semiconductor detector; always subtract background.
• Safety: shield with aluminium, keep sources away from skin, minimise exposure time, and store in lead containers.