Is there something special about the halfway point? Does the decay happen at a steady pace or exponentially?
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the full-life for any radioactive substance is dependent on the amount of the substance and is indefinite.
the half-life is constant.
the decay happens randomly but follows the rule that within the half-life probabistically half of the substance will decay. with large numbers of atoms of the substance this is a near absolute rule. with a few atoms it’s a crap shoot.
eg if I have a 1kg block of U235, I know that in 700 million years i’ll have 500grams left, another 700 millions years and i’ll have 250grams, but if I have 1 atom of U235 I might have to wait ’til the end of the universe before it decays.
Because the “full life” never arrives. It just gets closer and closer to it without ever quite reaching it.
Imagine the equation y = 1/x.
It has values like this:
x y
—— ——-
1 1
10 0.1
100 0.01
1000 0.001
10000 0.0001
No matter how big you make x, y never quite reaches zero. It gets closer and closer to it because the fraction 1/x gets smaller and smaller, but it never quite reaches zero.
There is no such thing as “how big does X have to get in order for Y to fall all the way to zero?” if Y won’t *ever* quite become zero all the way.
If you don’t already know what the graph 1/x looks like, click this link and you’ll see a graph of it: https://www.wolframalpha.com/input?i=y+%3D+1+%2F+x
A phenomenon like this is what radioactive decay is trying to describe. You can’t say “after X years all the radioactive isotopes will be gone and it will be all be done decaying”.
So instead what you can do to describe the “shape” of the decay is to just pick the point where about half of it will be gone. THAT is a point that can actually be reached. In the formula y = 1/x, y will be 1/2 when x gets up to 2.
Now, actual radioactive decay isn’t exactly a 1/x kind of phenomenon, but for ELI5 purposes it gets you the idea.
—–
Interesting footnote: because matter is made of countable quantum stuff, and not infinitely continuous, technically there *will* eventually be a point where literally all the decay is actually finished, as you cannot have less than one atom of an isotope left. But because there’s an *enormous* number of atoms, we may as well model it as if it’s infinitely divisible because it would be eons before any little chunk of material actually could reach that point.
It’s more like a speed than a time. The time it takes a chunk of stuff to decay will depend on how much of it you have, so you can’t just put some “decay time” on an element that works in every case.
Instead, half life tells us how fast it will decay, and we can apply that to any amount that we might have.
Now, the reason we use half life and not like atoms-per-second or something is because radioactive decay is exponential, not linear. The more of it you have, the more atoms will decay per given length of time. The thing that stays constant, though, is how long it takes for *half of whatever you have* to decay. Got a billion atoms? In one “half life” of time you’ll have 500 million. Then 250 million. Etc. You can see how the speed decreases over time, and that’s why a linear unit wouldn’t work.
(note that there’s nothing special about using half. We could just as well define third lives or ninth lives, which would tell us how long it takes for a third or ninth of whatever we have to decay. But this is just unnecessarily convoluted, so we use halves to keep things as simple as we can)
Lol eli5 “radioactive decay.” Because half go bye bye. No matter size, same time for half go bye bye.
Assume Half-life of 10 years.
A = first 10 years 50% of this substance remains
B = next 10 years 50% of A remains.
C = another 10 years 50% of B remains.
And this goes on forever, since you can never fully decay.
Thus you never can have a full life.
There is nothing special about half.
Imagine you had a million bajillion coins. If you flipped all of them and pulled out the heads, you’d expect 1 half life to be 1 flip. About half of them would be heads.
Do the rest of the tails become heads on the next flip? No. But about half of them do. In 1 flip, or 1 half-life.
Half-life is used because the decay is not on any kind of timer, but acts like the coin flips.
A small set of coins may be tails for several flips in a row and may seem to not follow the rules of chance and would be unlikely. But it would be really unlikely to have a million gazillion coins all tails over and over.
Atoms that decay are tiny, and even a teensy bit can have a million brazillion atoms. So they seem to follow the rules very well.
For fun, imagine flipping a million coins. I’m going to alter some numbers as I go to follow through easier.
1,000,000
500,000
250,000
128,000 (I know)
64,000
32,000
16,000
8,000
4,000
2,000
1,000 after 10 flips
999,000 decays in 10 flips.
How long will it take to go to 1?
1,000
500
250
128 (I know again)
64
32
16
8
4
2
1 after 10 more flips
1 of those 1,000,000 coins was tails 20 times in a row. 500,000 of them were heads on the first flip.
Will the 1 remaining coin flip to heads on the next toss?
Maybe.
Because a full life would be infinity !
You misunderstand what a half-life is. It isn’t ‘how long something lives, divided by two’.
It is a measure of a specific form of decay (originally radioactive decay but it could be anything that loses stuff in the same way).
The ‘same way’ is that, however much stuff you start with, it always takes a fixed time for the quantity of it to halve.
So, if you have a bag of 1000 potatoes and after 100 days, 500 of them have rotted away, and then after a further 100 days, 250 of those remaining 500 have rotted away, and after a furthet 100 days, 125 have rotted away, so that count-versus-time looks like this:
0 1000;
100 500;
200 250;
300 125;
400 62.5;
500 31.25
then you could say that this item has a half life of 100 days.
I’m not claiming that this really works like this for root crops but, if it did, you could legitimately use the ‘half life’ to describe it
As I said, it’s normally used to describe radioactive particles decaying into something else.
This is called an ‘exponential’ decay, meaning that the speed of decay is proprtional to how many there are.
You can see in the above that we get into decimal fractions quite easily. It’s not clear how this translates to the subatomic world, but it illustrates how something decaying like this will, theoretically, never drop to zero. That is what I meant by ‘full life being infinite’.
You don’t have to use half-life, you could use ‘quarter life’ or ‘one tenth life’. Nobody does this, however, because other people wouldn’t know whether you meant ‘a quarter have decayed’ or ‘ a quarter remain’. There is obviously no such ambiguity with ‘half’.
Half lives of radioactive elements can vary from below nano seconds to above milliions of years.
Let’s say I eat half of a pizza. And then I eat half of what’s left. Continuing to only eat half of what is leftover will go on forever, and so the “full-life” of the pizza is infinite. Inifity doesn’t help distinguish between things, so I might as well just tell you how long it took to eat the first half.
It’s graphed as a curve that never quite reached 0, but it has regular timing for every (percentage) loss. I discovered when I took a physics class a number of years ago that you can fact use a quarter life just as readily, and the math works, but half-life is easiest to grasp, intellectually.
If you take a piece of paper and fold it in half again and again. Then how many times do you have to fold it until the paper is gone?
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