# Solving carbon dating problems and solutions

### ChemTeam: Half-life problems involving carbon

Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over We can use a formula for carbon 14 dating to find the answer. Carbon is a radioactive isotope of carbon, containing 6 protons and 8 neutrons, that is present in the earth's First, we can solve the differential equation. Answer to Solve each lukonin.info Dating How long does it take for g of carbon to be reduced to g of Solutions for Chapter Problem 64E.

Atomic number, atomic mass, and isotopes Video transcript What I want to do in this video is kind of introduce you to the idea of, one, how carbon comes about, and how it gets into all living things.

And then either later in this video or in future videos we'll talk about how it's actually used to date things, how we use it actually figure out that that bone is 12, years old, or that person died 18, years ago, whatever it might be. So let me draw the Earth. So let me just draw the surface of the Earth like that. It's just a little section of the surface of the Earth. And then we have the atmosphere of the Earth. I'll draw that in yellow. So then you have the Earth's atmosphere right over here.

Let me write that down, atmosphere.

Half Life Chemistry Problems - Nuclear Radioactive Decay Calculations Practice Examples

And I'll write nitrogen. Its symbol is just N. And it has seven protons, and it also has seven neutrons. So it has an atomic mass of roughly Then this is the most typical isotope of nitrogen. And we talk about the word isotope in the chemistry playlist. An isotope, the protons define what element it is. But this number up here can change depending on the number of neutrons you have.

So the different versions of a given element, those are each called isotopes.

I just view in my head as versions of an element. So anyway, we have our atmosphere, and then coming from our sun, we have what's commonly called cosmic rays, but they're actually not rays.

You can view them as just single protons, which is the same thing as a hydrogen nucleus. They can also be alpha particles, which is the same thing as a helium nucleus. And there's even a few electrons. And they're going to come in, and they're going to bump into things in our atmosphere, and they're actually going to form neutrons. So they're actually going to form neutrons. And we'll show a neutron with a lowercase n, and a 1 for its mass number.

And we don't write anything, because it has no protons down here. Like we had for nitrogen, we had seven protons. So it's not really an element. It is a subatomic particle. But you have these neutrons form. And every now and then-- and let's just be clear-- this isn't like a typical reaction. But every now and then one of those neutrons will bump into one of the nitrogen's in just the right way so that it bumps off one of the protons in the nitrogen and essentially replaces that proton with itself.

So let me make it clear. So it bumps off one of the protons. So instead of seven protons we now have six protons. But this number 14 doesn't go down to 13 because it replaces it with itself.

## Carbon 14 dating

So this still stays at And now since it only has six protons, this is no longer nitrogen, by definition. This is now carbon.

And that proton that was bumped off just kind of gets emitted. So then let me just do that in another color. And a proton that's just flying around, you could call that hydrogen 1. And it can gain an electron some ways. If it doesn't gain an electron, it's just a hydrogen ion, a positive ion, either way, or a hydrogen nucleus. But this process-- and once again, it's not a typical process, but it happens every now and then-- this is how carbon forms.

So this right here is carbon You can essentially view it as a nitrogen where one of the protons is replaced with a neutron. And what's interesting about this is this is constantly being formed in our atmosphere, not in huge quantities, but in reasonable quantities.

### Carbon 14 dating 1 (video) | Khan Academy

So let me write this down. And let me be very clear.

• More exponential decay examples
• Carbon 14 dating 1

Let's look at the periodic table over here. Exponential decay and semi-log plots Video transcript SAL: Let's do a couple more of these exponential decay problems, because a lot of this really is just practice and being very comfortable with the general formula, and I'll write it again.

Where the amount of the element that's decaying, that we have at any period in time, is equal to the amount that we started with, times e to the minus kt. Where the k value is specific to any certain element with a certain half-life, and sometimes they don't even give you the half-life.

So let's try this interesting situation. Let's say that I have an element. Let me just give you a formula. Let's say that I have some magic element here, where its formula is, its k value I give to you, k is equal to minus, let me think of a-- [coughs] Excuse me, I just had a lot of walnuts and my throat is dry.

Let's say that k is equal to, well k, we're putting a minus in front of it, so I'll say the k value is a positive 0. So its exponential decay formula would be the amount that you start off with, times e to the minus 0. My question to you is, given this, what is the half-life of the compound that we're talking about?

What is the half-life? So let's do that. So we're starting off with N sub 0 This is just some value, our initial starting point. We could put there. Actually, let's do that, just to keep things less abstract. So let's say we start with I'm just picking out of air. I could have left it abstract with N.

Let's say I'm starting with And I take the times e to the minus 0. So this should be equal to We just solved for t. Divide both sides by You get e to the minus 0. You take the natural log of both sides of this. The natural log of this, the natural log of that. And then you get-- the natural log of e to anything, I've said it before, is just the anything.

So it is minus 0. So let's figure out what that is. Actually, someone just made a comment, and I might as well do that. I could just put this minus up here. I could make this a plus, and this a minus, if I just multiply the numerator and the denominator by negative 1. And if I want to, just to make the calculator math a little easier, if you put a minus in front of a natural log, or any logarithm, that's the same thing as the log of the inverse of 2 over 0.

It makes the calculator math a little bit easier. So if I do 2 natural log, divided by 0. So when t is equal to And I'm assuming that we're dealing with time in years.

That tends to be the convention, although sometimes it could be something else and you'd always have to convert to years.