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
I’ll just accept the caffeine half life as 5h without looking into it. This would be the decline over time.
At the start, let’s say there is 128mg from a coffee
After 5 hr, there is half (64mg)
After 10 hr, there is half again (32mg)
After 15hr, 16mg
After 20hr, 8mg…
After 100 hr, 122ng (0.122mg)…
After 200 hr, .116pg (0.000000116mg)
It halves every half-life, until there’s so little that you don’t notice it / can’t measure it. Bodies are complex so this reality might vary, but it’s the idea of a half life..
Why? Imagine a crowd of people flipping coins every 5 hours. Every coin flip, the people with heads remain and people with tails are eliminated. You’ll eliminate about half of the people every time, and it will take ages to eliminate them all. The caffeine is like a a mob of molecules flipping coins, they have a constant 50% chance of breaking down per 5 hours.
half life == easy math.
if half life 1 hour then:
amount of thing * 0,5^hours = how much thing left after hours
The half-life is always the same, no matter how much you start with.
An espresso has about 200mg of caffeine. The half life is 5 hours, which means that 5 hours later, you’ll have about 100mg of caffeine in your system. 5 hours after that, you’ll have 50mg. Another 5 hours later, you’ll have 25mg.
This means that if you drink two shots of espresso back to back, you’ll start out with 400mg, and 5 hours later, you’ll be down to 200mg.
Caffeine isn’t like the fuel in a car that depletes at fixed rate (assuming you’re running the engine in a consistent way). It’s not really possible to wait until it’s all gone, and it doesn’t really make sense to do that anyway.
With fuel in a car, whether the tank is full, half full, or only has a little bit of reserve left, it doesn’t change the power of the engine. But with caffeine, the power of the effect is related to how much you’ve taken. That 400mg double espresso is going to give you quite a kick, maybe even some jitters. When you only have 25mg left in your body, you’re not going to notice much of an effect any more.
So with a car, if you’re going for a road trip, you can fill the tank up all the way, and you’re good to go all day. But with coffee, there’s a big difference between starting the day with a double espresso versuses sipping chai latte throughout the day, even if it’s the same amount of caffeine overall. With the double espresso, you’ll get a big kick, which will taper off throughout the day, but sipping a lighter caffeine drink will maintain a more stable caffeine level.
Things decay at an exponential rate. Every certain amount of time, a certain percent decays.
If you limit this to pure math, take the number 100 and say it decays at a rate of 10% per day. The first day, 10% is 10, so 100-10 is 90. The second day, 10% is 9, so 90-9 is 81.
Let’s skip ahead to 50. 10% is now only 5. When we began, 10% was 10, now it is 5. You can see that we approached the halfway point very fast, but from here we will approach 0 very slow. This is what “half-life” means.
There are many things we really care about the potency of. Often, by the time we reach 50%, those things are no good for their original purpose. Medicine is a primary example of why this is important, because it loses potency as it decays and can even turn into something dangerous to consume in rare cases.
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.
Say you have 100 coins in front of you on a table. You flip all of them and discard every coin that comes up tails, keeping the heads. Then you take the remaining coins and start over, repeating the same procedure for another round, and then another, and so on.
After one round, you will have *approximately* 50 coins left. Not exactly, because it’s random, but chances are it will be close to 50, since every coin has a 1-in-2 probability of landing on tails. Similarly, if you start the second round with 50 coins, you’ll have roughly 25 coins left at the end of it, and so on.
This means the half-life of your coins is a single round of this silly game. In every round, you lose (on average) one half (50%) of your coins. However, **this does not mean that you lose all your coins in two rounds**. After all, we already said that after round 2, you’ll likely still have around 25 coins left. And it will take several more rounds to lose them all. After round 3, you’ll have about 12.5 of them (that is, if you played this game many many times, and every time you noted down how many coins you had left after round 3, it would average out to 12.5). After round 4, you have about 6.25, then 3.125 after round 5, and so on. On average, you can expect to lose your last coin in round 8, most of the time that you play this game (but sometimes you lose it earlier and other times later).
So you see that the “full life” of your initial 100 coins is a lot longer than twice the half life. Not only that, but if you started with more coins, then it would take longer still. With an initial stack of 1000 coins, you need another 3 rounds or so before you lose your last coin (on average). If you start with 10,000 coins, you’re up to 14 rounds. Even though all this time, the half life of your coins is still one single round.
Half-lives are useful to describe scenarios like this, where every element in a population has some chance of decaying, or vanishing, or otherwise being removed from the population, over a given interval. This is very different to things that decay, or diminish, or shrink (or whatever) at a fixed rate. If it takes me 10 minutes to empty half of my pool, then it probably takes me another 10 to empty the other half. If it takes me 3 days to finish a loaf of bread, it takes me 1.5 days to finish half a loaf. For those situations, it makes no sense to talk about a “half-life”, and that’s why we don’t do that – we just talk about whatever the (average) rate is at which something gets used up.
As for how you measure half-life, you don’t have to wait for all of your initial atoms to decay, or even for half of them to do so. For many elements, that could take millions of years. Instead, you can use math to work it out more quickly. Suppose, for instance, that in our game we used biased coins that came up heads 84% of the time. I could find out that probability pretty accurately just by observing one round of the game, if we started with enough coins (e.g. start with 10,000, have 8423 left after round 1, then my estimate of the probability is 84.23%). From that probability, I can extrapolate that it would take about 4 rounds (0.84^4 ≈ 0.5) to lose half the coins, and so that tells me the half-life. Similarly, starting with a sample of many atoms, you just need to measure for long enough to get a precise idea of the decay probability over a given time interval, and you can then extrapolate that to find the half-life. Half-life is just a convenient, standard way to express the probability that atoms will decay over a given time span, and you can convert between the two as needed.
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