Deduce the law of radioactive disintegration.



The Law of Radioactivity Disintegration:

Let, N be the number of atoms present in the radio element at a given instant t. Then the rate of decrease,


Here, λ is the disintegration constant. It is defined as the ratio of the amount of the substance which disintegrates in a unit time to the amount of substance present.





The equation (i) can be written as, 

Integrating,


Let, there are  number of atoms present initially.

Then, when t=0, N=N0


Substituting the value of C in equation (ii),





Thus the number of atoms of a given radioactive substance decreases exponentially with time.

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