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Half Life

Marie Curie thought that the strength of a radioactive source and therefore the number of particles or gamma rays that it emitted every second did not change with time but in fact she was wrong. The strength gets weaker as time goes by. Every time the source emits a particle its activity decreases. There will be fewer radioactive atoms and more stable ones.

The following graph shows how the activity of a source (in counts per second) decreases with time.

It's very difficult to decide when a source has lost ALL of its radioactivity but the time for it to drop to HALF its original value can be found easily.

The average time taken for the activity of a sample of radioactive material to drop to HALF its original value is called the HALF LIFE of the source (T).

This half-life depends only on the material of the source and different radioactive isotopes have different half lives.

This means that if we have some material that has a half life of 20 days then after 20 days it will only be HALF as radioactive as it was at the start, after another 20 days, i.e 40 days after the start it will only be a quarter as radioactive, one eight after 60 days and so on.

We can show this in another way by the following diagram. If we start with a sample of material where all the nuclei are radioactive and then watch how this changes as time goes by we will see that the number of radioactive nuclei gets less while the number of non-radioactive nuclei gets greater. The total number of nuclei in the sample stays the same.

As the source decays it looses alpha, beta or gamma radiation and so as time goes by there will be fewer radioactive atoms and more non - radioactive ones. The MASS of the RADIOACTIVE part of the sample gets less. Remember that the total number of atoms (radioactive and stable) stays the same.

For the schoolphysics animation of radioactive decay please click the symbol:

Radioactive decay and half life

We will see later that knowledge of the half-lives of radioactive isotopes has been useful in dating rocks and archaeological specimens. They are also the basis of atomic clocks.

Examples of some common half lives are shown in the following table:

Material Half life
Carbon 14 5700 years
Uranium 238 4500 million years
Radium 226 1600 years
Plutonium 239 24 000 years

The rate at which a particular radioactive source decays depends ONLY on the source. It cannot be changed by any physical (e.g. temperature, pressure) or chemical process.

Example problems
1. We have 48 g or radioactive material with a half life of 30 minutes. How much radioactive material will be left after:
(a) 30 minutes   (b) 60 minutes    (c) 90 minutes   (d) 120 minutes

(a) 24 g   (b) 12 g    (c) 6 g    (d) 3 g

2. If the count rate from a radioactive source is 500 counts per second and drops to 125 counts per minute in 20 minutes, what is the half life of the source?

The count rate has dropped to one quarter so TWO half lives will have passed.
Therefore half life = 20/2 = 10 minutes

© Keith Gibbs 2020