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  • (a) Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus. (b) How is the mean life of a given radioactive nucleus related to the decay constant?

(a) Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus.

(b) How is the mean life of a given radioactive nucleus related to the decay constant?

 

 

 

 
 
 
 
 

Answers (1)

(a) At t=0 let there be N_0 radioactive nuclei

If N number of nuclei is left after time t

\frac{-dN}{dt}\propto \; N

\frac{dN}{N}=-\lambda dt

\lambda =decay\; constant

On integrating

lnN=-\lambda t+C

at\; \; t=0

ln(N_{o})=C

\therefore lnN=-\lambda t+ln(N_{o})

ln\left ( \frac{N}{N_{o}} \right )=-\lambda t

N=N_{o}e^{-\lambda t}

(b) Mean life

\tau =\frac{1}{\lambda }

Posted by

Safeer PP

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