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Activity
Activity is the number of unstable nuclei that decay* per second.
*decay: break down, gives out radiation and change into new stable nucleus.
Example: Carbon-14 decays into
nitrogen-14 and beta radiation is given out.
The activity of radioactive elements decreases with time.
Half-life
Half-life of a radioactive material is the time
it takes half the unstable nuclei in a sample to decay.
or ...
Half-life of a radioactive material is the time
it takes the count rate from a sample to half.
Higher tier only:
Calculations of half-life can be used to date materials.

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