Know that isotopes of an element may be radioactive due to an excess of neutrons in the nucleus and/or the nucleus being too heavy

5.2 Radioactive Decay

Learning Objective

Understand that an isotope may be radioactive because it contains an excess of neutrons and/or because the nucleus is very heavy. Be able to describe how the instability is detected and how the nucleus decays to a more stable configuration.

5.2.1 Detection of Radioactivity

• Background radiation – low‑level ionising radiation that is always present (cosmic rays, radon gas, terrestrial rocks, food, etc.).
• Typical classroom sources – uranium‑containing rocks, thorium‑containing lantern mantles, potassium‑40 in salts, small sealed sources.
• Detectors

  • Geiger–Müller (GM) tube or scintillation counter – produces a “click” each time an ionising particle is detected.
  • Result is expressed as a count‑rate (counts s⁻¹ or counts min⁻¹).

• Safety note – keep the detector away from strong sources, use appropriate shielding (e.g., lead), and never look directly at a source.

5.2.2 Three Types of Nuclear Emission

Deflection in fields: α‑particles (massive, +2 e) are strongly deflected in electric and magnetic fields, β⁻ particles (light, –1 e) are deflected in the opposite direction, while γ‑rays are not deflected because they are uncharged.

5.2.3 Why Some Isotopes Are Radioactive

Two principal factors make a nucleus unstable:

1. Excess neutrons – For light nuclei a roughly 1 : 1 neutron‑to‑proton ratio (N/Z≈1) is stable. When N is too large the strong nuclear force cannot offset the extra mass, and the nucleus undergoes β⁻ decay, converting a neutron into a proton.
2. Very heavy nuclei – As Z increases, electrostatic repulsion between protons grows. Even with a higher N/Z ratio, the nucleus may be too massive to remain bound, favouring α decay (emission of a helium nucleus) which reduces both Z and A.

5.2.4 Neutron‑to‑Proton Ratio and the Valley of Stability

The stable N/Z ratio rises with atomic number. Approximate stable ranges are:

• Light elements (Z ≤ 20): N/Z ≈ 1.0
• Medium elements (20 < Z ≤ 40): N/Z ≈ 1.2–1.3
• Heavy elements (Z > 40): N/Z ≈ 1.5–1.6

If an isotope’s actual N/Z lies outside the stable band, it will decay in a direction that moves the point toward the “valley of stability” on an N‑vs‑Z plot.

5.2.5 Typical Decay Paths on the Valley‑of‑Stability Diagram

• β⁻ decay → moves the point one step upward (increase Z by 1, A unchanged).
• α decay → moves the point diagonally down‑left (decrease Z by 2 and A by 4).
• γ emission → vertical arrow (no change in Z or A, only de‑excitation).

5.2.6 Illustrative Examples of Radioactive Isotopes

5.2.7 Half‑Life and Decay Constant

The half‑life (\$t_{1/2}\$) is the time required for half of the nuclei in a sample to decay. It is related to the decay constant (\$\lambda\$) by:

\$t_{1/2}= \dfrac{\ln 2}{\lambda}\$

Half‑lives span an enormous range – from fractions of a second (e.g., \$^{214}\$Po, \$t{1/2}=164\;\mu\text{s}\$) to billions of years (e.g., \$^{238}\$U, \$t{1/2}=4.5\times10^{9}\,\$yr). This reflects the varying degrees of nuclear stability.

5.2.8 Summary Checklist

• Isotopes have the same \$Z\$ (protons) but different \$N\$ (neutrons).
• Excess neutrons → β⁻ decay (neutron → proton + electron + antineutrino).
• Very heavy nuclei → α decay (helium nucleus emitted).
• After α or β decay the daughter nucleus may be left in an excited state and emit γ radiation.
• Stability is governed by the \$N/Z\$ ratio and the total mass number \$A\$.
• Radioactivity is detected with a GM tube or scintillation counter; results are recorded as counts s⁻¹ after subtracting the background count‑rate.