Derive an expression for average life of radionuclide
Answers
Average life of a decaying nucleus is also known as the mean life , τ. Let the activity be R . Then the number of nuclei decayed during the very small time interval dt is given by Rdt = Nλdt = N0e-λt λ .
All these nuclei have lived for a time t.
The total life of these nuclei = N0e-λt λ t dt,
But clearly , some nuclei will live more or less life than these . In order to get mean life , we need to take the sum of lifes of all particles and we need to divide it by total number of particles ( N0 ).
So mean life = Life of Particle 1 + Life of particle 2 + .........../N0
This sum involves infinitely many terms . So it is an integral .
I will show you how to integrate this but it is not really necessary . Even for the exam , you could write up to the first step in the integral . Then you can write " By performing this integral , we get " and directly write the final answer .
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