# How Does Carbon 14 Decay so well

#### ashesmi

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?

#### Woody

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.

#### benit13

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...

topsquark

#### ashesmi

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

#### ashesmi

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

#### Woody

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.

#### benit13

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!

topsquark

#### ashesmi

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!

#### ashesmi

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.