Nucleus and radioactivity

MDCAT Physics · Physics · Nuclear physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A nucleus has Z protons and N neutrons, and its mass number is A = Z + N. Isotopes of an element have the same Z but different N.

A nucleus has less mass than its separate protons and neutrons. This difference is the mass defect, and its energy equivalent is the binding energy that holds the nucleus together. The higher the binding energy per nucleon, the more stable the nucleus. It is greatest near iron-56.

Unstable nuclei decay by emitting α-particles (helium nuclei), β-particles (electrons) or γ-rays (photons). Decay is random, but for a large sample the half-life, the time for half the nuclei to decay, is constant. The activity halves in each half-life too.

Rules to remember

Common mistake

Read whether the question asks for the fraction left or the fraction decayed: after 3 half-lives 1/8 is left but 7/8 has decayed. In decay chains, find the number of α-particles from the mass number first, because β decay does not change A.

Worked example

A sample contains 2.0 × 1010 nuclei of an isotope with a half-life of 6930 s. Find its activity.

  1. Decay constant λ = 0.693 ÷ T½ = 0.693 ÷ 6930 = 1.0 × 10−4 s−1.
  2. Activity = λN = 1.0 × 10−4 × 2.0 × 1010 = 2.0 × 106 Bq.

Answer: Activity = 2.0 × 106 Bq (2.0 MBq).

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