TAP 515-1: Smoothed out radioactive decay
Here is the first step in making a model – idealisation and simplification of a messy process
Smoothed out radioactive decay
Actual, random decay
N
N
t
t
time t
probability p of decay in short time t is proportional to t:
p =  t
average number of decays in time t is pN
t short so that N much less than N
change in N = N = –number of decays
N = –N
t
N = –pN
N = –N t
Simplified, smooth decay
rate of change
= slope
dN
= dt
time t
Consider only the smooth form of the average behaviour.
In an interval dt as small as you please:
probability of decay p =  dt
number of decays in time dt is pN
change in N = dN = –number of decays
dN = –pN
dN = –N dt
dN = –N
dt
Practical advice
The diagram could be used for an OHT
External reference
This activity is taken from Advancing Physics chapter 10, display material 10O