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Half-life and carbon dating | Nuclear chemistry | Chemistry | Khan Academy

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In the previous video, we saw all possible types From isotopes of atoms that undergo radioactive decay And turn into other atoms or get rid of different types Of particles The important question, however, is when to decide the atom or nucleus To go through the process of radioactive decay Let’s say I have a group of, let’s say all of these are atoms I have a bunch of atoms here And let’s say we’re talking about the type of radiation where The atom turns into another atom So the number of protons will change Then your atomic number will change So this could be a beta-type dissolution that will be released Electrons from neutrons and convert them into protons Or maybe a positron emission that turns protons into neutrons But this does not belong to us at present So let’s say we have a bunch of atoms.

It is natural that when We have to have any small amount of any ingredient Huge quantities of atoms of this element And we talked about malls and – you know – one gram of Carbon-12 .. I apologize .. 12 grams of carbon-12 It has one mole of carbon-12 inside One mole of carbon-12 And what is one mole of carbon-12? This is 6.02 times 10 by 23 of the carbon-12 atoms, that’s it A huge number This is more than we can and more than our brains realize About growing this number And this is what we have when we have 12 grams, 12 grams is not Big block For example, 1 kg – approximately 2 pounds – So this relates to what I want to say (1/50) From the pound if I was doing that But in the end it is not a big lump Pounds are clearly a force You understand the idea On the ground, well, anywhere the block is fixed This is not a great deal So with that in mind, let’s go back to our question of how we can To know if these particles are going to Atomization somehow And maybe not carbon-12, maybe we are talking about carbon-14 Or something like that How do we know they are going to degenerate? And the answer is, you can’t All of them have some possibility of dissolution At any point, for a specific type of item or There is a certain type of isotope, there is some kind of The likelihood that someone will dissolve This, you know, maybe this atom can go through dissolution during this second And then nothing happens for a long time, a long period and Two other atoms suddenly dissolve And so, like anything in chemistry, and much more We start dealing with it in chemistry and quantum mechanics Everything is related to probability I mean, maybe if we really get detailed in Kernel distribution maybe we can We are doing a little better on our prospects, but we don’t know What happens inside the nucleus so all we can do Is to assign some possibilities to something interactive Now you can say, well then what is the probability of any A given part to interact in one second? Or you can define it in this way But we are used to dealing with things of great perspective To handle, as you know, large amounts of molecules So what we do is come to terms that help us We better treat it And one of these items is the half-life “silence” Let me just wipe these things off from here So, I have a description that we can hope through Gain an understanding of what the half-life means So I wrote the decay reaction here Where you have carbon-14 Which is dissolved into nitrogen-14 And we can just do a little bit of revision It goes from 6 protons to 7 protons The mass number is constant So one of the neutrons must turn into a proton This is what happened And you do this by editing an electron that also It is called a beta particle We can write this as a negative charge Mass is approximately zero It has a little bit of mass, but it is written as zero This is a kind of blogging method So this is called beta-decay Beta-type decay is just a review But the way we think about the half-life is Scientists studied carbon and then they said, look if we start with 10 grams If I had just a carbon block weighing 10 grams If you wait for the half-life of carbon-14 This is one of the isotopes of carbon.

Remember, isotopes, if there is carbon, may have carbon-12 A block number is equal to 12, or it may equal 14, or as I mean there Different types of isotopes of different atoms And the atomic number here defines carbon as an element Because it contains 6 protons Carbon-12 has 6 protons Carbon-14 has 6 protons But they have different numbers of neutrons So when you have the same item with different The number of neutrons, this is the isotope So the carbon-14 version or this isotope of carbon let’s say We will start with 10 grams, if we say that his half-life is It is equal to 5,740 years, which means that on the first day we will start With 10 grams of pure carbon-14, after 5,740 years Half of this block will have turned To nitrogen-14 by decomposition of beta-type And you might say well then maybe – let’s see let’s make it Nitrogen in purple over there – so you might say well Perhaps this half turns into nitrogen And I saw this decree this way In some chapters of chemistry or physics and was My immediate question is how this half is known Should it be converted to nitrogen? How does this half know that it must remain carbon? And the answer is, they don’t even know And that the drawing should not be done this way So, let me repaint it So this is our original block of carbon-14 What happens throughout these 5740 years is that Possibly some of these atoms begin to just shift Random nitrogen at random points And for 5740 years, you can decide that there is a 50% chance Which of these carbon atoms can be converted to? Nitrogen atoms So after 5740 years – the half-life of carbon – There is a 50 percent possibility that any of these carbon atoms It will turn into nitrogen So if you come back after the half-life has passed, half the atoms You will have turned into nitrogen So now you have one half life span, so Let’s ignore this So we started with this With 10 grams of carbon 10 grams of carbon-14 This is after one half-life And now we have 5 grams of carbon-14 And we have 5 grams of nitrogen-14 This is fair enough Let’s think about what happens after another half-life has passed Well, we said that during the 5740 years This state of carbon-14 has all the different elements it has Different half-lives are radiant throughout 5740 year there is 50% – and if you only look at any single atom There is a 50% chance it will dissolve So if we go through another half-life From there, I had 5 grams of carbon-14 So let me just copy and paste this one This is what we started with “silence” Now that another half-life has passed – we can ignore all of this Actually, let me wipe some of this up Let me clean this up a little bit After half-life has passed, what happens? Well now it’s left five grams of carbon-14 These five grams of carbon-14 each of these atoms are still He has during – whatever this number was 5740 years – After 5740 years, all of these Once again, they have a 50% chance.

And by law for large numbers, half of them will be It has been converted to nitrogen-14 So we will have a further shift to nitrogen-14 So now half of the five grams, so now we have the rest It is 2.5 grams of carbon-14 And how much nitrogen-14? Well we have another 2.5 grams of those converted to nitrogen So we now have 7.5 grams of nitrogen-14 We can continue to repeat this in the future And after the expiration of each half-life, i.e. 5740 years, we will have half The carbon with which we started the process But we will always have it A small percentage of carbon But let me ask a question Let’s say I stare at one carbon atom So let’s say I only have this carbon atom As you know, it has its own carbon-14 core So she has six protons 1,2,3,4,5,6 It has its own eight neutrons It has six electrons 1, 2, 3, 4, 5, 6, whatever what is going to happen ? What will happen after a second pass? Well I do not know It is possible that a carbon atom is still there Another possibility is that after one second has passed you will have It turned into nitrogen-14 What will happen after a billion years? Okay .

After a billion years, I will say well, you know It is possible that it will have turned into nitrogen-14 at this point But I am not sure This atom may only be super stable It happened to her, kind of out on The base remains carbon-14 So, after one half life span if you only look at One atom after 5,740 years, you don’t know if it’s turned To nitrogen or not This specific atom, you only know it has a 50% chance that It turns into nitrogen Now if we look at a huge number of atoms, I mean If we start getting close to – you know – Avogadro’s number or Anything bigger than that – I erased it – Then suddenly you can use the law of large numbers And she says, well on average, if each atom of this should be The probability is 50%, and if it has gasoline from it Half of them will be converted to nitrogen I don’t know which half, but half of them It will turn into nitrogen So you might have a question like, I start with, oh I don’t know Let’s say I started with 80 grams of something Let’s just call it X and it has a half-life of two years I just make this compound Half-life is estimated at two years “Silence” And then, let’s say we went with a time machine and took a look Back on the sample, let’s say we only have 10 grams The remainder of the sample And by doing this, we want to know how long we have been So 10 grams is left of X How long – you know – X is going through decay all the time How long has it passed? Well, let’s think about this We start at time = 0 with a mass of 80 grams after two years How much of this substance will remain? We’ll have 40 grams, so (t) is equal to 2 But after another two years, how much material will be left? So we’re going to have 20 grams in this case (t) equal 3 Sorry, this (t) is 4 years old And then, after another two years have passed, I will only have half of this Remains again So, now I will only have 10 grams This is where I am now Here (t) is 6 So if you know that you have some substance And it starts with 80 grams of it knowing that it has Two years as a half-life It is a time machine After that, you didn’t build the tack well You do not know if the calibration of time is correct or not All you have to look at is your sample And she says, “Oh, I only have 10 grams left.” And you know that 1,2,3 half-lives have passed You can also think about it this way 1/2 to the power of 3, because every time you have half The original sample – this is the number of half-lives – after After three half-lives, you will have 1/8 of the original sample And this is what we have now We have 1/8 of 80 grams, and this only happens when we do Do this cautiously – you know – when you’re accurate About the half-life point In the next video we’ll explore, what if I ask you A question, how many particles, or how many grams Exactly what will you get in 10 days? Or in two and a half years? And this is what we will do in the next video

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