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.??