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This is a truly random proceses. The probability of decay is constant. The probabilty that a nucleus undergoes radioactive decay in time dt is p:
p = L dt (for L dt <<1)
where L (decay constant) is probability per unit time for the decay of each nucleus of a given nuclide.Consider a system initially having N0 unstable nuclei. How does the number of parent nuclei, N, change with time?
Theoretically, the number of undecayed nuclei at time t is given by:
N = N 0 exp (- L t )
where N0 is the number of parent(undecayed) nuclei at t = 0.
Alogrithm:
Determine N (initial number of parents)
Determine L (decay constant)
Determine Tmax (any time)
Determine dt (time step)
LOOP from t=0 to Tmax, step dt
LOOP over each remaining parent nucleus
Generate a random number R from a uniform distribution
Decide if the nucleus decays:
Check IF( R < L dt ) THEN
reduce the number of parents by 1
END IF
END LOOP over nuclei
PLOT or Record N vs t
END LOOP over time
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