Radio Carbon Dating (Earth, choice, pray)

[yossarian22]

Originally Posted by pray4me

You mean long half lives as in, something that is newer versus something that is older right?

No.
I mean in plain length of half life. Carbon 14 has a half life of some 5700 years. That means that after 5700 years, all else constant, the carbon 14 present in a location will be precisely half of the carbon 14 initially present.

Something with a very short half life, say Helium 12 (I just made this up, I can't recall anything with a very short half life off hand) would be harder to measure with our equipment. Lets say the half life of Helium 12 is 0.2 seconds. That means every 0.2 seconds, we lose 50% of the helium 12 we have present. It will be tough to measure that (due to human error and lab difficulties) and we will have a large margin of error. Carbon 14 is much nicer, as a few seconds is pretty irrelevant to how much carbon 14 has decayed. So something with a bigger half life tends to be easier to measure, provided it is not a very big half life, such as uranium. Uranium has a half life of over 500 million years, so very very small amounts of uranium will decay in a lab setting. That requires very precise equipment.

[pray4me]

how do you measure the half life of a substance if the substance has a half life over the span of a human life? How were half lives first discovered? It must have been using something with a smaller half-life than carbon one that would run it's course in enough time to be measured by one human being.

[yossarian22]

Originally Posted by pray4me

I don't understand all the symbols in equations can you put it into + x - and / for divide

Do you know what the natural log is? I am going to assume you do.

ln[A]= -kxt+H0[A]

H0[A] is the initial concentration of A present.

ln[A] is the natural log of the concentration of A at the end

k is the rate law

t is time.

If you don't know what the natural log is, just remember this.
ln(b)=x b=e^x
e is the natural number 2.71 if I remember correctly.

[yossarian22]

Originally Posted by pray4me

how do you measure the half life of a substance if the substance has a half life over the span of a human life? How were half lives first discovered? It must have been using something with a smaller half-life than carbon one that would run it's course in enough time to be measured by one human being.

By looking at it in a smaller time frame.
Some amount of substance will decay in 10 hours. Not anywhere near half, but still some amount. From that amount, we can calculate k, and from k we can calculate the half life of a reaction
the half life is equal to 0.693/k

[pray4me]

okay, here's what I understand and what I don't. If a substance decays so much in 10 hours, logically in 20 hours it will decay twice as much. so far so good right? If you measure the amount of decay and it's decaying at the same rate for your entire lifetime then you can assume it will continue decaying at the same rate. What I don't get is half life, how was it discovered? How can it be proven?

[pray4me]

Originally Posted by yossarian22

Do you know what the natural log is? I am going to assume you do.

ln[A]= -kxt+H0[A]

H0[A] is the initial concentration of A present.

ln[A] is the natural log of the concentration of A at the end

k is the rate law

t is time.

If you don't know what the natural log is, just remember this.
ln(b)=x b=e^x
e is the natural number 2.71 if I remember correctly.

I don't understand what the brackets are for. what is the ln for? I understand that t is time and the previous post said k is the rate constant. I don't know what a natural log is. I don't understand these kind of equations. I have to know what all the letters represent and then be able to figure out what numbers to put in their place.

[yossarian22]

Originally Posted by pray4me

okay, here's what I understand and what I don't. If a substance decays so much in 10 hours, logically in 20 hours it will decay twice as much. so far so good right? If you measure the amount of decay and it's decaying at the same rate for your entire lifetime then you can assume it will continue decaying at the same rate. What I don't get is half life, how was it discovered? How can it be proven?

You have the concept of half life wrong still.
After 10 hours, you have half.
After 20 hours, you have half of a half, or a quarter.
After 30 hours, you have a half of a half of a half, or an eight.
And it just keeps going.
Proving half life goes beyond the level of this discussion. We can show in labs that radioactive decay is a first order reaction, and therefore subject to the laws that govern first order reactions.

Why first order reactions are the way they are is complicated.

Originally Posted by pray4me

I don't understand what the brackets are for. what is the ln for? I understand that t is time and the previous post said k is the rate constant. I don't know what a natural log is. I don't understand these kind of equations. I have to know what all the letters represent and then be able to figure out what numbers to put in their place.

I can't reduce the ^ or the ln symbols any further. You should take an algebra 2 class and brush up on logarithms and exponents.

Does anybody happen to know the non integrated rate law for first order reactions? That may be simpler.

[pray4me]

I just thought of a way to prove it. Take something which has lost half of it's carbon exactly then take something which hasn't lost any. Measure the rate of decay in both. If the one which has lost half decays at half the rate of the one which hasn't lost any then half life is proven. I'd like to do that experiment myself, does anyone know how to manually measure the amount of carbon in something?

[yossarian22]

Originally Posted by pray4me

I just thought of a way to prove it. Take something which has lost half of it's carbon exactly then take something which hasn't lost any. Measure the rate of decay in both. If the one which has lost half decays at half the rate of the one which hasn't lost any then half life is proven. I'd like to do that experiment myself, does anyone know how to manually measure the amount of carbon in something?

You can do it yourself, but I wouldn't recommend it. Radiation has this annoying ability to cause cancer. Nothing quite like breathing in alpha particles. Assuming you don't mind the health risk, you will need either a Geiger meter to measure beta decay or some kind of spectrometer. And a giant wad of carbon 14.
Half life has already been proven a couple hundred thousand times already. No sense in beating a dead horse

[pray4me]

not to me it hasn't. where do you get carbon 14?