Rate of radioactive decay
In accordance to the law of the radioactive decay, the quantity of a radio-element which disappears in unit time (the rate of disintegration) is directly proportional to amount present.
The law of the radioactive decay can also be expressed mathematically.
Suppose N0 be the number of atoms of the radioactive element present at the commencement of observation, t=0 and after time t, the number of atoms remaining unchanged is Nt. The rate of disintegration 
at any time t is directly proportional to N. Then we get
where λ is a radioactive constant or decay constant.
The various forms of equation for the radioactive decay are as follows,
This equation is similar to that of the first order reaction, hence we can say that the radioactive disintegration are instances of first order reactions. Though, unlike first the order rate constant (K), the decay constant (λ) is independent of the temperature.
Rate of decay of the nuclide is independent of the temperature, so its energy of activation remains zero.
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