Is there something special about the halfway point? Does the decay happen at a steady pace or exponentially?
In: 910
So radioactive decay is probabilistic, technically an isotope could exist forever without decaying, it is just increasingly unlikely that this will happen.
Think of it like this, you have to roll 2000 6 sided dice, everytime these dice roll a 1 they are pulled out of the pool. Now we can ask the question what is the half-life of this pool of dice? Well each roll we can expect about 1/6 of the dice to disappear on the first roll we lose 1/6 of the dice but on the second roll we don’t have 2000 dice we have on average 1666, so after this roll we will have on average 1388 dice left, after the third roll we will have 1156 dice left, and finally after the 4th roll we will have 963 dice left.
So in this case we could say the half life of a set of 6 dice is about 4 rolls, but this is on average technically it is possible for more than half of the dice to still be there after 4 rolls, or even less than half, technically you did this experiment until you had no dice you could be rolling dice for all of eternity. Saying something could last for “maybe all of eternity” isn’t really a useful metric for these sorts of things and it is more useful for us to talk about the time it takes for them to reduce by half, because while dice aren’t really harmful but radioactivity and radiation sources are dangerous, and they will stay dangerous for quite a while and are proportionally dangerous to the amount of radioactive material is still there so a way to estimate the amount of radioactive material that still exists is very useful.
But we can take this further if we know the amount of time it takes for a radioactive substance to decay to another stable substance we can calculate the amount of half lives have occurred if we also measure the amount of each of those substances, like if we take the previous example and I said we started off 1 million dice and we now have around 500 dice left you could figure out the amount rolls have occurred:
First half-life we would have around 500k dice left and would take about 4 rolls
Second half life we would have 250k dice left and would take a total of 8 rolls
Third half life we would have 127.5k dice left and would take a total of 12 rolls
Fourth half life we would have 63750 dice left and would take a total of 16 rolls
Fifth half life we would have 31875 dice left and would take a total of 20 rolls.
Sixth half life we would have 15937 dice left and would take a total of 24 rolls.
Seventh half life we would have 7968 dice left and would take a total of 28 rolls.
Eighth half life we would have 3984 dice left and would take a total of 32 rolls.
Ninth half life we would have 1992 dice left and would take a total 36 rolls.
Tenth half life we would have 996 dice left and would take a total of 40 rolls.
And finally on the eleventh half life we would have 498 dice left and it would take on average about 44 rolls.
So the time it would take for 1 million dice to “decay” to 500 dice would take on average about 44 rolls.
And this is the idea behind carbon dating.
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