Question

define average life and half life of radio active substance.what is the relation between them.

Answer 1

The half-life (median lifetime) is the time required for ½ of the radioactive atoms to decay. A radioactive half-life of one hour will decay half of its element in one hour. The half-life is necessary for the decay formula. [1] 
    The mean life (average lifetime) is the expected life for the radioactive atom within a sample. It is the average of the lifetimes of the individual atoms. For example, “If we took a sample of radioactive atoms and wait for all of them to decay away, and keep track of how long each atom lasts. The sum of all the lifetimes of the atoms, divided by the original number of atoms, is the mean lifetime.” [2] 

        The relationship between mean life and half-life is:

        Mean life = (t1/2)(1.44)1

    By chance, there are always a few atoms among a sample that live longer than the usual. These longer living atoms do not effect the median lifetime but pull up the average lifetime. The shortest life of an atom is zero. Therefore, atoms cannot lower the average lifetime. Because of this, the average lifetime is longer than the median. [2]   This can also be seen in the following formulas: 

        Half-life = (mean life)*ln(2) 

        Mean life = (half-life)/ln(2)

        Ln(2) = .693

    The half-life is smaller than the mean life by a factor of the natural logarithm of 2. 2