Question

Obtain the exponential law of radioactive disintegration.

Answer 1

The Radioactive Decay Law Exponential decay law Consider a system of particles, N0 in number at time, t = 0.

Each of these particles has an independent, but equal probability of decay per unit time, λ.

Thus, the change in N us given by:  

dN = −λNdt; N(0) = N0  

dN/ N = −λdt  

d[log N] = −λdt  

log N − log N0 = −λt  

log N = log N0 − λt

N = N0 exp(−λt)  

Thus we have derived the well-known exponential decay law,

N(t) = N0e −λt .