So we see that the decay is given by a geometric progression. The number of undecayed dice obtained using this method for the first 12 throws is shown in table 1.
We now need to make a link between the actual elapsed time t used in radioactive decay formulae, and the time interval represented by each mass
throwing of the dice. The decay of real nuclei is given by the exponential equation
where Nt is the number of undecayed nuclei remaining after a time t. If we now make the decay constant 1/6 h−1 and let N0 be equal to 1000 nuclei, this equation becomes
and we can count the number of undecayed real nuclei once every hour just like the dice. These values are also shown in table 1 for the first 12 h of decay.
The two decays, a histogram for the dice and a continuous curve for the nuclei, are shown in figure 1.
Inspecting the number of undecayed dice in the table tells us that the number halves from 1000 to 500 somewhere between throws 3 and 4. In fact using logarithms tells us that if
Consider the time interval 0–1 h, i.e. the very first hour, of the two decays. The dice only decay when they are thrown at the end of that hour. The number of undecayed dice stays constant at 1000, throughout the hour, and then suddenly drops to 833 at the end of that time, which is why the decay is represented in figure 1 by a histogram.