Now you could say, OK, what's the probability of any given molecule reacting in one second? But we're used to dealing with things on the macro level, on dealing with, you know, huge amounts of atoms. So I have a description, **and** we're going to hopefully get an intuition of what **half**-**life** means. **And** how does this **half** know that it must stay as carbon? So if you go back after a **half**-**life**, **half** of the atoms will now be nitrogen. Then all of a sudden you can use the law of large numbers **and** say, OK, on average, if each of those atoms must have had a 50% chance, **and** if I have gazillions of them, **half** of them will have turned into nitrogen. How much time, you know, x is decaying the whole time, how much time has passed?

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. *And* it does that by releasing an electron, which is also call a beta particle. *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? So that after 5,740 years, the *half*-*life* of carbon, a 50% chance that any of the guys that are carbon will turn to nitrogen. But we'll always have an infinitesimal amount of carbon. Let's say I'm just staring at one carbon atom. You know, I've got its nucleus, with its c-14. I mean, if you start approaching, you know, Avogadro's number or anything larger-- I erased that. After two years, how much are we going to have left? *And* then after two more years, I'll only have *half* of that left again.

C **and** counting the amount of each) allows one to date the death of the once-living things.

Perhaps you have heard of Ice Man, a man living in the Alps who died *and* was entombed in glacial ice until recently when the ice moved *and* melted.

So you might get a question like, I start with, oh I don't know, let's say I start with 80 grams of something with, let's just call it x, **and** it has a **half**-**life** of two years.

So what we do is we come up with terms that help us get our head around this. So I wrote a decay reaction right here, where you have carbon-14. So now you have, after one *half*-*life*-- So let's ignore this. I don't know which *half*, but *half* of them will turn into it. *And* then let's say we go into a time machine *and* we look back at our sample, *and* let's say we only have 10 grams of our sample left.

The Geologic Time Scale was originally laid out using relative *dating* principles.

Numerical **dating**, the focus of this exercise, takes advantage of the "clocks in rocks" - **radioactive** isotopes ("parents") that spontaneously decay to form new isotopes ("daughters") while releasing energy.

The best estimate from this **dating** technique says the man lived between 33 BC. From the ratio, the time since the formation of the rock can be calculated. 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. That, you know, maybe this guy will decay this second. 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. So the carbon-14 version, or this isotope of carbon, let's say we start with 10 grams. Well we said that during a **half**-**life**, 5,740 years in the case of carbon-14-- all different elements have a different **half**-**life**, if they're **radioactive**-- over 5,740 years there's a 50%-- **and** if I just look at any one atom-- there's a 50% chance it'll decay. Now after another **half**-**life**-- you can ignore all my little, actually let me erase some of this up here. So we'll have even more conversion into nitrogen-14. So now we're only left with 2.5 grams of c-14. Well we have another two **and** a **half** went to nitrogen. So after one **half**-**life**, if you're just looking at one atom after 5,740 years, you don't know whether this turned into a nitrogen or not. Learn about different types of radiometric *dating*, such as carbon *dating*.If one knows how much of this *radioactive* material was present initially in the object (by determining how much of the material has decayed), *and* one knows the *half*-*life* of the material, one can deduce the age of the object.SAL: In the last video we saw all sorts of different types of isotopes of atoms experiencing *radioactive* decay *and* turning into other atoms or releasing different types of particles. Understand how decay **and** **half** **life** work to enable radiometric **dating**.

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