Radioactive Source - Radioactive Decay Rates

Radioactive Decay Rates

The decay rate, or activity, of a radioactive substance are characterized by:

Constant quantities:

• The half-life—t_1/2, is the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value; see List of nuclides.
• The mean lifetime— τ, "tau" the average lifetime of a radioactive particle before decay.
• The decay constant— λ, "lambda" the inverse of the mean lifetime.

Although these are constants, they are associated with statistically random behavior of populations of atoms. In consequence predictions using these constants are less accurate for small number of atoms.

In principle the reciprocal of any number greater than one— a half-life, a third-life, or even a (1/√2)-life—can be used in exactly the same way as half-life; but the half-life t_1/2 is adopted as the standard time associated with exponential decay.

Time-variable quantities:

• Total activity— A, is number of decays per unit time of a radioactive sample.
• Number of particles—N, is the total number of particles in the sample.
• Specific activity—S_A, number of decays per unit time per amount of substance of the sample at time set to zero (t = 0). "Amount of substance" can be the mass, volume or moles of the initial sample.

These are related as follows:

where N₀ is the initial amount of active substance — substance that has the same percentage of unstable particles as when the substance was formed.