Beta decay | Physics | Khan Academy

Did you know that paper industries can use radioactivity to ensure consistent thickness throughout the paper? That's right! But doesn't it make you wonder how do you use radioactivity to do that? Well, let's find out.

If you have a very heavy nucleus, then there will be too many protons in it causing repulsion, making the nucleus very unstable. When that happens, it just spits out a helium nucleus and becomes lighter. Now the daughter nucleus is more stable. This is what we call an alpha decay. We've talked a lot about this in great detail in our previous video on alpha decay.

But guess what? Even light nuclei can be unstable for a completely different reason. It has now nothing to do with the number of protons, but now it has something to do with the ratio of protons and neutrons. Turns out that certain ratios of protons and neutrons just don't work for the nucleus, making it very unstable.

Now what does it do? How does it stabilize? Well, now it undergoes a beta decay. In fact, we will see that there are two kinds of beta decay. But what exactly happens over here? What is a beta particle? Well, let's explore all of that by taking a couple of examples.

For our first example, let's consider carbon-14. It's a radioactive isotope and it's unstable, so what it does is it changes into nitrogen-14, spitting out a beta particle. So again, the question is: what's going on over here? What's this beta particle? Of course, we can Google it, but where's the fun in that? Instead, let's put thinking caps on and see if we can logically deduce this.

The way I like to think about it is just keep track of protons and neutrons. If you look at carbon, it has six protons in it, and since the total number of particles is 14, the remaining eight must be neutrons. So there are eight neutrons in it. Okay, what about nitrogen? Well, it has seven protons in it, and because the mass number stayed the same, it’s still 14, there must be seven more neutrons in it.

Now, if you look at the protons carefully, you can see there's one extra proton over here. But if you look at the neutrons, there is one extra neutron over here. So, can we guess what might have happened? Well, we can guess that the neutron must have converted into a proton, and guess what? That's exactly what happened over here. That's what a beta decay is, or at least one kind of beta decay: a neutron gets converted into a proton.

That's incredible, isn't it? But that's not it, folks. We can now also guess what this particle is, or at least guess the properties of this particle just by using charge conservation. I mean, whether you're dealing with chemical processes or nuclear processes, the charges must always be conserved.

Now, for all the particles that we've accounted for, of course the charge stays conserved. But look at this: a neutron is a neutral particle, but when it gets converted to a proton, you get a positive charge. Now we need to account for it. The right-hand side should also be neutral; that means along with the positive charge, there must be a negatively charged particle that comes out. That's what a beta particle is! It must have an equal negative charge, and guess what that is?

It turns out, experimentally, we found out that that is an electron. So in this particular process, it's spitting out an electron. It's the good old electron that we're all familiar with, except for the fact that it came from the nucleus. And so, whenever we have electrons coming from the nucleus, we call it the beta minus particle.

And this decay, we call it the beta minus decay. Now, of course, we need to write this in the same notation because this is still a nuclear process. So how do we write that? Well, here we have a six, but here we have a seven. So if I want this total number to be six over here, I just have to subtract one, so I'll write this as minus one. So that you have six here, and 7 minus 1 equals 6 here.

I know you must be wondering, "Well, what does it mean to have minus one over here? Because this is supposed to be the atomic number?" Right? What does it mean to have a minus one of an atomic number? Well, don't worry too much about it. I like to think about it as just a negative charge that’s written over here. I mean of course, it doesn't make sense for an electron to have an atomic number or a mass number, but it's just a way to keep our notation consistent.

Okay, anyways, so that's for this one. What about the mass number? Well, the mass number did not change. So we have 14 here, 14 here, that's good, so we'll just write a zero. So that's how we represent an electron in a nuclear process: a beta minus particle.

Now you may be wondering, what is this question mark over here? Well, we'll get to that. But before that, we'll take another example. This time, we have nitrogen turning into carbon. Why don't you pause the video and do the same analysis? Is even here the same thing that's happening, or is something else happening? Is this the same beta particle or something else? Why don't you pause and give it a shot?

All right, let's see. So again, here there are seven protons, and since the total mass number is 13, that means there are six neutrons over here. And over here there are six protons, and again the mass number stayed the same, so there must be seven neutrons over here.

Again, if you try to account for them, you will see there is one less proton over here, but there is one more neutron over here. So what happened over here? Hey, it's the exact opposite this time: a proton got converted into a neutron.

And again, if we try to account for the charge, because charges must be conserved, there's a positive charge here on the left-hand side, so on the right-hand side there must be positive. This is neutral, so that means this particle must be positively charged. It must have the same charge as the proton. So what is it?

Well, it turns out this is what we call a positron. But what exactly is a positron? Think of a positron as kind of a twin, an evil twin of an electron. It has almost all the properties similar to that of an electron, like the same mass. It will have similar spin and all the quantum properties, but just one thing will be the opposite: its charge will be opposite.

Okay, so this is probably a new particle for us; it's kind of like the electron but with a positive charge. We call this positron. However, in general, if you have particles that have pretty much the same properties as some other particles except for a few that are the opposite, like maybe the charge or other quantum properties, that can be opposite as well. In that case, we call this an antimatter.

So this positron is an antimatter of an electron. Protons also have their antimatter; it's called antiprotons. Neutrons will also have their antimatter; it's called anti-neutrons, and so on and so forth.

And the beautiful thing about antimatter is that when antimatter comes in contact with matter, they destroy each other; they annihilate each other, giving out energy. But anyways, in this beta decay, we get a positron, an anti-electron, antimatter of an electron that comes out. And because it is positively charged, we call this beta plus decay.

And just like before, we want to write it with the proper notations. This time we will write a plus one over here. And again, don't worry too much about what this is; we're just making sure that the total number stays the same. And over here, because the mass number never changes, we'll call it zero. So this is how you write a positron in a nuclear process.

But that leaves us with the last piece of the puzzle over here: what exactly are these question marks? We have accounted for all the particles, right? Well, let me ask you this: we know that in any radioactive process things are supposed to become more stable. More stable means it should have less energy, right? Well, where does the energy go?

Well, the energy goes as the kinetic energy of these particles. But when we looked at it experimentally, we found that there was some missing kinetic energy. And to account for that, we hypothesize that there must be some other particle that is taking away that energy. It must be neutral because we've accounted for all the charges, it must be very tiny, it must have very tiny mass, and it must not be interacting with a lot of matter because we couldn't detect it for a long time.

But eventually, we did! You know what we call these particles? We call them neutrinos and anti-neutrinos. Even neutrinos have antimatter.

Okay, now the big question is which one comes where? Where do we get a neutrino and where do we get an anti-neutrino? Well, it turns out that wherever we get an electron, we get an anti-neutrino. And wherever we get an anti-electron, that is, a positron, that's where we get a neutrino.

So the symbol for neutrino is "ν," and the "E" over here just represents that these neutrinos and anti-neutrinos came along with the electrons. And of course, the bar over here represents it’s an anti-neutrino.

Now, we might be overwhelmed thinking that, "Oh my God, there are so many particles to keep track of. How will we remember this?" Well, most of it can be done logically. First of all, if you zoom out, you can see a beta decay is basically neutrons converting into protons or a proton converting into a neutron.

And the reason they do that is to improve the ratio. Remember, the whole reason was the proton to neutron ratio didn’t work for them, making them unstable. So by doing that, they will change that ratio.

That's the whole motivation over here. And then you can use charge conservation to figure out where we'll get a beta minus particle and where we’ll get a beta plus particle. And finally, remember that wherever we have electron matter along with that, I'll get the antimatter of neutrino anti-neutrino.

And wherever I have antimatter, the positron, which is the anti-electron along with that, I'll get the normal matter neutrino which is just the neutrino. And by the way, if you are ever thinking about, "Hey, what allows this to happen? What kind of force allows this weird neutron to proton conversion and proton to neutron conversion?" Well, it's the weak nuclear force—the fourth fundamental force of nature.

Now let's answer the original question: How do industries use beta decays to ensure consistent thickness of papers? Well, it turns out that beta decay beta particles, both positive and negative beta particles, have a much higher penetrating power compared to alpha particles. Remember alpha particles, because they have a high ionization power, because they have a +2 charge and they're bulky, they can easily stop by even paper.

Beta particles are much tinier; because they have a single charge, they have smaller ionization power. And because they're much more tiny, they can easily pass through paper. In fact, you will need something like plastic or glass or maybe aluminum to stop it.

So now, let's imagine what happens if you have a lot of beta particles coming and you keep paper in front of it. Well, some beta particles will get absorbed, but a lot of particles will get through. Now the amount of particles that will get through will depend upon the thickness of the paper, right? Because if you have thicker paper, more beta particles get absorbed.

So by looking at how many particles are coming out from the back of the paper, you can figure out what the thickness at that particular point is. And this is how industries use beta decay to ensure that you have a consistent thickness. You can see we can't use alpha particles for that because it just gets stopped very easily.

Beta particles have the right penetration power to do that job. I find this fascinating because I would have never imagined using beta decay for ensuring consistent thickness in paper. I mean, that's just amazing if you ask me!