I’m sure there is an easy answer to this, but for some reason I can’t wrap my head around how a sample of an element can ever decay all the way to zero, when measured in half lives. It seems like you could always split a number in half, it would just be infinitesimally small.
In: Chemistry
Half life isn’t perfect… If we had an infinite number of atoms then half of them would theoretically decay within the half life, however with a finite number of atoms more than half of them can decay within said half life as its just repeated probability…
Here is an example, take 100 **fair** coins and place them face up on a cookie sheet…. Dump them on the floor, now remove any coins that are face down. The face up coins you can put back on the cookie sheet and repeat and count how many repetitions it takes for there to be no coins left. Then repeat this a few times…. The coins, when doing this, have a theoretical half life of 1 iteration (dumping coins) meaning that each time you will expect about 50% of the coins to be taken away… However sometimes more than 50% are taken away and sometimes less than 50% will be taken away. If you increase the number of coins to 1000 then the ratio will move closer to 50% (say it might be 506 heads up and 494 heads down)… Increase it again to say 100,000 coins and you might see something like 50,012 up and 49,988 down, still its getting closer and closer to being 50-50. When you hypothetically increase it to an infinite number of coins the ratio will be 50-50
That is the analogy for half life… Now if I have a 10kg rock of uranium, then I will have something like 10^22 uranium atoms so the ratio is going to be very very close to 50-50. This is also a good introduction to the laws of large numbers.
Edit: bolded the fair in “fair coins” to emphasize that.
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