# State the Law of Radioactive Decay. Hence Derive The Expression N = Noe^-λT Where Symbols Have Their Usual Meanings. - Physics

State the law of radioactive decay.

#### Solution

The number of nuclei undergoing the decay per unit time is proportional to the number of unchanged nuclei present at that instant.

If ‘N’ is the number of nuclei present at any instant ‘t’, ‘dN’ is the number of nuclei that disintegrated in short interval of time ‘dt’, then according to decay law,

- (dN)/dt ∝ N

:.(dN)/dt = -lambda N

where, lambda is known as decay constant or disintegration constant. The negative sign indicates disintegration of atoms.

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