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 daugh nucleus is more stable this is what we call an alpha DK and we've talked a lot about this in great detail in our previous

video on Alpha DK but guess what even light nuclei can be unstable for a completely different reason it has now nothing to do with the to 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 doesn't work for the nucleus making it very unstable now what does it do now how does it stabilize it well now it under goes a beta dek in fact we will see that there are two kinds of beta dekay but what exactly happens over

here what is a beta particle well let's 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 and 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 I mean 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 mass number stayed the same oh it's still the 14 um there must be seven more neutrons in it now if you look at the protons carefully you you can see there's one extra proton over here but if you look at the neutrons well 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 DK is or at least one kind of beta Decay is 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 part 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 get converted to a proton you get a positive charge now we need to account for it the right hand side should also be be neutral that means along with the positive charge there must be a negatively charged particle that comes out that's what a be a particle is it must have an equal negative charge and guess what that is it turns

out you know 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 DK we call it the beta minus DK now of course we need to write this in the same notation because this is still the 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 - 1 6 here and I know you must be wondering well mahes 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 it's just

it's a negative charge that be written over here I mean of course it doesn't make sense for an electron you know to have an atomic number or a mass number but it's just a way to make sure that you know our notation stay put 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 okay now you may be

wondering what is this question mark over here 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 is it the same thing that's happening or something else is 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 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 that means this particle must be positively charged it must have the same charge as the proton so what is it Well turns out this is what we call a positron but what exactly is a positron think of positron as kind of a twin an evil twin of 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 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 which have pretty much the same properties as some other particles except for a few that is the opposite like maybe the charge or there are some other Quantum properties that can be opposite as well that case we call this an antimatter so this positron is an antimatter of electron proton also have their antimatter it's called antiprotons neutrons will also have their antimatter it's called anti- neutrons and so 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 bet DK 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 DK and just like before just like before we want to write it you know we want to write it with the proper notations this time we will write it+ one over here and again don't worry too much about what this is we're

just making sure that it you know this 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 more stable means it should have more 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 and so the symbol for neutrino is new and the E over here just represents that these neutros and antin neutros 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 well first of all if you zoom out you can see a beta dek is basically neutrons converting into proton 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 I 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 dks to ensure consistent thickness of papers Well turns out that beta DK beta particles sorry both positive and negative beta particles they have a much higher penetrating power compared to Alpha particles remember alpha particles because they are have a high ionization power because they have plus two 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 aluminium 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 a 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 industri is use you know beta DK 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 DK for ensuring consistent

thickness in paper I mean that's just amazing if you ask me