Decay Law

Contents

Radioactive Decay Law

The radioactive decay law states that the loss of atoms in a radioactive source per unit time is proportional to the number of radioactive atoms. Thus, letting N represent the number of radioactive atoms in the source (and treating it as a continuous quantity), we have

where is the decay constant in units of inverse time for a given radionuclide.

clear;close all;clc;

Equations

% deine the symbols and the expresion
syms N0 L N(t)
decay_law=-diff(N,t)==L*N

 
decay_law(t) =
 
-diff(N(t), t) == L*N(t)
 

Solution

% solve for N(t) at N(0)=N0
Nt=dsolve(decay_law,N(0)==N0)

 
Nt =
 
N0*exp(-L*t)
 

Substitute

% substitute the values for a specific radionuclide
N0=1e8;         % number of atoms at t=0
L=2.6742e-6;    % decay constant in 1/s
t=10*24*60*60;  % 10 days converted to seconds

% calculate the number of atoms after 10 days
Nout=subs(Nt,{'N0','L','t'},{N0,L,t});
Nout=double(Nout);

% display results
fprintf('Starting with %g atoms at a decay constant of %g 1/s\n',N0,L);
fprintf('After %d days the number of atoms is %g\n',t/24/60/60,Nout);

Starting with 1e+08 atoms at a decay constant of 2.6742e-06 1/s
After 10 days the number of atoms is 9.92108e+06

Published with MATLAB® R2021a