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State the law of radioactive decay.

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#### Solution

Law of radioactive decay:

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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