Difference between half- life and average life of a radioactive substance.

The terms "half-life" and "average life" are both related to the decay of radioactive substances, but they represent different concepts:

Half-life:
The half-life of a radioactive substance is the time it takes for half of the radioactive atoms in a given sample to decay. In other words, it is the time required for the quantity of the radioactive substance to reduce by half. Half-life is a constant characteristic of a specific radioactive isotope and is independent of the initial amount of the substance.
For example, if you start with 100 grams of a radioactive substance with a half-life of 1 hour, after 1 hour, you would have 50 grams remaining, after 2 hours, 25 grams remaining, and so on. Regardless of the starting amount, it will always take one half-life for the quantity to decrease by half.

Average life (also known as the mean life):
The average life of a radioactive substance is the average time it takes for an individual radioactive atom to decay. It is a statistical quantity and is calculated by considering the sum of the lifetimes of all radioactive atoms in a sample, divided by the total number of radioactive atoms present.
Unlike the half-life, the average life is dependent on the initial amount of the radioactive substance. As the number of radioactive atoms decreases due to decay, the average life also changes. However, for a large number of atoms, the average life converges to a more stable value, and this value is often close to the half-life.

To summarize, the half-life is the time it takes for the quantity of a radioactive substance to reduce by half, whereas the average life is the average time it takes for a single radioactive atom to decay. Both of these properties are essential in understanding the decay behavior and stability of radioactive materials.