# How does carbon 14 have such a perfect halflife?

## Summary:

How do the atoms know which ones must decay first in carbon 14

## Main Question or Discussion Point

Summary: How do the atoms know which ones must decay first in carbon 14

Summary: How do the atoms know which ones must decay first in carbon 14

Carbon 14 has a half life of 5700 years. How do the Atoms know which ones will decay as we have such a perfect half life, why don't they all just decay at the same time or like when you make popcorn and a bunch develope then only and a few a few pop...How do the atoms know which atoms must decay first to give it such a perfect halflife?

## Answers and Replies

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phinds
Gold Member
2019 Award
Atomic decay is a statistical phenomenon. You cannot look at any given atom and say that it will decay in exactly this amount of time. What you CAN do is look at the probability of its decaying in a given amount of time and then use statistics to say what a large number of such atoms will do in the aggregate.

BvU
Homework Helper
2019 Award
Hello Kevin, $\qquad$ $\qquad$ !

Wrong question: it is well known that atoms don't have brains and therefore they can't 'know' anything. It's all really probability. A good thing: the sun would be a hefty atomic bomb if there wasn't.

Drat, Paul was faster ! I really should learn to type faster and keep it legible !

davenn
Gold Member
2019 Award
I really should learn to type faster and keep it legible !
yeah ... get ya act together hahahaa

BvU
jtbell
Mentor
How do the Atoms know which ones will decay
They don't. Each individual undecayed atom "knows" only that it has a probability of 3.8394 x 10-12 of decaying during the next second. In terms of lottery odds, this is one chance in about 260,460,000,000. If it hasn't decayed at the end of that second, it then has a probability of 3.8394 x 10-12 of decaying during the second after that. If it hasn't decayed at the end of that second... etc.

Think of it as a series of separate, independent Powerball lotteries for each individual undecayed atom, one lottery per undecayed atom per second. Each lottery has the same odds, and a new lottery begins every second for an atom that hasn't yet decayed.

(If you're not in the US, replace "Powerball" with whatever super-high-stakes lottery is popular in your country. )

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EPR
Gold Member
He's asking why it has the rather definite probability that it has.

davenn
Gold Member
2019 Award
He's asking why it has the rather definite probability that it has.

No, the OP never mentioned probability. Probably because, until phinds' post,
he didnt know it was a probability/statistical thing

256bits
Gold Member
They don't. Each individual undecayed atom "knows" only that it has a probability of 3.8394 x 10-12 of decaying during the next second. In terms of lottery odds, this is one chance in about 260,460,000,000. If it hasn't decayed at the end of that second, it then has a probability of 3.8394 x 10-12 of decaying during the second after that. If it hasn't decayed at the end of that second... etc.

Think of it as a series of separate, independent Powerball lotteries for each individual undecayed atom, one lottery per undecayed atom per second. Each lottery has the same odds, and a new lottery begins every second for an atom that hasn't yet decayed.

(If you're not in the US, replace "Powerball" with whatever super-high-stakes lottery is popular in your country. )
Could play with that a bit I bet.
Such as, during 5700 years, the probability of decay would be 0.5, or a chance of one out of two.

But on another vein,
Taking your example, could we not state also that, say one microsecond( or nanosecond, picosecond, ... ) after the start of the first second, the undecayed atom has a probability of decaying of 3.8394 x 10-12 during a time interval of 1 second, ( regardless of when the second starts rather than consecutive second ).
Or maybe that is a different probability - just checking my statistics.

DrClaude
Mentor
Carbon 14 has a half life of 5700 years. How do the Atoms know which ones will decay as we have such a perfect half life
What do you mean by perfect? If it is because of the round number, its simply because we don't know the actual value:
https://en.wikipedia.org/wiki/Carbon-14
Wikipedia said:
carbon-14 is unstable and has a half-life of 5,730 ± 40 years

sophiecentaur
Gold Member
What do you mean by perfect? If it is because of the round number, its simply because we don't know the actual value:
https://en.wikipedia.org/wiki/Carbon-14
. . . . .so things cannot be dated with better than 40 years of error. Not as good as that, of course, due to practicalities of measurements in a lab. They measure the relative masses of C14 and products in a sample, I think, rather than using any actual time measurements.

jtbell
Mentor
Could play with that a bit I bet.
Such as, during 5700 years, the probability of decay would be 0.5, or a chance of one out of two.
Quite right. In fact, you can choose any fixed time period (1 year, 10 days, π hours, whatever), which would have a correspondingly different probability or odds.
could we not state also that, say one microsecond( or nanosecond, picosecond, ... ) after the start of the first second, the undecayed atom has a probability of decaying of 3.8394 x 10-12 during a time interval of 1 second, (regardless of when the second starts rather than consecutive second).
Correct. The only thing that matters is that the atom has not yet decayed, at the point in time at which you start its "decay clock."

A related statement is that an unstable atom has no "memory" of how long it's "lived" already. At every instant, it "starts from scratch", so to speak, as far as its decay probability is concerned.

Ibix
I remember asking how atoms knew when to decay. My physics teacher had us do an experiment - we got a box of cubes with one face painted red, and dumped them on the bench. We counted the ones that came up red and discarded them as "decayed" and put the rest back in the box. Repeat.

Since each iteration, on average, leaves you with 5/6 of the survivors from the previous round, you expect the number decaying in the $n$th iteration to be $(5/6)^{n-1}/6$ times the number you start with. It's easy to plot this and see that it's an exponential decay, just like radioactivity. And clearly the little cubes have no memory, nor any way to decide when they should come up red.

You can simulate very large numbers of cubes in a computer fairly easily. The larger the number the less noisy the exponential is.

Tangential: Long, long ago, when I did a 'Nuclear & Radio-Chemistry' (sic) course, I had to extract a trace element and measure its half-life. PDQ handling, 'Seeded Precipitation' etc etc.

I collected and graphed lots of lovely data, but the half-life was waaay too short. Not just 10% off, not even 20% but precisely 50%. So I did it again. Similar results. And a third time, like-wise. In the end, I showed my wonky data to the lab supervisor. He checked my math three ways, queried every failure mode --And he'd seen lots !!-- but agreed I'd (eventually) covered them all. My results stood.

Then, he sucked his teeth, shook his head, wryly warned me to stay away from 'hot' isotopes and, to be sure, to be sure, not tour any nuclear power stations...

Staff Emeritus
2019 Award
. . . . .so things cannot be dated with better than 40 years of error.
No, it means things cannot be dated with better than a fractional error of 40/5730. That is, an item that has gone through two half-lives could only be dated to, at best, 80 years.

As a practical matter, dating accuracy is driven by other factors.

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sophiecentaur
Gold Member
As a practical matter, dating accuracy is driven by other factors.
Dendrochronology is very smart and can span almost the total lifetimes of many very old individual trees - to +/- 1 year.

No, the OP never mentioned probability. Probably because, until phinds' post,
he didnt know it was a probability/statistical thing
I Think I get it, this only works for HUGE Amounts of Atoms, if we were to Try and Carbon Date a Sample with only 100,000 atoms half life it wouldn't work...what would be the smallest sample we could carbon date, like how many atoms for the Statistics to work because it has to be large numbers of atoms or we can get the popcorn effect I am only guessing...

phinds
Gold Member
2019 Award
I Think I get it, this only works for HUGE Amounts of Atoms, if we were to Try and Carbon Date a Sample with only 100,000 atoms half life it wouldn't work...what would be the smallest sample we could carbon date, like how many atoms for the Statistics to work because it has to be large numbers of atoms or we can get the popcorn effect I am only guessing...
You have the right idea, but there is no specific number. You choose how much of an error you are willing to live with in the answer and that, using statistics, tells you how many atoms you need at a minimum to give that degree of accuracy for the amount of time over which you want the accuracy.

No, it means things cannot be dated with better than a fractional error of 40/5730.
It seems odd to me that the uncertainty in this number is that large (it being so widely used). Is it really that big and why?

Staff Emeritus
2019 Award
That uncertainty works out to 0.7%. Ra-226 (half life of 1600 years) is 0.4%. Pu-240 (6600 years) is 0.1%. Th-229 is 0.6%. Cm-246 (4760 years) is 0.8%. Am-243 (7370 years) is 0.3%. Mo-93 (4000 years) is 20%.

So I would say it's more or less typical. It's certainly not an outlier.

mfb
Mentor
No, it means things cannot be dated with better than a fractional error of 40/5730. That is, an item that has gone through two half-lives could only be dated to, at best, 80 years.

As a practical matter, dating accuracy is driven by other factors.
That would only be true if we would do a simple extrapolation. Such an extrapolation would come with a larger uncertainty as the natural C14 fraction in the biosphere does vary a bit over time. Reference samples from trees help calibrating the method over a long timescale, and they don't come with that 0.7% uncertainty.
I Think I get it, this only works for HUGE Amounts of Atoms, if we were to Try and Carbon Date a Sample with only 100,000 atoms half life it wouldn't work...what would be the smallest sample we could carbon date, like how many atoms for the Statistics to work because it has to be large numbers of atoms or we can get the popcorn effect I am only guessing...
The theoretical limit: Let's say you expect that 40,000 C-14 atoms were present initially (based on the amount of stable carbon) and find 10,000. You conclude that 0.25 of the original atoms are still there (corresponding to two half lives, 11460 years), and a calculator computes you the 95% confidence interval: 0.2458 to 0.2543, corresponding to 11320 to 11600 years (small statistical shortcut, don't do that in publications). With a sample that size the randomness of the radioactive decay doesn't introduce a large uncertainty. This sample would have just about 1 microgram of carbon. In practice you'll need larger samples.

Staff Emeritus
2019 Award
Reference samples from trees help calibrating the method over a long timescale, and they don't come with that 0.7% uncertainty.
Is there any object that has been dated to better than 0.7%?

mfb
Mentor
Not to my knowledge, but at least in principle it would be possible to make dating more accurate without knowing the half life better. Calibration (taking into account the variable C-14 ratio in the source material) seems to be the largest uncertainty. Discussion here.

Staff Emeritus
2019 Award
I was thinking the reverse - if you had better dating than the current half-life permits, you use that to improve the knowledge of the half-life.

mfb
Mentor
How, if you don't know the original concentration from an independent source?