I’ve been reading about HL, but I still don’t get why would you use it. So, if half life of coffee is 5h, how that info is relevant when we know that full life is 10 (roughly)? On top of that, how do you get the half-life of a material other than waiting to be completely ‘dead’ and say, ok full life is X, the half life is X/2.
Also, let’s take uranium which in Earth’s crust has a half-life of almost 4.5 billion years.. how did we get this number?
Thank you!
In: Chemistry
Imagine you are a blind person and you lost a lot of coins at home. So now you are trying to find them. So you go through everything, touching with your hand, and the beginning you find coins relatively easily. It’s because there’s a high abundance of coins so anywhere you try there’s one.
But as the coins get rare, the time between two coins get longer and longer. Maybe in tbe beginning you find a coin every five second but later you need a minute for every coin, and as they get really scarce, you perhaps spend hours with the last few coins.
As it turns out, many things in nature have a similar progress. If you drink a cup of coffee, the first bunch of caffeine breaks down very easily (because the enzyme that breaks it down finds them blindly, but at a high rate). Later as the enzyme finds it at lower rates, the amount of caffeine breaking down per minute, gets less and less.
So such things have a very interesting behavior. As the blind person finds less and less coins you cant say that if you lose 100 coins and find 50 of them in one hour, then you certainly find the other 50 in another hour. As you see it’s not the case. In fact what’s happening in such situations is that if you find half of the coins in 1 hour, then you will need another 1 hour to find the half of the leftovers, and another 1 hour to find half of the leftover of leftovers. So if you loose 100 coins, then you find 50 in 1 hour, then you find 25 in another 1 hour, and about 12 in the third hour, and 6 in the fourth hour and 3 more in the fifth hour. And you still haven’t found all of them.
Similarly, if you drink 100mg of caffeine, 5 hours of halflife means that in 5 hours you broke down 50 mg, then another 5 hours 25 mg etc. After a day you still have a couple of milligrams lingering in your body.
As it turns out, braking down of radioactive material follows the same principles. If you have let’s say hundred million of uranium, it takes 4 billions of years to get fifty million of uranium to break down.
But here’s a thing. You don’t need to wait 4 billion years to figure that half is gone. You can wait let’s say one year, measure how little of the uranium is gone and use a mathematical formula to figure how much it takes to decay half of it. Because we know it is gradually slowing, so if I know that finding the first coin takes 5 seconds, and then the next takes 6, the next takes 8, then 10, I can figure how much it will take to find the first 50. Because the slowing has a rule that I can use in a formula. Similarly I can follow the uranium for a year and take it into a formula.
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