Is there something special about the halfway point? Does the decay happen at a steady pace or exponentially?
In: 910
It’s not half the time it takes to decay, it’s the time it takes for half the substance to decay, it’s more like halving-life
the reason you can’t measure the “full life” is because it’s exponential, the more you have the faster it decays, the less, the slower, which is why it takes the same time to decay one half no matter the size you have
So you can basically keep dividing in two forever, after 2 half-lives you have 1/4 th of the original, after 3 you have 1/8 th and so on, since there’s a huge amount of atoms it’s almost impossible for them to all decay
It’s exponential decay, which for a large number of atoms is very steady. Which means that for a given sample the number of atoms decaying per second isn’t constant.
Half-life is just a convenient way to characterize the rate; you could also use the chance of an atom decaying in the next second, year, whatever. Or the number of atoms decaying per second per gram of an isotope.
[edit]E.g. Iodine-131 (https://www.wolframalpha.com/input?i=iodine-131 ):
* half-life | 8.025 days (8.024 to 8.026 days)
* mean lifetime | 11.578 days (11.574 to 11.582 days)
* decay constant | 9.9967×10^-7 per second
* specific activity | 4598.8 TBq/g (terabecquerels [trillion decays per second] per gram)
The half-life isn’t the half-way point. That is, if something has a half-life of 5 years, that doesn’t mean it all decays in 10 years, it means that it takes 5 years for half the substance to decay. In the next 5 years half the remaining substance will decay, and so forth.
In broad terms, any element’s ‘full-life’ is infinite.
Like that thought experiment about only being able to travel half the distance between two points (which would require an infinite amount of travels), the “half-life” can only decay half of the element at a time. And unlike the thought experiment, it does not take less and less time as the amount gets smaller so it really is improbable to get from the start and end up at 0 in conventional physics (exceptions exist outside of ELI5).
Radioactive decay work so each atom has a low probability of decaying at each moment in time. They have also no memory so the probability does not change over time.
Let’s say we have 1000 million atoms and 5% decay in each time unit, that means 95% survive. So after 1-time unit we have 1000* 0.95 = 950 million after two time units we have 1000* 0.95 * 0.95 = 1000 * 0.95 ^(2) = 902.5 million
Lets do that. The number is rounder than do integer million but calculations are done with decimals. The number are at the end of the post
We have 500 between 13-14 time units we have 250 at 27= 13.5 * 2 we have 125 after 40-41 time units 13.5 * 3 = 40.5
So the number of atoms we have get halved after around 13.5 time tune if we use 5% each time unit. You always get a result like this is if you in each unit of time use come a percentage of all. You could do the calculation 0.95 ^ t = 1/2 and the solution is t is aproximalty 13.5134
This only works if you have a huger number of atoms, there is a reason I used millions. If you only have a single atom you have no idea when it will decay but if you have a billions you can be quite sure how many will decay in a unit of time. A single atom can in principle last forever and never decay even if it is radioactive. It is not likely but possible.
So half-life is the average time it takes for half of a large sample of atoms to decay. There is not a full life for an atome.
It is a bit like if you have a single six-sided dice each throw can be 1 to 6 but if you have 100 dice and throw all of them and take the average value it will be close to 3.5.
0 1000
1 950
2 903
3 857
4 815
5 774
6 735
7 698
8 663
9 630
10 599
11 569
12 540
13 513
14 488
15 463
16 440
17 418
18 397
19 377
20 358
21 341
22 324
23 307
24 292
25 277
26 264
27 250
28 238
29 226
30 215
31 204
32 194
33 184
34 175
35 166
36 158
37 150
38 142
39 135
40 129
41 122
42 116
I like to think of Radioactive decay like an onion. Consider each half-life like a layer of an onion, but each layer is equivalent to half of its original size.
So lets the onion has a half-life of 5 years. After 5 years, is will lose a layer, which equivalent to have its size. The size is reduced by half, but subsequent layers will take another 5 years to shed and so on until there are no more layers to shed
Because it is random it never totally decays so there is no full life. So if you have an element with a half life of a year, after a year half of it would have decayed, then over another year a half of the remaining will have decayed so you still have a quarter still yet to decay another year an eighth remains another year a sixteenth continuing on forever. https://youtu.be/AaDwk8UCrew
These isotopes don’t have a fixed lifespan.
What they do have as a fixed chance for an atom to decay at any single moment.
This means you can say that in x-time half of the atoms you currently have will have decayed.
Take cobalt-60 for example.
It has a half life of 5.27 years.
So if you have some cobalt 60 right now you will have half of it left after 5 years and quarter years.
This does not mean that in 10 and a half years all of it will be gone.
Every 5 and a quarter years the amount you will have left halves.
After 10 and a half years you will have a quatre left and after 15 3 quarter years you will have an eight left and after 21 years you will have a sixteenth left.
At some point in the future you will have so little left that it will become undetectable and eventually the last atom will really be gone.
However those points aren’t really useful to know.
You want to know how fast it disappears and half life is a useful measure to know about that.
Explanations of half-life on the thread are excellent. There actually is a case where we consider “full life”, at least sort of. For nuclear medicine purposes, we consider a radioactive material no longer physiologically relevant after 10 half-lives, so that can be considered the “full life” biologically speaking. For instance, iodine 131, used to treat overactive thyroid and some types of thyroid cancers, has a half-life of 8 days. After 80 days, or 10 half-lives, there’s simply not enough radioactivity left to be effectively bombarding cancer cells. (There’s also the biological half-life, which is the body eliminating the foreign material, but that’s outside of ELI5 considerations.)
Imagine you have 1 person sitting in a concert hall. You want to know when they’ll cough. Issue is that there us no reason why they should ever cough. They could sit there for all eternity and not cough once.
Right so… you do this with two people. Still hard to say. However if you get enough people, someone will cough and when they do you ask them to leave. Someone will statistically cough up almost instantly if you got enough people. However the less people you have less likely they are to, since there is no reason why they should ever cough.
Half life is just the definition we have for statistical probability of half of the audience having coughed and left the concert hall.
Since atoms are not actually “real solid” things. They are made of particles of which we can only say that they are probably in a certain position at a certain time. Electrons for example can be wherever they want to be in their probability space; there is no reason why they should be in a specific place at a specific time, so we can only say that they are probably there. Issue we face as our microchips are getting smaller is that electrons can pass (tunnel) through insolators. Since they just decrese the possibility of electron being at the other side of it.
It is the same thing with light. You don’t know where it is until you have interacted with it. Until that it can be anywhere it isn’t probability area. There us no reason why light released from decay of an atom has to go to certain direction; it is just a burst of energy, it goes where ever it wants and you can only say that it probably is somewhere.
So in short, once your mass of atoms has decayd to on last atom. There is no reason why it should ever decay. Halflife just says that in this time period there is 50% chance that it has.
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