LAWS OF RADIOACTIVE DECAY

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LAWS OF RADIOACTIVE DECAY

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1. Nuclei of all radioactive elements undergo spontaneous disintegration & from new radioactive element with emission of alpha or beta along with gamma rays.

2. The disintegration is random i.e. which nuclei will disintegrate first is only a matter of chance.

3. Number of nuclei undergoing the decay per unit time is proportional to total number of nuclei present in the sample.

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It is independent of all physical & chemical conditions (like temperature, pressure and chemical combination etc.)

Let ‘N’ be number of nuclei in the sample.

clip_image006Then

clip_image008where clip_image010is called radioactive decay constant or disintegration constant.

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On integrating both sides, we have

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\ln \,N\, = \, - \lambda t\, + c where C is integration constant.

At t=0, N= N0

ln N0 = 0 + C or C = ln No

Put in above equation

\begin{array}{l} \ln \,N\, = - \lambda t\, + \ln \,{N_0}\\ \ln N\, - \,\ln \,{N_0}\, = \, - \lambda t \end{array}

\ln \left( {\frac{N}{{{N_o}}}} \right) = - \lambda t\,\,\,\,\,or\,\,\,\frac{N}{{{N_0}}} = {e^{ - \lambda t}}

N = {N_0}{e^{ - \lambda t}}

NOTE:

The above equation gives exponential decay & it can also be written as

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or

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