Why Half life radiation is constant

[pallidin]

One cannot establish "half' unless one knows the "whole"
Else there is no half.

How is it that nuclear decay "knows" this?
Some type of entanglement?

 

[cjl]

One cannot establish "half' unless one knows the "whole"
Else there is no half.

How is it that nuclear decay "knows" this?
Some type of entanglement?

The half is as compared to the total number of atoms. No entanglement needed. If it would make you happier, another way to look at the half life is that it is the time in which any given atom has a 50% probability of decaying. No connection to any other atoms (or knowledge of them) is needed.

 

[russ_watters]

One cannot establish "half' unless one knows the "whole"
Else there is no half.

I thought you said above you were onboard with exponential decay and just wanted to know why? You even gave an example of radioactive decay you accepted. Now you're not accepting it anymore? Did you read the above posts regarding stability?

 

[QuantumPion]

One cannot establish "half' unless one knows the "whole"
Else there is no half.

How is it that nuclear decay "knows" this?
Some type of entanglement?

No. You are thinking of the semantics of the phrase "half-life" incorrectly. The half-life is NOT the time it takes a particular sample to decay by half. There is no difference between the sample you started with, and half of that sample. It is the time it takes ANY AMOUNT to decay by half. The half-life is completely independent of how much material you have. The half-life is defined as:

$t_{1/2}=\frac{ln \: 2}{\lambda}$

Lambda is the decay constant, which is a particular value for each isotope. The half-life is just a different mathematical representation of this decay constant. Another way of expressing half-life is the mean lifetime, tau:

$t_{1/2}=\tau \: ln \: 2$

The mean lifetime is the average time it takes for any atom of a particular isotope to decay, even if it is just a single atom by itself.

The nuclear decay of an atom does not know about any other atoms around it. There is no entanglement. This is precisely the point.

 

[sophiecentaur]

One cannot establish "half' unless one knows the "whole"
Else there is no half.

How is it that nuclear decay "knows" this?
Some type of entanglement?

Exactly the same exponential decrease happens with charge stored on a capacitor or water draining from a small hole in the bottom of a cylindrical tank. In all cases, the rate of decrease is proportional to the level at any given time.
Why introduce "entanglement" when it's not necessary. You seem to be introducing it as just a buzzword, for no reason.

 

[nasu]

One cannot establish "half' unless one knows the "whole"
Else there is no half.

How is it that nuclear decay "knows" this?
Some type of entanglement?

The "whole" is the initial quantity. "Half" does not refer to "half of the whole life" but to "half of the initial quantity", which is well established.

 

[pallidin]

No. You are thinking of the semantics of the phrase "half-life" incorrectly. The half-life is NOT the time it takes a particular sample to decay by half. There is no difference between the sample you started with, and half of that sample. It is the time it takes ANY AMOUNT to decay by half. The half-life is completely independent of how much material you have. The half-life is defined as:

$t_{1/2}=\frac{ln \: 2}{\lambda}$

Lambda is the decay constant, which is a particular value for each isotope. The half-life is just a different mathematical representation of this decay constant. Another way of expressing half-life is the mean lifetime, tau:

$t_{1/2}=\tau \: ln \: 2$

The mean lifetime is the average time it takes for any atom of a particular isotope to decay, even if it is just a single atom by itself.

The nuclear decay of an atom does not know about any other atoms around it. There is no entanglement. This is precisely the point.

Ah, yes, I think I'm beginning to understand. Thank you.