Upon completion of this topic, learners will be able to:

• Explain the role of half-life in the stability of the nucleus.
• Define half-life.
• Draw a typical half-life decay curve of a radioactive element.

Radioactive nuclides do not all decay at the same rate. Some decay very rapidly; others undergo disintegration at extremely low rates. This indicates that radionuclides are not all equally unstable. The greater the decay rate, the lower the stability of the nuclide.

The concept of half-life is used to express nuclear stability quantitatively. A half-life (t_½) is the time required for one-half of a given quantity of a radioactive substance to undergo decay. For example, if a radionuclide’s half-life is 12 days and you have a 4.00 g sample of it, then after 12 days (1 half-life), only 2.00 g of the sample (one-half of the original amount) will remain undecayed; the other half will have decayed into some other substance.

Figure 2. Decay of 80.0 mg of 131I, which has a half-life of 8.0 days. After each half-life period, the quantity of material present at the beginning of the period is reduced by half.

Calculations involving amounts of radioactive material decayed, amounts remaining undecayed, and time elapsed can be carried out by using the following equation: