The rate of radioactive decay is proportional to the number of atoms
where λ is the disintegration constant or decay rate.
Integrating both sides gives
where N is the number of unchanged atoms at time t
and N0 is the number of atoms at any chosen t=0
The radioactive half life is defined as the time required for the number of parent atoms to fall from
Isotopes can have very long half-lives e.g.
uranium-234: half life = 244 thousand years,
uranium-235: half life = 704 million years
uranium-238: half life = 4.5 billion years
potassium-40: half-life = 1.25 billion years
plutonium-244: half-life of about 82 million years
or relatively short half-lives e.g.
Technetium-99m: half life =6 h (the m denotes that it is a metastable state of 99Tc)
Dysprosium-165: half life =2 h
Potassium-42: half life =12 h
Selenium-75: half life =120 d
Cobalt-57: half life =272 d
Thallium-201: half life =73 h
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