How Does Carbon 14 Decay so well

Nov 2019
11
0
toronto
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 a few a few pop...How do the atoms know which atoms must decay first to give it such a perfect halflife?
 
Jun 2016
1,198
565
England
Just 14 grams of Carbon 14 contains over 600,000,000,000,000,000,000,000 atoms
every now and again 1 of them pops
5700 years is 999340416000000 seconds
a bit of arithmetic gives over 300,000,000 atoms decaying per second.
So each individual atom decays in a totally random way,
But in the end the numbers are so huge that it averages out statistically to a clearly defined half life.
 
Oct 2017
578
297
Glasgow
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 a few a few pop...How do the atoms know which atoms must decay first to give it such a perfect halflife?
Decay is a random process, just like rolling a die. Sure, if you roll 10 dice, you might get 10 sixes, but the probability is very, very small. Now imagine the probability or rolling \(\displaystyle 10^{22}\) dice and getting all sixes...
 
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Nov 2019
11
0
toronto
So if the Sample is so small in the amount of Atoms, lets say 100,000 atoms Half Life Does Not Apply and Carbon Dating Will Not Apply. What is the Smallest Sample one can take to get the half life to show up? BTW Thank You for the well Thought out Answer. How many Atoms do we need to do Carbon Dating as it Only works for HUGE Amounts, after we break up the sample so small we could get the popcorne effect...Thank You Again
 
Nov 2019
11
0
toronto
Just 14 grams of Carbon 14 contains over 600,000,000,000,000,000,000,000 atoms
every now and again 1 of them pops
5700 years is 999340416000000 seconds
a bit of arithmetic gives over 300,000,000 atoms decaying per second.
So each individual atom decays in a totally random way,
But in the end the numbers are so huge that it averages out statistically to a clearly defined half life.
So if the Sample is so small in the amount of Atoms, lets say 100,000 atoms Half Life Does Not Apply and Carbon Dating Will Not Apply. What is the Smallest Sample one can take to get the half life to show up? BTW Thank You for the well Thought out Answer. How many Atoms do we need to do Carbon Dating as it Only works for HUGE Amounts, after we break up the sample so small we could get the popcorne effect or see the randomness with no halflife...Thank You Again
 
Jun 2016
1,198
565
England
1 milligram of carbon contains over 50,000,000,000,000,000,000 atoms,
however, carbon 14 is rare, only about 1.5 atoms per 10^12 of carbon atoms are carbon 14
so about 40,000,000 atoms of carbon 14, per 1 milligram of carbon.
Gives about 3500 carbon 14 atoms decaying per year per milligram of carbon.
So the radio carbon dating does get less accurate with micro samples.
 
Oct 2017
578
297
Glasgow
So if the Sample is so small in the amount of Atoms, lets say 100,000 atoms Half Life Does Not Apply and Carbon Dating Will Not Apply?
Yes, they will still apply, but as you start to have a smaller and smaller sample of atoms, you will have a more discrete looking decay curve (i.e. it will start to look "chunkier" rather than smoother) and you might notice more deviations away from the curve since a few decays will now be resolvable on your graph.

What is the Smallest Sample one can take to get the half life to show up?
The half-life is independent of sample size, but having a very small sample makes it harder to derive a reliable half-life (just like anything else).

For very small samples, another measurable quantity is the decay time, where the time taken for a particle's state to decay is measured. This also allows an estimate of the half-life to be determined.

BTW Thank You for the well Thought out Answer. How many Atoms do we need to do Carbon Dating as it Only works for HUGE Amounts, after we break up the sample so small we could get the popcorne effect or see the randomness with no halflife...Thank You Again
Because your sample is smaller, the discrete nature of your system is more obvious.

Half-life is a property of the type of decay, along with others (like the decay constant), and is independent of sample size, but like all random systems, deviations from estimates become more obvious at smaller scales. In some ways, it is a lot like popcorn!
 
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Nov 2019
11
0
toronto
Yes, they will still apply, but as you start to have a smaller and smaller sample of atoms, you will have a more discrete looking decay curve (i.e. it will start to look "chunkier" rather than smoother) and you might notice more deviations away from the curve since a few decays will now be resolvable on your graph.



The half-life is independent of sample size, but having a very small sample makes it harder to derive a reliable half-life (just like anything else).

For very small samples, another measurable quantity is the decay time, where the time taken for a particle's state to decay is measured. This also allows an estimate of the half-life to be determined.



Because your sample is smaller, the discrete nature of your system is more obvious.

Half-life is a property of the type of decay, along with others (like the decay constant), and is independent of sample size, but like all random systems, deviations from estimates become more obvious at smaller scales. In some ways, it is a lot like popcorn!
AMAZING Thank You for your Amazing Answer...
 
Nov 2019
11
0
toronto
1 milligram of carbon contains over 50,000,000,000,000,000,000 atoms,
however, carbon 14 is rare, only about 1.5 atoms per 10^12 of carbon atoms are carbon 14
so about 40,000,000 atoms of carbon 14, per 1 milligram of carbon.
Gives about 3500 carbon 14 atoms decaying per year per milligram of carbon.
So the radio carbon dating does get less accurate with micro samples.
Thank YOU To for your amazing Answer
 
Apr 2017
525
130
Thank YOU To for your amazing Answer
I think your being magnanimous , ashesmi ... that was a very probing question , and I don't think it's been answered yet ...

You are basically asking what is the mechanism by which the atoms know when to pop .... This of course applies to ALL atoms ...every single isotope of every single element has a half life , so called "stable" isotopes just have very long half lives ....

What causes them to pop? ...no one knows ... One idea (off the top of my head) is that there is a flux of unknown particles whizzing around ... different isotopes have different interaction cross sections for them , when an atom interacts with one it just pops ...Imagine bullets flying around and atoms are balloons of different sizes, a big balloon equates to a short half life