Give the answer to three significant figures. The time period calculated in this example is called the half-life of carbon In fact over any period of years, the amount of carbon in an isolated sample will decay by half.

### Radiometric dating

Roughly speaking, while an organism is alive, its interactions with its environment maintain a constant ratio of carbon to carbon in the organism; but after it dies, the carbon is no longer replenished, and the ratio of carbon to carbon decays in a predictable way. See Wikipedia for more on radiocarbon dating. Let us see why. Next page - Content - Population growth and doubling time. Content Radioactive decay and half-life Decay of carbon Carbon is a radioactive isotope of carbon, containing 6 protons and 8 neutrons, that is present in the earth's atmosphere in extremely low concentrations.

Contributors Term of use. Let's say I have a bunch of, let's say these are all atoms. I have a bunch of atoms here. And let's say we're talking about the type of decay where an atom turns into another atom.

So your proton number is going to change. Your atomic number is going to change. So it could either be beta decay, which would release electrons from the neutrons and turn them into protons. Or maybe positron emission turning protons into neutrons. But that's not what's relevant here. Let's say we have a collection of atoms. And normally when we have any small amount of any element, we really have huge amounts of atoms of that element. And we've talked about moles and, you know, one gram of carbon I'm sorry, 12 grams-- 12 grams of carbon has one mole of carbon in it.

One mole of carbon And what is one mole of carbon? This is a ginormous number. This is more than we can, than my head can really grasp around how large of a number this is.

And this is only when we have 12 grams. For example, one kilogram is about two pounds. So this is about, what? I want to say [?

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## Half-life and carbon dating (video) | Nuclei | Khan Academy

And pounds is obviously force. You get the idea. On Earth, well anywhere, mass is invariant. This is not a tremendous amount. So with that said, let's go back to the question of how do we know if one of these guys are going to decay in some way. And maybe not carbon, maybe we're talking about carbon or something. How do we know that they're going to decay?

And the answer is, you don't. They all have some probability of the decaying. At any given moment, for a certain type of element or a certain type of isotope of an element, there's some probability that one of them will decay. That, you know, maybe this guy will decay this second. And then nothing happens for a long time, a long time, and all of a sudden two more guys decay. And so, like everything in chemistry, and a lot of what we're starting to deal with in physics and quantum mechanics, everything is probabilistic.

I mean, maybe if we really got in detail on the configurations of the nucleus, maybe we could get a little bit better in terms of our probabilities, but we don't know what's going on inside of the nucleus, so all we can do is ascribe some probabilities to something reacting. Now you could say, OK, what's the probability of any given molecule reacting in one second? Or you could define it that way.

But we're used to dealing with things on the macro level, on dealing with, you know, huge amounts of atoms. So what we do is we come up with terms that help us get our head around this. And one of those terms is the term half-life. And let me erase this stuff down here.

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So I have a description, and we're going to hopefully get an intuition of what half-life means. So I wrote a decay reaction right here, where you have carbon It decays into nitrogen And we could just do a little bit of review.

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You go from six protons to seven protons. Your mass changes the same. So one of the neutrons must have turned into a proton and that is what happened. And it does that by releasing an electron, which is also call a beta particle. We could have written this as minus 1 charge. It does have some mass, but they write zero. This is kind of notation.

### Half Life Calculator

So this is beta decay. Beta decay, this is just a review. But the way we think about half-life is, people have studied carbon and they said, look, if I start off with 10 grams-- if I have just a block of carbon that's 10 grams. If I wait carbon's half-life-- this is a specific isotope of carbon. Remember, isotopes, if there's carbon, can come in 12, with an atomic mass number of 12, or with 14, or I mean, there's different isotopes of different elements.

And the atomic number defines the carbon, because it has six protons. Carbon has six protons.

## Carbon 14 dating

But they have a different number of neutrons. So when you have the same element with varying number of neutrons, that's an isotope. So the carbon version, or this isotope of carbon, let's say we start with 10 grams. If they say that it's half-life is 5, years, that means that if on day one we start off with 10 grams of pure carbon, after 5, years, half of this will have turned into nitrogen, by beta decay.

## Radioactive Dating

And you might say, oh OK, so maybe-- let's see, let me make nitrogen magenta, right there-- so you might say, OK, maybe that half turns into nitrogen. And I've actually seen this drawn this way in some chemistry classes or physics classes, and my immediate question is how does this half know that it must turn into nitrogen? And how does this half know that it must stay as carbon? And the answer is they don't know. And it really shouldn't be drawn this way.

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So let me redraw it. So this is our original block of our carbon What happens over that 5, years is that, probabilistically, some of these guys just start turning into nitrogen randomly, at random points. So if you go back after a half-life, half of the atoms will now be nitrogen. So now you have, after one half-life-- So let's ignore this. So we started with this. All 10 grams were carbon. This is after one half-life. And now we have five grams of c And we have five grams of nitrogen Let's think about what happens after another half-life.

So if we go to another half-life, if we go another half-life from there, I had five grams of carbon