Radioactive Dating

Radiometric Dating: Methods, Uses & the Significance of Half-Life

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Carbon 14 dating 1. Carbon 14 dating 2. Atomic number, atomic mass, and isotopes. Google Classroom Facebook Twitter Email. In the last video, we give a bit of an overview of potassium-argon dating. In this video, I want to go through a concrete example. And it'll get a little bit mathy, usually involving a little bit of algebra or a little bit of exponential decay, but to metgod show you how you can actually figure out the age of some volcanic rock using this technique, using a little bit of mathematics.

So we know that anything that datingg experiencing radioactive decay, it's experiencing exponential decay. And we know that there's radiometric dating method formulas generalized way to describe that. And we go into more depth and kind of prove it in other Khan Academy videos. But we know that the amount as a function of time-- so if we say N is the amount of a radioactive sample we have at some time-- we know that's equal to the initial amount we have.

We'll call that N sub 0, times e to the negative kt-- where this constant rxdiometric particular to that thing's half-life. In order to do this for raduometric example of potassium, we know that when time is 1. So let's write it that way. So let's say we start with N0, whatever that might sating. It might be 1 gram, kilogram, 5 grams-- radiometric dating method formulas it might be-- whatever we start with, we take e to the negative k times 1.

That's the half-life of potassium We know, after that long, that datibg of the sample will be left. Whatever we started with, we're going to have half left after 1. Divide both sides by N0. And then to solve for k, we can radiometric dating method formulas the natural log of both sides. The natural log is just saying-- to what power do I have to raise e to get e to the negative formuulas times 1. So the natural log of this-- the power radiometric dating method formulas have to raise e to to get methdo e to the negative k times 1.

Or I could write it as negative 1. That's the same thing as 1. Radjometric have our negative sign, and we have our k. And then, to solve for k, we can divide both sides by negative 1. And so we get k. And I'll just flip the sides here. And what we can do is we can multiply the negative times the top. Or you could view it as multiplying the numerator and the denominator by a negative so that a negative formuas up at the top.

And so we could make this as over 1. Let me write it over here in fating different color. The negative natural log-- well, I could just write dsting this way. If I have a natural log of b-- we know from our logarithm properties, this is the same thing as the natural log of b to radiomeetric a power. And radiometrid this is the same thing. Anything to the negative power is just its multiplicative inverse.

So this is just the natural log of 2. So negative natural log of 1 half is just the natural log of 2 over here. So we were able to figure out our k. It's essentially the natural log of 2 over the half-life of the substance. So we could actually generalize this if we were talking about some other datinh substance.

And now let's think about a situation-- now that we've figured out radiometric dating method formulas k-- let's think about a situation where we find in some sample-- so let's say the potassium that we find is 1 milligram. I'm just going to make up these numbers. And usually, these aren't measured directly, and you really care about the relative amounts. But let's say you were able to figure out the potassium is 1 milligram. And let's say that the argon-- actually, I'm going to say the potassium found, and let's say the argon found-- let's say it is 0.

So how can we use this information-- in what we just figured metuod here, which is derived from the half-life-- to figure out how old this sample right datkng here? How do we figure out how old this sample is right over there? Well, what we need to figure out-- we know that n, the amount we were left with, is this thing right over here. So we know that we're left with 1 milligram. And that's going to be equal to some initial amount-- when we use both of this information to figure that initial amount out-- times e to the negative kt.

And we know what k methid. And we'll figure it out later. So k is this thing right over here. So we need to figure out dting our initial amount is. We know what k is, and then we can solve for methkd. How old is this sample? Hook up boost gauge saw that in the last video. So if you want to think about the total number of potassiums that have decayed since this was kind of stuck in the lava.

And we learned that anything that was there before, any argon that was there before would have been able to get out datiing the liquid lava before it froze or before it hardened. So maybe I could say k initial-- the potassium initial-- is going to be equal to the amount of potassium 40 we have today-- 1 milligram-- plus the amount of potassium we needed to get this amount of argon We have this amount of argon 0.

The rest of it turned into calcium And this isn't the exact number, but it'll get the general idea. And so our initial-- which is really this thing right over here. I could call this N0. This is going to be equal to-- and I won't do any of the math-- so we have 1 milligram we have left is equal radiometric dating method formulas 1 milligram-- which is what we found-- plus 0.

And then, all of that times e to the negative kt. And what you see here is, when we want to solve for radiometric dating method formulas assuming we know k, and we do know k now-- that really, the absolute amount doesn't matter. What radiometric dating method formulas matters is the ratio. Because if we're solving for t, you want to divide both sides of this equation by this quantity right over here. So you get this side-- the left-hand side-- divide both sides.

Carbon-14 Radioactive Dating Worked Example