How is the mean life of a radioactive source determined?

The mean life, or average lifetime, of a radioactive source is determined using the relationship with its half-life. The mean life is defined as the average time interval that a particle exists before decaying, and it is mathematically expressed as being approximately 1.44 times the half-life.

The factor of 1.44 comes from the derivation that involves the principles of exponential decay and how the decay constant relates to the half-life. The decay constant (λ) is related to the half-life (T1/2) through the equation T1/2 = ln(2)/λ. By rearranging and substituting into the mean life formula, we arrive at the relationship that connects mean life and half-life.

This means that the mean life provides a more comprehensive understanding of the decay process, offering insights into the average decay time of any number of radioactive atoms, whereas the half-life primarily measures the time it takes for half of the radioactive atoms to decay.

Thus, when calculating mean life, using the value 1.44 multiplied by the half-life gives you the appropriate estimate of the average survival time of the radioactive atoms in that sample.