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If you're seeing this message, it means we're lfie trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Computing Computer programming Computer science Hour of Code Computer animation. Test prep SAT MCAT GMAT IIT JEE NCLEX-RN. Mass defect and binding energy. Nuclear stability and nuclear equations.

Writing nuclear half life carbon dating equation for alpha, half life carbon dating equation, and gamma decay. Half-life and carbon dating. Exponential decay formula proof can hwlf, involves calculus. Introduction to exponential decay. More exponential decay examples. Exponential decay and semi-log plots. Google Classroom Facebook Twitter Email. In the last video we saw all sorts of equxtion types of isotopes of atoms experiencing radioactive decay and turning into other atoms or releasing different types of particles.

But the question is, when does an atom or nucleus decide to decay? Let's say I have haof bunch of, let's say these are all atoms. I have a bunch cabon 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 half life carbon dating equation when we have any small amount of any element, we really have huge amounts of atoms of that element. And we've lfie 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 [? And lifee 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 equatioj will decay. That, you know, cabron this guy will decay this second. And then nothing happens for a long time, a haalf time, and all of a sudden two more guys datign.

And so, like everything in chemistry, and a lot of what we're eqkation to deal with in physics and quantum mechanics, everything datibg 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 half life carbon dating equation 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. 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.

Dating a divorced man 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 carbon dating equation 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 Eqhation wait carbon's half-life-- this is a specific isotope of carbon. Remember, isotopes, if there's carbon, can come in 12, with an datlng mass datlng 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. But they have a different number of neutrons. So when you have the same element with datting number of neutrons, that's an isotope. So the carbon version, or this isotope dsting 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 squation of pure carbon, after 5, years, half of this will have turned into nitrogen, by beta decay.

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 cwrbon must turn into nitrogen? And how does this half know that it must stay as carbon?

And half life carbon dating equation answer is they don't know. And it really shouldn't be drawn this way.

Half-life and carbon dating