The Radioactive Decay model.

In this presentation we will learn: 1.What is meant by the terms Probability of decay per second Activity Radioactive decay constant Becquerel 2. A simple mathematical model of how radioactive elements decay.

The decay of a radioactive element is totally random. (Rutherford found this hard to believe. He tried heating, pressure, cooling – to no avail). A particle has a small probability of being emitted from a nucleus in a given time. There is just one rule for each nucleus: It can decay with a fixed probability in a given time.

Predict a result when decay occurs. What happens to the population? It declines…….. …….the number left to decay gets less and less. But…the number decaying (proportional to the number left behind) also gets less. The population decline gets slower and slower. We’ll be dealing with a RATE of decline, which means using small time-chunks (  t).

It’s important to understand the idea of PROBABILITY of decay and PROBABILITY of decay PER SECOND. If each nucleus has a probability p to decay, and there are N nuclei at any moment, Number decaying = p N The longer you wait, the more chance there is for a decay. p   t p =  t p =  t is called the DECAY CONSTANT in s -1 is called the DECAY CONSTANT in s -1

This may seem confusing, so think of the decay constant as THE CHANCE OF DECAY IN ONE SECOND. Activity The activity of a radioactive source is THE NUMBER OF NUCLEI DECAYING PER SECOND. (UNITS: Bq or Bequerels) We can now link activity to probability. Activity a = NNNN tttt no. decaying per second

But p N =  t N So, Activity a =  t N  t N tttt And so a = N If you know the activity of the source and the number of nuclei (using Avogadro’s number) you can find the decay constant for any radioactive material. This is a very useful constant, as we shall find out later.

Fading away……. The number of nuclei present at any moment decreases at a rate equal to the activity. NNNN tttt = - N N = activity N = activity decay Differential of N wrt time

This equation captures the SMOOTH behaviour of decay. It works for many different types of decay – a very useful MODEL. This sort of equation, involving the RATE of CHANGE of a quantity, is called a DIFFERENTIAL EQUATION. It works for GROWTH as well as DECAY; just use a + instead of a – sign.