Why Half life radiation is constant

[brainyman89]

what makes half life(T) of radiation independent of the quantity of radioactive substance? why is it constant whatever the amount of the radioactive substance is?

 

[mathman]

By definition, half life is the time it takes for half of the sample to decay. Since the decay of an individual nucleus is independent of the size of the sample, the half life doesn't depend on the size of the sample.

 

[pallidin]

By definition, half life is the time it takes for half of the sample to decay. Since the decay of an individual nucleus is independent of the size of the sample, the half life doesn't depend on the size of the sample.

Uh... why not just use "full life"?
Wouldn't that make more sense?

 

[Vanadium 50]

Because there is no time in which all the sample decays. If the half-life is 1 year, after a year 50% is left. After two years, 25% is less. After three, 12.5%.

 

[gmax137]

Uh... why not just use "full life"?
Wouldn't that make more sense?

you're kidding, right??

the 'full life' does depend on the quantity

 

[JDude13]

The half life is the period of time in which there is a 50% chance of a specific atom of the isotope decaying.

 

[pallidin]

you're kidding, right??

the 'full life' does depend on the quantity

And "half life" does not?

 

[pallidin]

By definition, half life is the time it takes for half of the sample to decay. Since the decay of an individual nucleus is independent of the size of the sample, the half life doesn't depend on the size of the sample.

Half of the sample?
What the heck is that?
Why not just use the full sample? As, you said, the result is independent of the size of the sample.

Let's just use half of DNA to convict criminals.

 

[DrGreg]

Half of the sample?
What the heck is that?
Why not just use the full sample? As, you said, the result is independent of the size of the sample.

Let's just use half of DNA to convict criminals.

The half-life is the time it takes for 50 g of a 100 g sample to decay. Which is the same time it takes for 500 mg of a 1000 mg sample to decay. Which is the same time it takes for 1 lb of a 2 lb sample to decay.

The time it takes for 100 g of a 100 g sample to decay is theoretically infinite.

 

[pallidin]

The half-life is the time it takes for 50 g of a 100 g sample to decay. Which is the same time it takes for 500 mg of a 1000 mg sample to decay. Which is the same time it takes for 1 lb of a 2 lb sample to decay.

The time it takes for 100 g of a 100 g sample to decay is theoretically infinite.

That makes no sense AT ALL.
If half of the product decays in a predicitable manner, yet 100% does not, there is something seriously wrong.

 

[Drakkith]

That makes no sense AT ALL.
If half of the product decays in a predicitable manner, yet 100% does not, there is something seriously wrong.

Think of it in terms of individual atoms. The half life is the average time it takes for any atom of that element/isotope to have a 50% change of decaying. That means that if you look at every atom of that element that was created at the same time, 50% of all those will have decayed at the half life point.

Be aware that this means that if the half life for something is 100 years, then every 100 years each atom has a 50% chance of decaying. After 200 years the remaining materiel STILL hass a 50% chance of decaying after another 100 years. Since this is a chance per timeframe, there is never a time frame where you have 100% chance of every atom decaying by that point. There's always a chance that it hasn't.

 

[russ_watters]

The half life is the average time it takes for any atom of that element/isotope to have a 50% change of decaying. That means that if you look at every atom of that element that was created at the same time, 50% of all those will have decayed at the half life point.

I don't think that first sentence is quite right: it's just the average time it takes for one to decay. In other words, if you do the experiment over and over again with one particle at a time, half the time it will decay in that amount of time and half the time it won't.

 

[KingNothing]

The half life is the average time it takes for any atom of that element/isotope to have a 50% change of decaying.

I don't think that first sentence is quite right: it's just the average time it takes for one to decay.

I believe he means a single atom would have a 50% chance of decaying before the half-life, and a 50% chance of decaying after the half-life. It's a more quantum-physics-esque way of stating the same thing.

 

[sophiecentaur]

you're kidding, right??

the 'full life' does depend on the quantity

When you get down to the last nucleus that hasn't changed, there is still no defined time for that single nucleus to decay. So, even in a practical sense, there is no such thing as "full life". And, if you are talking in terms of a mathematical model - the exponential function never reaches zero.

 

[Dadface]

We could define other fractional lives instead such as third life or quarter life.There is nothing fundamentally special about half life but half is the preferred fraction because it is the easiest one to deal with.Because of the exponential nature of decay the concept of "full life" is meaningless but as a very rough rule of thumb we might describe that after a certain number of half lives the substance has more or less decayed completely.As an example after ten half lives the activity will drop to about one thousandth of its original value and depending on the original activity the remaining activity may be considered as negligible.

 

[sophiecentaur]

I was discussing this very thing with a student, yesterday. Half life is only (afaik) used in the context of radioactive decay. It's the one instance where the 'general Public' need an appreciation of what exponential decay applies to their lives. All other situations involving exponential decay seem to use a 'decay constant' or 'time constant', both of which represent the time for decay to fall to 1/e. This is because the Maths comes out without having to introduce an extra constant in the calculations.

 

[gmax137]

... Half life is only (afaik) used in the context of radioactive decay...

That is kind of weird. I'm sure that Mr. Bequerel & Mme. Curie knew about natural logarithms and what 1/e is; so why did they (or whoever it was back then) use 'half life' rather than e-folding time? Maybe one of our historians can shed light on this? Who was the first to use 'half life' to characterize the decay rate?

 

[QuantumPion]

I was discussing this very thing with a student, yesterday. Half life is only (afaik) used in the context of radioactive decay. It's the one instance where the 'general Public' need an appreciation of what exponential decay applies to their lives. All other situations involving exponential decay seem to use a 'decay constant' or 'time constant', both of which represent the time for decay to fall to 1/e. This is because the Maths comes out without having to introduce an extra constant in the calculations.

Half life is also used in biology. The biological half-life is the time needed for an organism to process some chemical. E.g. the biological half life of iodine (which is completely different from the radioactive half-life) is about 100 days.

 

[sophiecentaur]

Half life is also used in biology. The biological half-life is the time needed for an organism to process some chemical. E.g. the biological half life of iodine (which is completely different from the radioactive half-life) is about 100 days.

Well, there you go. Biological half life as well.
But it's reasonable in that it's a very meaningful measure and is probably not taken into further Mathematical manipulation.
'Doubling time' is also a useful concept in population growth, too.

 

[KingNothing]

Half-values are used in a lot of fields for exponential functions. In control theory, it is common to give the half-value rise time for a given control system.

It's no more or less meaningful than a 1/e time. They are a measurement of the same thing. It's just that a half-value is easier to present.

 

[sophiecentaur]

Half values are OK and so is frequency but e and ω are a lot better for doing sums with because you don't end up having to decide when to multiply or divide by 2π or loge2 every time you differentiate or integrate.

 

[pallidin]

Hmmm...

Let's see: A 1-pound sample half-life decays in 100 years(theorectically speaking)
Therefore 8oz decays, presenting a remaining 8oz.
That remaining 8oz should decay in an additional 100 years.
Full-life... 200 years.

If that is not true, how is the first half of the sample somehow subject to different rules than the second half?

 

[DrGreg]

Hmmm...

Let's see: A 1-pound sample half-life decays in 100 years(theorectically speaking)
Therefore 8oz decays, presenting a remaining 8oz.
That remaining 8oz should decay in an additional 100 years.
Full-life... 200 years.

If that is not true, how is the first half of the sample somehow subject to different rules than the second half?

Atoms have no memory. They don't "know" how old they are. A 100-year-old undecayed atom is just as likely to decay as a 0-year-old undecayed atom. So after 100 years your remaining 8oz of undecayed material behaves as if you had started with 8oz of material in the first place. And it takes 100 years for 4oz of it to decay. And then another 100 years for 2oz of the remaining 4oz to decay, and another 100 years for 1oz of the remaining 2oz to decay, and so on.

 

[Drakkith]

Hmmm...

Let's see: A 1-pound sample half-life decays in 100 years(theorectically speaking)
Therefore 8oz decays, presenting a remaining 8oz.
That remaining 8oz should decay in an additional 100 years.
Full-life... 200 years.

If that is not true, how is the first half of the sample somehow subject to different rules than the second half?

Lets say we have X substance with only 1000 total atoms in your sample with a half life of 100 years. So, in 100 years each atom has a 50% chance of decaying.

After the first 100 years we look and see that 500 out of the 1000 atoms have decayed (or close to that). Alright.

Now, let's look at another 100 years later. 500 atoms STILL have a 50% chance of decaying in those 100 years. So we look and we see that about 250 atoms have decayed, leaving 250 behind. And so forth and so forth.

 

[Mapes]

Hmmm...

Let's see: A 1-pound sample half-life decays in 100 years(theorectically speaking)
Therefore 8oz decays, presenting a remaining 8oz.
That remaining 8oz should decay in an additional 100 years.
Full-life... 200 years.

If that is not true, how is the first half of the sample somehow subject to different rules than the second half?

Hmmm...

Let's see: 1000 quarters, flipped, should give 500 heads (theoretically speaking)
Therefore 500 come up heads on the first flip, giving 500 tails.
Those 500 quarters that came up 500 tails should come up heads on the next flip.
1000 quarters will come up all heads in two flips.

If that is not true, how is is first flip somehow subject to different rules than the second flip?

 

[sophiecentaur]

There is no such thing as "full life".
How many times do you have to multiply by 1/2 to get exactly Zero?
Try it on your calculator and then realize that you are not dealing with ten digit numbers but more than twenty digit numbers. When do you reach your "full life"? (even with the limited accuracy of your calculator!)
What use would that number be to you in any case?
Don't use the term "theoretically" unless you are actually quoting some established 'theory'.

 

[pallidin]

There is no such thing as "full life".

Well, there had better be, else reality has a huge problem.

 

[DrGreg]

There is no such thing as "full life".

Well, there had better be, else reality has a huge problem.

Why?

 

[QuantumPion]

Well, there had better be, else reality has a huge problem.

Take a pile of 100 pennies. Toss them all. Throw out all the ones that are tails. You should have around 50 left. 50 pennies have been lost.

Wait 1 minute, then toss the remaining 50 pennies. Throw out all the ones that are tails. You should have around 25 left. After the 1st minute, around 25 pennies have been lost.

Wait 1 minute, then toss the remaining 25 pennies. Toss out all the ones that are tails. You should have around 12 left. After the 2nd minute, around 12 pennies have been lost.

Wait 1 minute, then toss the remaining 12 pennies. Toss out all the ones that are tails. You should have around 6 left. After the 3rd minute, around 6 pennies have been lost.

Wait 1 minute, then toss the remaining 6 pennies. Toss out all the ones that are tails. You should have around 3 left. After the 4th minute, around 3 pennies have been lost.

After the 5th minute, you might be out of pennies, but maybe not. It might take a few more minutes of this before you lose your last pennies. So where as on the first toss you had to throw out 50 pennies, by minute 5 you are lucky if you even throw out one penny.

Your penny-tossing half-life is 1 minute. The "full-life" in this example might be around 6 minutes, but if you instead started with 10 trillion pennies, it might take ~40 minutes before you finally lose the last penny. The "full-life" depends on how many pennies you start with. The half-life is independent of the number of pennies, because it only depends on how long you wait between coin flips, which in our example is a constant.

 

[AtomicJoe]

what makes half life(T) of radiation independent of the quantity of radioactive substance? why is it constant whatever the amount of the radioactive substance is?

It is like a room full of balloons, on any day there is a 50% chance a balloon will pop.

So you start with 128 balloons on day one, then 64 on day 2 and 32 on day 3 16 on day 4 etc...

It is also like bacteria breading in reverse, the population doubles every day.

All of the above is for a life of 1 day, it could be any time 1 month 1 year or whatever :)

 

[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 PROBABILTY.
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 probabilty 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.