Half Life and Rate of Decay
Rate of Radioactive Decay
It is sometimes referred to as the 'count' for a sample.
You should realize that the geiger counter only gives an indication of the activity as it does not detect ALL particles - only a proportion of them! Changing the setting on the meter changes the 'count' but not the activity it is measuring. When doing an experiment it is important not to change the settings on your counter - keep them the same! You can then make valid comparisons.
The decay Constant ()
The rate of decay or activity (A) depends on the number of radioactive atoms present. It is proportional to the number that have not yet decayed in the sample. The constant of proportionality is called the decay constant and given the symbol (lamda).
A = n
The decay constant is characteristic to each radioactive isotope. It is the probability of a decay occurring. We can calculate the expected activity of a sample if we know its size and decay constant. The half life of a radioactive isotope is inversley proportional to the decay constant.
T1/2 = ln2/
The activity of radioisotopes decreases exponentially with time. After a given time period the amount that has yet to decay is halved. This is the case no matter when you start to measure the activity of the sample. The time taken for this 'halving' of activity is called the half-life.
Half-lives vary widely from microseconds to millions of years!
Uranium-238 has a half-life of 4.5 x 109 years (4,500,000,000 years) whereas Polonium-212 only has a half-life of 3 x 10-7 seconds (0.000 000 3 seconds). Also the tables of isotopes in the decay series section show a wide variation in half-lives.
Working out a half-life is best explained with an example:
you have a radioisotope producing a count rate of 640 Bq and after
14 minutes this had dropped to 5 Bq. What would be the half-life?
Suppose you have a radioisotope producing a count rate of 640 Bq and after 14 minutes this had dropped to 5 Bq. What would be the half-life?
Well, it would take:
So it would take seven half lives for the activity to drop from 640 Bq to 5 Bq. The time for this to happen was 14 minutes so the half-life must be 2 minutes.
Sometimes questions include a value for the background rate. This is the rate of activity that is due to background radiation NOT the sample and must therefore be deducted before any calculations are done.
E.g. The background count for the laboratory was found to be 6 Bq. If it took 10 minutes for the count-rate to drop from 102 Bq to 12 Bq when a radioactive substance was being measured, what was the half-life of the sample?
Initial count-rate due only to the sample was (102-6) Bq = 96 Bq
Final count-rate due
only to the sample was (12-6) Bq = 6 Bq
So it would take four half lives for the activity of the sample alone to drop from 96 Bq to 6 Bq. The time for this to happen was 10 minutes so the half-life must be 2.5 minutes.
Questions of this type are not uncommon at GCSEThis topic requires the drawing and interpretation of graphs, so although it is suitable to use with spreadsheets on a computer, time needs to be spent ensuring that the work can be done by the pupils in an exam room too.
It is a useful rule of thumb to know that the activity of a sample drops to less than 1% of its value in seven half lives (see Tc99-m)
See site below for diagram of how a Geiger-counter works
When dealing with radioacive materials inside a human body we have to look at the effective half life, rather than just the physical one.