Why Half life radiation is constant

[pallidin]

Huh, well, how about this:

I have 1 gallon of gasoline in an engine.
With a constant load, 1/2 gallon is "burned" in x amount of time.
The remaining 1/2 gallon will "burn" at the same rate.
The "full life" is 2x.

The above is obviously true, to me anyway.

Of course, nuclear decay is obviously a different process than combustion.
I'm OK with that, so I must be missing something here.

 

[Vanadium 50]

The rate of combustion is constant.
The rate of nuclear decay is proportional to the amopunt of material.

 

[QuantumPion]

Huh, well, how about this:

I have 1 gallon of gasoline in an engine.
With a constant load, 1/2 gallon is "burned" in x amount of time.
The remaining 1/2 gallon will "burn" at the same rate.
The "full life" is 2x.

The above is obviously true, to me anyway.

Of course, nuclear decay is obviously a different process than combustion.
I'm OK with that, so I must be missing something here.

Nuclear decay is not a constant load. There is no good car analogy I can make since they are completely unrelated processes in every way. You just have to go back to my penny analogy.

 

[pallidin]

The rate of combustion is constant.
The rate of nuclear decay is proportional to the amopunt of material.

@Vanadium
Is there a specific reason for that differentiation?

 

[pallidin]

Nuclear decay is not a constant load...

I assume, with natural nuclear decay, that there is no load at all.??

 

[DrGreg]

Huh, well, how about this:

I have 1 gallon of gasoline in an engine.
With a constant load, 1/2 gallon is "burned" in x amount of time.
The remaining 1/2 gallon will "burn" at the same rate.
The "full life" is 2x.

The above is obviously true, to me anyway.

Of course, nuclear decay is obviously a different process than combustion.
I'm OK with that, so I must be missing something here.

The difference is that radioactive decay is a random process. Burning gasoline is not.

Go back and read post #30, or post #25. They are useful analogies.

The probability that an undecayed atom will decay within any period of time equal to a half-life is always 50%. The atom has no memory of the past, so that last sentence is true no matter whether the atom has just been created or it has remained undecayed for 100 years.

 

[pallidin]

The difference is that radioactive decay is a random process. .

But, the first half is definitive. That's not random.

 

[russ_watters]

@Vanadium
Is there a specific reason for that differentiation?

Do you understand the coin flipping analogy? Just because you flip 100 pennies and get 50 "heads" the first time doesn't mean the other 50 will be heads the second time.

But, the first half is definitive. That's not random.

What's random is which atom (or which penny) decays in that half life. It is completely impossible to predict which will decay and which won't.

 

[pallidin]

It is completely impossible to predict which will decay and which won't.

Therefore, the first 1/2 is random as well. Right?

As such, two bulk same-element samples will decay differently. They are random.

 

[russ_watters]

Therefore, the first 1/2 is random as well. Right?

As such, two bulk same-element samples will decay differently. They are random.

I said it is impossible to tell which will decay. But the half life itself is not random, it is a matter of probability.

Again, do you understand how it works with coin flipping? It is exactly the same phenomena, mathematically.

 

[pallidin]

Coin flipping has absolutely nothing to do with this.
Coin flipping is a macroscopic phenomenon with specific determinism; By virtue of uneven halves, a coin flipped is subject to strick deterministic rules.
Complicated? Yes, but wholly deterministic.

Anyway, back to the subject...

 

[russ_watters]

Coin flipping has absolutely nothing to do with this.

Whether you want to believe it or not, they obey exactly the same mathematical rules. The universe doesn't care if you like the way it works.

You do realize that radioactive decay and the phenomena of a half life has actually been observed, right? We're not making this stuff up!

Half life - or exponential decay - is a mathematical phenomena that describes the behavior of many physical systems: http://en.wikipedia.org/wiki/Half-life
http://en.wikipedia.org/wiki/Exponential_decay#Applications_and_examples

 

[Dadface]

Pallidin
Suppose I had N particles of a particular radioisotope and you had twice as much in other words 2N particles of the same isotope.

Do you think it is reasonable to say that the activity,A,(number of decays in one second)of your sample is twice the activity of my sample?
Whatever you may think experiment shows that if N is "large" the assumption is a good one and that on average A is proportional to N.The constant of proportionality is the "decay constant" which is a constant of the isotope.you can look up the details in any half decent textbook.
What these results show us is that the isotope is not decaying at a constant rate but at a reducing rate.As N gets smaller then so does A and A reduces exponentially with time.
Exponentials never reach zero so some may argue that the activity never becomes zero.There is no evidence to back this up because as N gets smaller the assumption that A is proportional to N becomes less valid and the maths goes flying out the window.As an example suppose we reached a point where just one particle remained.No one can predict when that will decay,it may go in the next nanosecond or remain intact for billions of years.

 

[sophiecentaur]

If people refuse to believe in exponential processes then that is up to them. This thread has more than enough explanatios and justifications for accepting the use of half life. I could just ask why Half Life is used if, indeed, it's not necessessary. Do they think the Scientists. Are just being awkward?

 

[I_am_learning]

Don't feel bad but this thread is humorus. Its like Dozen of people trying to explain to a old person that the Earth revolves round the sun and the person exclaiming again and again --"Ok. Ok. But whatever you said don't make sense. If the Earth revolved round the sun, then why don't my door in east be at the west at night?" Not a good analogy to this case, though.
Remember -"You can't solve the problem by thinking in the same way you created it!"

 

[pallidin]

If people refuse to believe in exponential processes then that is up to them. This thread has more than enough explanatios and justifications for accepting the use of half life. I could just ask why Half Life is used if, indeed, it's not necessessary. Do they think the Scientists. Are just being awkward?

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??

 

[DrGreg]

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

You don't like the coin-tossing analogy, but tough, the analogy is correct.

Toss 1000 coins and you'd expect about 500 heads.
Toss 2000 coins and you'd expect about 1000 heads.
Toss 1000000 coins and you'd expect about 500000 heads...

Toss N coins and you'd expect about N/2 heads.

Take N radioactive atoms and you'd expect about N/2 of them to decay within a half-life.

 

[I_am_learning]

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

It has been told to you a lot of time and you aren't paying attention to it.
As told already (many times!) each atom are independent. They don't care if they are in cluster or are signle. The fact you are missing is probability.
If you take (look at) one particular atom, No one knows when it will disintegrate, pherhaps immediately, pherphaps after a million of years!

So, if you have only a group of few atoms, none of the laws about half life etc etc works. The no. of atoms may remain the same for years and out of a sudden all of them can disintegrate at once. Its matter of probability.

But if you have a lot of them Zillions and Zillons, by the probability distirbution, you will have atoms disintegrating every now and then. The frequency of atoms disintegrating every now and then depends on how many atoms you have. The larger the no. of atoms available larger is the chance that atoms will be disintegrating every now and then.

But, probabilistically speaking, it may happen with astronomically small probability that a sample of radioactive material may not follow the law of Half Life (or quarter Life or whaterver) and stay intact for years, and out of a certain vanish!

 

[Dadface]

And the same statistical laws of chance that govern coin tossing and other analogous situation apply to half life.Pallidin does it not make sense to you that the greater the number of radioactive atoms the greater the rate of decay the two,on average,being proportional?If so then the concept of half life drops neatly out of the maths.If it doesn't make sense answer this question.
If someone was forced to carry some uranium 235 why would they prefer to carry a picogram rather than a kilogram?

 

[gmax137]

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.

 

[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 )