How does carbon 14 have such a perfect halflife?

  • B
  • Thread starter kevinmorais
  • Start date
  • Tags
    Carbon
In summary, atoms do not "know" which ones will decay first in carbon 14. The decay process is a statistical phenomenon, where each individual undecayed atom has a probability of decaying during a given time interval. This probability remains the same for each atom, resulting in a half-life of 5700 years for carbon 14. This half-life is not a perfect, round number, but rather a result of our current understanding and measurement capabilities.
  • #1
kevinmorais
8
2
TL;DR 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

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?
 
  • Like
Likes atyy
Physics news on Phys.org
  • #2
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.
 
  • Like
Likes WWGD, symbolipoint, davenn and 1 other person
  • #3
Hello Kevin, ##\qquad## :welcome: ##\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 !
 
  • Like
Likes WWGD and phinds
  • #4
BvU said:
I really should learn to type faster and keep it legible !

yeah ... get you act together hahahaa :wink: :wink: :wink: :wink: :biggrin:
 
  • Skeptical
Likes BvU
  • #5
kevinmorais said:
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. :smile:)
 
Last edited:
  • #6
He's asking why it has the rather definite probability that it has.
 
  • Like
Likes Nutbreaker
  • #7
EPR said:
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
 
  • Wow
Likes Nutbreaker
  • #8
jtbell said:
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. :smile:)
Interesting answer.
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.
 
  • #9
kevinmorais said:
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
 
  • Like
Likes sysprog
  • #10
DrClaude said:
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.
 
  • #11
256bits said:
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.
256bits said:
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.
 
  • Like
Likes 256bits
  • #12
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.
 
  • Like
Likes Spinnor, WWGD, haushofer and 3 others
  • #13
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...
 
  • Like
Likes sysprog, kevinmorais and BvU
  • #14
sophiecentaur said:
. . . . .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.
 
Last edited:
  • Like
Likes rbelli1, sysprog, phinds and 1 other person
  • #15
Vanadium 50 said:
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.
 
  • #16
davenn said:
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...
 
  • #17
kevinmorais said:
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.
 
  • Like
Likes sysprog
  • #18
Vanadium 50 said:
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?
 
  • #19
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.
 
  • Informative
Likes phinds
  • #20
Vanadium 50 said:
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.
kevinmorais said:
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.
 
  • Like
Likes kevinmorais and sysprog
  • #21
mfb said:
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%?
 
  • #22
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.
 
  • #23
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.
 
  • #24
How, if you don't know the original concentration from an independent source?
 
  • #25
To do better than 0.7% with radiocarbon dating means someone has solved that problem.
 
  • #26
Tree rings ??
Dendrochronology is sufficiently advanced that workers now argue over some big volcanic eruptions' cold-snaps possibly causing a one (1) year skip in hemispheric growth.

From such calibration, IIRC, 'tis apparent that atmospheric C14 varies with solar activity etc, leaving the 'calibration curve' for some eras with ambiguities. Context and stratigraphy required...
 
  • Like
  • Informative
Likes vanhees71 and phinds
  • #27
mfb said:
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.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.
Thank You Very Much for all your Help
 
  • #28
Vanadium 50 said:
To do better than 0.7% with radiocarbon dating means someone has solved that problem.
The raw (uncalibrated, and assuming 5730 years) radiocarbon ages can be better than 0.7% as far as I understand. The uncertainty comes from the calibration and other systematic uncertainties. The half life of C-14 doesn't enter the equation any more if there is a calibration available. You look up the C14 fraction you found in a table.
 
  • Like
Likes hutchphd
  • #29
Ibix said:
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.
We still do this - sometimes with dice/die, sometimes with m&ms or skittles ;)
 
  • Like
Likes Ibix
  • #30
rsk said:
We still do this - sometimes with dice/die, sometimes with m&ms or skittles ;)
And do we get to eat the ones that "decay"?
 
  • #31
rsk said:
We still do this - sometimes with dice/die, sometimes with m&ms or skittles ;)
I'm allergic to M&Ms, but I'm not surprised it's still done. It's simple and it does bring home why exponential decay is called "memoryless".
 
  • #32
As a physicist, I'm going to pose a philosophical viewpoint to this whole decay concept. Theoretically, if one started with 1,000 atoms and were able to identify, separate and isolate the 500 atoms that were going to decay sometime within 5700 years, one would end up with the remaining half that would not decay until the 5700 years had expired. Although this challenge has not been attempted yet, it is not really "foolish thinking" because we are applying a perfect "tool," which is a mathematical statistical equation of probability, to a phenomenon of physics, which scientists do not thoroughly understand, (although of course, the tool works quite well). It seems to me, however, that something is changing within the atom, like an internal stop watch, or a clock of sorts, and it is reasonable to assume that an atom that will decay one second from now does not possesses the exact same characteristics or qualities, if you will, as an atom that will not decay for another 5,700 years, or longer. I am proposing that to maintain that these two atoms are identical physically, electromagnetically and in every nuclear-atomic way, is illogical.
 
  • #33
Auston Louis said:
As a physicist, I'm going to pose a philosophical viewpoint to this whole decay concept. Theoretically, if one started with 1,000 atoms and were able to identify, separate and isolate the 500 atoms that were going to decay sometime within 5700 years, one would end up with the remaining half that would not decay until the 5700 years had expired. Although this challenge has not been attempted yet, it is not really "foolish thinking" because we are applying a perfect "tool," which is a mathematical statistical equation of probability, to a phenomenon of physics, which scientists do not thoroughly understand, (although of course, the tool works quite well). It seems to me, however, that something is changing within the atom, like an internal stop watch, or a clock of sorts, and it is reasonable to assume that an atom that will decay one second from now does not possesses the exact same characteristics or qualities, if you will, as an atom that will not decay for another 5,700 years, or longer. I am proposing that to maintain that these two atoms are identical physically, electromagnetically and in every nuclear-atomic way, is illogical.

In other words, there must be an internal "hidden" variable. When a Carbon-14 atom is created, there must be an internal timer set to say after how long it will decay?
 
  • Like
Likes Ibix
  • #34
PeroK said:
In other words, there must be an internal "hidden" variable. When a Carbon-14 atom is created, there must be an internal timer set to say after how long it will decay?
One wonders whether this question will ring any Bells...
 
  • Like
  • Haha
Likes kith, vanhees71, mfb and 2 others
  • #35
Auston Louis said:
I am proposing that to maintain that these two atoms are identical physically, electromagnetically and in every nuclear-atomic way, is illogical.

A proposal that contradicts what we know about thermodynamics.
Are you sure you want to argue from authority here?
 
  • Like
Likes weirdoguy and BvU
<h2>1. How is carbon-14 created?</h2><p>Carbon-14 is created in the Earth's upper atmosphere when cosmic rays from the sun collide with nitrogen atoms. This collision causes a neutron to be knocked out of the nitrogen atom, creating carbon-14.</p><h2>2. How does carbon-14 have a perfect halflife?</h2><p>The halflife of carbon-14 is not technically perfect, but it is very close. This is because carbon-14 has a relatively long halflife of about 5,730 years, which means it takes a long time for half of the original amount to decay. This makes it appear as though it has a perfect halflife.</p><h2>3. How is carbon-14 used for dating objects?</h2><p>Carbon-14 dating works by measuring the amount of carbon-14 in a sample and comparing it to the amount of stable carbon-12. By knowing the halflife of carbon-14, scientists can determine how long it has been since the organism or object died.</p><h2>4. Can carbon-14 be used to date anything?</h2><p>Carbon-14 dating is most commonly used to date organic materials, such as plants and animals, up to about 50,000 years old. It cannot be used to date rocks or other inorganic materials.</p><h2>5. How accurate is carbon-14 dating?</h2><p>Carbon-14 dating is generally considered accurate within a range of a few hundred years. However, there are factors that can affect the accuracy, such as contamination of the sample or changes in the Earth's magnetic field. It is important for scientists to use multiple methods of dating and to carefully consider all factors when determining the age of an object.</p>

1. How is carbon-14 created?

Carbon-14 is created in the Earth's upper atmosphere when cosmic rays from the sun collide with nitrogen atoms. This collision causes a neutron to be knocked out of the nitrogen atom, creating carbon-14.

2. How does carbon-14 have a perfect halflife?

The halflife of carbon-14 is not technically perfect, but it is very close. This is because carbon-14 has a relatively long halflife of about 5,730 years, which means it takes a long time for half of the original amount to decay. This makes it appear as though it has a perfect halflife.

3. How is carbon-14 used for dating objects?

Carbon-14 dating works by measuring the amount of carbon-14 in a sample and comparing it to the amount of stable carbon-12. By knowing the halflife of carbon-14, scientists can determine how long it has been since the organism or object died.

4. Can carbon-14 be used to date anything?

Carbon-14 dating is most commonly used to date organic materials, such as plants and animals, up to about 50,000 years old. It cannot be used to date rocks or other inorganic materials.

5. How accurate is carbon-14 dating?

Carbon-14 dating is generally considered accurate within a range of a few hundred years. However, there are factors that can affect the accuracy, such as contamination of the sample or changes in the Earth's magnetic field. It is important for scientists to use multiple methods of dating and to carefully consider all factors when determining the age of an object.

Similar threads

  • High Energy, Nuclear, Particle Physics
Replies
4
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
7
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
6
Views
1K
  • Art, Music, History, and Linguistics
Replies
3
Views
794
  • High Energy, Nuclear, Particle Physics
Replies
4
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
6
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
24
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
4K
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
986
Back
Top