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# Nuclear stability and nuclear equations

## Video transcript

the last video we talked about the helium nucleus which contains two protons and two neutrons protons and neutrons the nucleus are called nucleons and so I'll use that term a few times in this video so here's a picture of the nucleus right with two protons and two neutrons and we know it's stable even though we know like charges repel and so these two protons are repelling each other and that's the electrostatic force so let me go ahead and write that here so the electrostatic force says like charges repel we know that this nucleus is stable so there must be something else holding the nucleus together which we call the strong force so the nuclear strong force is stronger than the electrostatic force the strong force acts only over short distances though but does act between all nucleons for example a proton proton interaction is the same as a proton Neutron interaction which is the same as a neutron neutron interaction and you can get into much more detail about the strong force that's not really the point of this video the point is that this nucleus is stable alright and let's think about why we have equal numbers of protons and neutrons and so that's interesting and so let's let's think about the atomic number right which tells us the number of protons which we represent by Z and the number of neutrons we could say is capital n and so if we're concerned with the ratio all right the ratio of neutrons to protons so the N to Z ratio in this example we have two protons and two neutrons so two neutrons over two protons equal to one so we've an end to Z ratio of 1 and it turns out that nuclei that have small numbers of protons so if you're talking about Z is less than 20 they have stable nuclei when the n to Z ratio is equal to 1 so when n over Z is equal to 1 you can say you have a stable nucleus so equal numbers of protons and neutrons turns out to be stable so for this example the helium four nucleus is stable thinking about that let's look at carbon 14 next so we have carbon-14 so let's get a little space right down here so carbon-14 atomic number of six therefore carbon has six protons in the nucleus right so there are six protons number of neutrons will be 14 minus 6 so 8 neutrons so what's the neutron to proton ratio so what's the N to Z ratio here the n2z ratio would be 8 neutrons and 6 protons and obviously that number is greater than 1 so we have an unstable nucleus the carbon-14 nucleus is unstable it's radioactive it's undergoing to undergo spontaneous decay all right it's going to try to get a better neutron to proton ratio so let's look at the nuclear equation which represents the spontaneous decay of carbon-14 and so here is our nuclear equation and when you're writing nuclear equations you're representing only the nuclei here so for example on the left side of my nuclear equation I have carbon-14 we're talking about only the nucleus so we're talking about talking about six protons and eight neutrons in the nucleus and so let's look and see what happens here so carbon-14 are the nucleus the carbon-14 nucleus is actually going to give off an electron and so that's pretty weird and we'll talk about more why in the next video it's a it's a it's a conversion that's governed by the the weak nuclear force all right but we know that an electron has a negative one charge and so that's what we're talking about here right so here for carbon we have six protons and we go and write that six protons here an electron has a negative one charge let's write a negative one charge here for the electron and the carbon-14 nucleus is turning into the nucleus for nitrogen here so let's look at what we have so our atomic number is seven right so we have seven protons so let's go and write that here seven protons and 14 minus 7 gives us seven neutrons right look at the mass number here so 14-7 gives us seven neutrons and so that ratio right the the ratio of neutrons to protons is 7 over 7 which is equal to 1 so that implies that we have a stable nucleus here so so that's that's the reason why carbon-14 undergoes radioactive decay let's look at more details about a nuclear equation because that's really what I'm most concerned about here in this video so the the number of nucleons is conserved so let's use a different color here so we have 14 nucleons on the Left we have six protons and eight neutrons on the right we also have 14 nucleons 7 protons and seven neutrons so obviously an electron is not a proton or a neutron so nucleons are conserved alright so we have 14 on the left and we have 0 plus 14 on the right also charge is conserved and so that's what we see down here we have 6 positive charges on the left side on the right side we have 1 negative charge and 7 positive charges so negative 1 & 7 give us plus 6 right so we have plus 6 so nucleons are conserved and charge is conserved in a nuclear equation and notice what happened here all right we changed the identity right we went from carbon to nitrogen because we change the number of protons went from 6 protons to 7 protons and so that's the idea of transmutation so changing one element into another element alright so for 4 nuclei with small numbers of protons the n2z ratio the ideal one is one to one so four protons so four nuclei with more protons it turns out the ratio changes so let's look at that so as you increase the number of protons the ratio changes for a stable nucleus so the n2z ratio turns out to be 1.5 so as you as you increase in Z alright so as you go above Z is equal to 20 so as you get more and more protons you need more neutrons you need more neutrons and let's think about why so if I have a bigger nucleus here so this is a very poor representation of a nucleus I think about two protons let me use use magenta here so I have two protons really close to each other all right we know that there is a a weak electrostatic repulsion here and there's a strong nuclear force right there's a strong nuclear force between between those protons and the strong nuclear force winds but this is only when you're talking about short distances remember the strong force acts only over short distances so if you have protons that are far away from each other all right so these two protons here are far away from each other there's still a repulsive force the electrostatic force is still present so they're still repelling each other but you don't have the strong force anymore and because you don't have the strong force anymore eventually as you keep increasing the number of protons right you're you're increasing in the electrostatic force and you get to a point where you need more of the strong force and so you need to add in more neutrons all right to balance things out so you need to add in more neutrons here and that's the reason for this increased ratio you need more neutrons as you increase the number of protons here all right so when you get beyond approximately 83 all right so let me go ahead and write this down here so once you get an atomic number greater than 83 so bismuth the repulsive force of the protons right this electrostatic repulsive force that we talked about here is so great that pretty much all the nuclei are unstable and will undergo radioactive decay and so we'll talk in the next video about the types of radioactive decay that you might see