How is exponential decay related to a half-life?

1 Answer
Alan N.
May 5, 2018

Half-life is a form of exponential decay over time.
See below.

Explanation:

Assume you have an initial quantity (#Q_0#) of a substance with a half-life period of #h#, then after #t# time periods the quantity remaining (#Q_t#) will be given by:

#Q_t = Q_0*(1/2)^(t/h)#

This means that the quantity will halve in value after #h# time periods.

An example:

The half-life of Plutonium-241 is 14.4 years. If I start with 1000 gm after 5 years and 50 years I will have:

#Q_5 = 1000 * (1/2)^(5/14.4) approx 786.1# gm

#Q_50 = 1000 *(1/2)^(50/14.4) approx 90.1# gm

This is a form of exponential decay.

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