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We now know how the radiation is produced and that the amount of radiation determines the danger (or benefit) but when does a nucleus decay? Every application you saw in previous chapters can only work if the radiation is released over an amount of time, it won’t do any good if all nuclei decay at the same time. As it happens, the moment a specific nucleus decays if governed by quantum mechanics and is therefore inherently unknown, a game of chance if you will. Like any good game of chance however, if one tries enough times (and because the amount of atoms is astonishingly large, we do) the game can be described statistically and thus, is not without a certain measure of predictability.
Assignment
78. Every nucleus that is unstable has a certain chance of decaying and we can simulate that process with an amount of dice. Take the 20 dice and copy the next table in your notebook.
Let’s say that every one of these dice is a nucleus of the rare metal Unobtainium and they have a 1/3 chance of decaying when rolled and in this simulation, 1 roll equals 1 second.
Roll all 20 dice and all the dice that show a five or six have decayed, place them apart and write down the amount in the table. The next roll is with the remaining dice of which a couple will decay during this roll and so on. Continue until you’ve rolled seven times and do this experiment 5 times. The first experiment has been filled in the table already. In the last row, calculate the average amount of dice that decayed during that roll. These averages are the activity, the amount of nuclei that decay per second.
The unit of activity is the Becquerel (Bq), which is indeed equal to the amount of decayed nuclei per second.
Using the measurements, fill in the next table. It tells you the amount of dice that were remaining active after a certain roll.
Now draw two graphs:
1: The average amount of decays against the time
2: The average amount of remaining nuclei against the time.
As you can see, they have a similar shape. Let’s take a gamble, if you compare the amount of remaining nuclei after t=1s and t=2,5s, you’ll see that the amount has just about halved. If you compare the activity on t=1s and t=2,5s, you’ll hopefully see that the activity has halved as well.
Of course, we did this with just 20 nuclei and 6 experiments, if you were to try this with a couple of billion nuclei and a couple of billion experiments, you would find that when the amount of remaining nuclei drops by a certain percentage, the activity drops by that same percentage.
Half-life
In the experiment of the previous paragraph, we used a radioisotope that has a 1/3 chance of decaying every second. We could have used a 1/6 chance and the actual amounts would have changed but the shape of the graph wouldn’t. We could have said that every roll equals one hour, and the graph would still look the same. Every radioisotope we do this experiment with would yield the same shape of graph but with different numbers. Those numbers are determined by the isotope itself, it is a distinctive material property.
We could define that material property as, “the chance of decay every second” or “the percentage that will decay in a year” but we haven’t chosen those. What we have is the half-life.
The half-life of a radioisotope is the time it takes for half of the remaining nuclei to decay.
That also means:
The half-life of a radioisotope is the time is takes for the activity to decrease by 50%.
Some radioisotopes have a really short half-life; Polonium-212 has a half-life of 3.10-7 seconds. Other have a really long half-life, Uranium-238 has a half-life of 4,46.109 years.
Assignments
Observe the graph to the right, it gives you the activity measured over 30 days.
79. How much time does it take for the activity to drop from 80 to 40 counts per second?
80. And from 40 to 20?
81. And from 20 to 10?
82. What is the half-life of this isotope?
83. Determine the half-life of the Unobtainium we used in the previous paragraph.
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