The half-life ( T_½ ) of a quantity subject to exponential decay is the time required for the quantity (mass, number of atom or activity) to decay to half of its initial value.
The decay curve of a radioactive source can be found experimentally – provided the activity of the source decreases over a practicable time period (minutes, hours or days for example).
The corrected count-rate is then plotted against time to give the decay curve. The half-life of the source can be found from the curve as indicated above.

(Decay Curve)

Example 1
A radioisotope has a half-life of 8 hours. Initially, there were 3.6 x 10¹⁸ radioisotope atoms in a sample. How much time is taken for the number of atoms of the radioisotope to fall to 4.5 x 10¹⁷?

Answer:

The sample takes 3 half-lifes to decay from 3.6 x 10¹⁸ radioisotope atoms to 4.5 x 10¹⁷. Therefore, the time taken

Example 2

The diagram shows the graph of the activity of a radioisotope, X, against time. What is the half-life of the radioactive substance?

Answer:
The half-life is the time taken for the activity to decrease to become half of the initial value.

From the graph we can see that the radioisotope take 6 days for the activity to become half. Therefore

Half-life = 6 days

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