Activity, Half-life and Decay constant

The activity of a radioactive substance is defined as the average number of atoms disintegrating per unit time.

  • An activity of one decay per second is one Becquerel (1 Bq)

Activity A is directly proportional to the number of parent nuclei N present at that instant:

$\begin{aligned}A & \propto N \\ A & = \, – \, \frac{dN}{dt} \\ & = \lambda N \end{aligned}$

, where

  • N is number of parent nuclei,
  • t is the time,
  • λ is the decay constant.

The decay constant λ of a nucleus is defined as its probability of decay per unit time.

Half-life is defined as the time taken for half the original number of radioactive nuclei to decay.

Useful Equations:

$N = N_{o} \, e^{-\lambda t}$, where

  • No is the initial number of radioactive nuclides and
  • N is the number of nuclides remaining after a time t.


$t_{\frac{1}{2}} = \frac{ln \, 2}{\lambda}$, t1/2 is half-life.

$\left( \frac{N}{N_{o}} \right) = \left( \frac{1}{2} \right)^{n}$ , where n is the number of half-life passed.


Graphical Representation of Decay of Parent Nuclide

Graphical Representation of Decay of Parent Nuclide


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