Why Half life radiation is constant

[sophiecentaur]

Probability

 

[I_am_learning]

Oh! wow, I don't know the answer to gmax. Perhaps quantum mechanics has the answer.

 

[Dadface]

OK - suppose I get 1000 people in a room & give them each a coin. Then I shout 'one, two, three, flip!' and they all flip. Those with heads, leave the room. Then we do it again, "1, 2, 3, flip!' and so on. What's the half-life? It depends on how frequently I call for the flip. If they flip once every 30 seconds, then the half life is 30 sec. So far so good, right?

So why does Iodine 131 'flip its coin' every eight days, vs, say, cesium-137 which 'flips its coin' every 30 years? What's the mechanism? Not to speak for palladin, but I think maybe that's really his question.

That makes a more interesting question.In terms of mathematics we can say that if the activity is directly proportional to the number of atoms then the activity is equal to the number of atoms times a constant which is a property of the isotope this constant being related to half life. The question now becomes:
Why do different isotopes have different constants and half lives,in other words what is the mechanism?
The answer ,quite simply is er

I don't know and if I did know I have forgotten it

A great question

 

[sophiecentaur]

I could ask WHY they would all be the same and, if they were, what would that 'same' value be?

 

[Dadface]

Probability

Yes but why is the probability different for different isotopes?What is it about the structure of isotopes that makes them decay at different rates?

 

[russ_watters]

But why is nuclear decay qauntity dependent? Why?
WHAT is the mechanism that demands that dependency??

Radioactive particles decay based on probability because they are unstable. A simplistic way of thinking about it is that the nucleus of the atom is vibrating and the forces holding it together aren't quite strong enough to hold it together. The vibration is a random motion but has a certain intensity and eventually a proton gets tossed-out.

It's similar to what happens if you take an empty soda can, put a pebble in it and shake it. The motion of the pebble is more or less random, but it will eventually find the hole and escape.

 

[sophiecentaur]

Radioactive particles decay based on probability because they are unstable. A simplistic way of thinking about it is that the nucleus of the atom is vibrating and the forces holding it together aren't quite strong enough to hold it together. The vibration is a random motion but has a certain intensity and eventually a proton gets tossed-out.

It's similar to what happens if you take an empty soda can, put a pebble in it and shake it. The motion of the pebble is more or less random, but it will eventually find the hole and escape.

To pursue the analogy further, the size of the hole would represent the stability of the atom. Big hole - less stability and small hole - more stabiltiy. Each isotope has its own particular size of 'hole'. Not surprisingly.

 

[pallidin]

So why does Iodine 131 'flip its coin' every eight days, vs, say, cesium-137 which 'flips its coin' every 30 years? What's the mechanism? Not to speak for palladin, but I think maybe that's really his question.

Exactly.

 

[AtomicJoe]

I have no problem with the exponential process.
Without it we would not have, for example, carbon dating.

As such, it has been indicated that my example of gasoline combustion is a linear, quantity-independent phenomenon.
Fine. I'm OK with that.

But why is nuclear decay qauntity dependent? Why?
WHAT is the mechanism that demands that dependency??

The burn of fuel in an engine is controlled by the carb or fuel injection settings.
That is independent of the quantity of fuel (until it runs out).

The rate of decay of an atom is controlled by a random process, God playing dice if you like,
if he rolls a 6 the atom decays. The more atoms you start with the more will decay, leaving less atoms. The chance of an atom decaying remains the same though, you just have less atoms and hence less decays per second.

Nobody really know what controls the decay as far as I am aware, at that level things seem to be governed by probability alone.

Einstein once said God does not play dice, seems he was wrong!?

 

[AtomicJoe]

Exactly.

Different atoms are more stable than others, I am not sure if the reason for this is known.
I have an idea but it is speculation so I will not say.
(Also there might be Nobel prize on offer for it )

 

[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.