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The half-life of an element is the time it takes for half the atoms of a radioisotope to decay into other atoms.
[link] gives some examples of the half-lives of different elements.
Radioisotope | Chemical symbol | Half-life |
Polonium-212 | Po-212 | 0.16 seconds |
Sodium-24 | Na-24 | 15 hours |
Strontium-90 | Sr-90 | 28 days |
Cobalt-60 | Co-60 | 5.3 years |
Caesium-137 | Cs-137 | 30 years |
Carbon-14 | C-14 | 5 760 years |
Calcium-41 | Ca-41 | 100 000 years |
Beryllium-10 | Be-10 | 2 700 000 years |
Uranium-235 | U-235 | 7.1 billion years |
So, in the case of Sr-90, it will take 28 days for half of the atoms to decay into other atoms. It will take another 28 days for half of the remaining atoms to decay. Let's assume that we have a sample of strontium that weighs 8g. After the first 28 days there will be:
1/2 x 8 = 4 g Sr-90 left
After 56 days, there will be:
1/2 x 4 g = 2 g Sr-90 left
After 84 days, there will be:
1/2 x 2 g = 1 g Sr-90 left
If we convert these amounts to a fraction of the original sample, then after 28 days 1/2 of the sample remains undecayed. After 56 days 1/4 is undecayed and after 84 days, 1/8 and so on.
Work in groups of 4-5
You will need:
16 sheets of A4 paper per group, scissors, 2 boxes per group, a marking pen and timer/stopwatch.
What to do:
Questions:
A 100 g sample of Cs-137 is allowed to decay. Calculate the mass of Cs-137 that will be left after 90 years
The half-life of Cs-137 is 30 years.
If the half-life of Cs-137 is 30 years, and the sample is left to decay for 90 years, then the number of times the quantity of sample will be halved is 90/30 = 3.
1. After 30 years, the mass left is 100 g $\times $ 1/2 = 50 g
2. After 60 years, the mass left is 50 g $\times $ 1/2 = 25 g
3. After 90 years, the mass left is 25 g $\times $ 1/2 = 12.5 g
Note that a quicker way to do this calculation is as follows:
Mass left after 90 years = (1/2) ${}^{3}$ $\times $ 100 g = 12.5 g (The exponent is the number of times the quantity is halved)
An 80 g sample of Po-212 decays until only 10 g is left. How long did it take for this decay to take place?
Fraction remaining = 10 g/80 g = 1/8
Therefore, x = 3
The half-life of Po-212 is 0.16 seconds. Therefore if there were three periods of decay, then the total time is 0.16 $\times $ 3. The time that the sample was left to decay is 0.48 seconds.
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