The Law of Radioactive Decay

The law of radioactive decay predicts how the number of the not decayed nuclei of a given radioactive substance decreases in the course of time. The red circles of this simulation symbolize 1000 atomic nuclei of a radioactive substance whose half-life period (T) amounts to 20 seconds. The diagram in the lower part of the applet represents the fraction of the not yet decayed nuclei (N/N0) at a given time t, predicted by the following law:

N   =   N0 ·   2−t/T

N .... number of the not decayed nuclei
N0 ... number of the initially existing nuclei
t .... time
T .... half-life period

As soon as the applet is started with the yellow button, the atomic nuclei will begin to "decay" (change of color from red to black). You can stop and continue the simulation by using the button "Pause / Resume". In this case a blue point for the time and the fraction of the not yet decayed nuclei is drawn into the diagram. (Note that often these points don't lie exactly on the curve!) If you want to restore the initial state, you will have to click on the "Reset" button.

It is possible to give the probability that a single atomic nucleus will "survive" during a given interval. This probability amounts to 50 % for one half-life period. In an interval twice as long (2 T) the nucleus survives only with a 25 % probability (half of 50 %), in an interval of three half-life periods (3 T) only with 12,5 % (half of 25 %) and so on.

You can't, however, predict the time at which a given atomic nucleus will decay. For example, even if the probability of a decay within the next second is 99 %, it is nevertheless possible (but improbable) that the nucleus decays after millions of years.

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Physics Applets

© Walter Fendt, July 16, 1998
Last modification: February 4, 2010