 Some nuclei are stable while some are unstable. Those nuclei that are unstable did decay by emitting alpha particles, beta particles or electromagnetic radiation like gamma radiation and they become stable in the process. We can call such unstable nuclei as radioactive in nature. But how do we know when each type of decay occurs? How do we know if an unstable nucleus will undergo either alpha decay or beta plus or beta minus decay? That is what we will explore in this video. We know that for lighter nuclei, for nuclei with a topic number less than 20, the ratio of neutrons to protons, the ratio of n by z, this is equal to 1. This means that for atoms with a topic number less than 20, the nucleus contains equal number of neutrons and protons. The strong nuclear force which acts between all the nucleons, that is between neutron, neutron, neutron, proton and also proton and proton, that strong nuclear force is more than the electrostatic force, that strong nuclear force is more than the electrostatic force, the Coulombic force of repulsion between the protons. But this strong nuclear force acts only over a short range. So if we talk about heavier nuclei, nuclei with a very high atomic number, it turns out that the ratio does not remain as one, the ratio changes for heavier nuclei. These are the ones with a very high atomic number. For them, the ratio turns out to be equal to 1.5. This means that there are more neutrons than protons in the nucleus of such atoms. Let's quickly see why. So if you draw a nucleus, just a random nucleus like this and if you have protons, they will undergo Coulombic repulsion because both of them have positive electrical charge. So they will tend to break the nucleus apart. But because these two protons are so close to each other, the strong nuclear force overcomes the electrostatic repulsion force and the nucleus can remain happy, it can remain stable. But for a larger nucleus, you can have protons, you can have one proton over here and one proton over here. Now these two protons are quite far apart. So they are still undergoing Coulombic repulsion. But now the strong nuclear force will not act between them because the strong nuclear force acts only over very short distances. So the Coulombic repulsion, the electrostatic repulsion will tend to tear the nucleus apart. And what you need are more neutrons. You need more neutrons so that you can insulate the protons from the effects of each other. Now if you have a neutron next to these protons, there will be a strong nuclear force between them and that will tend to keep the nucleus stable. But if you keep on increasing the protons, if you keep on increasing the protons, there is a limit beyond 83, adding more neutrons. They do not overcome the Coulombic repulsion force because now there are so many protons that the electrostatic repulsion sort of wins. And just adding more neutrons, they do not overcome, they do not insulate the protons from the effects of each other and the nucleus is very unstable. So all the atoms with atomic number more than 83, their nuclei are unstable. They are radioactive in nature. So this ratio goes from 1, it does not directly jump to 1.5, it goes from 1 to 1.2, 1.3, then it goes to 1.5. Now we can plot this ratio n by z. So let's try to plot this first, let's make some space. Alright so if we have number of neutrons on the y-axis and number of protons on the x-axis, then this line, the straight line, this will represent n by z equal to 1. So this is n equal to z and a line making an angle of 45 from both the axes that represents n by z equal to 1. So let's write that. This is n by z equal to 1. But if we try and plot all the atoms with whatever ratio they have, they will not all lie on this line. That will only happen up till z, the atomic number z equal to 20. And after that the ratio increases. So as a result of which the line, the line kind of looks like this. All the atoms, all the stable atoms with stable nuclei, they lie on this blue line. Up till z equal to 20, we do have a straight line, but then the ratio increases. It increases from 1 to 1.2, 1.3 up till 1.5. This blue line right here, this line is called line of stability. Let's write that. This is called line of stability. So all the stable nuclei, they will lie on this line and all the unstable nuclei, they won't lie on this line. Some might lie above on the left hand side, over here, some might lie over here to the right hand side. Some might lie on the top. If a nucleus lies in this shaded region, in the blue, light blue shaded region, what can we say about the ratio? Well up till, even up till z equal to 20, if it lies in this shaded region, the ratio is still not 1. And beyond that, beyond that as well, the ratio is still not equal to 1.5. There are too many neutrons relative to the number of protons. The ratio over here is not 1. It might be 1.3, 1.4. The ratio over here is again not 1.5, might be 1.6 or 7. And that is because it has more neutrons, more the required number of neutrons than the number of protons. So it needs to get rid of some neutrons. Nucleus will be stable if the ratio of n by z is pushed in this direction. And how will that happen? So for this to happen, there needs to be a decrease in the number of neutrons. We can see there has to be some decrease in the number of neutrons. And there has to be some increase in the number of protons. So a neutron needs to be changed to a proton. Only then the unstable nuclei which lie in this shaded region will become stable by being pushed towards a line of stability. So a neutron needs to be changed to a proton for the nuclei which are lying in this shaded region. And this is beta minus decay. Whenever a neutron changes to a proton, an electron is also emitted. And this is a beta minus decay. So all the unstable nuclei which lie in this shaded region, they are called beta minus emitters. A neutron is being changed to a proton. So let's see what that does to the ratio. One neutron decreases and one proton increases. The ratio, the ratio of n by z decreases. And that is good because the ratio was higher than required. It was above the blue line. The ratio was more. The number of neutrons were more than required. So let's take an example. If we have carbon-14, let's take an example of carbon-14. This undergoes beta minus decay. And carbon-14, after undergoing the beta minus decay forms nitrogen and one electron is released. If we calculate the ratio n by z for carbon-14, we have 14 minus 6, 8 neutrons, 8 neutrons divided by 6, 8 divided by 6. That is the n by z ratio. So that is 1.3. And for nitrogen, 14 minus 7 is 7. So 7 neutrons divided by 7 protons. So that is 1. So that's good. Maybe this carbon-14 was lying maybe somewhere over here. Now it is pushed towards the line of stability by a beta minus decay. What about the unstable nuclei which lie in this pink shaded region? Now here, the number of protons are more than the required value. The nuclei has too many protons relative to the number of neutrons. The ratio n by z over here would be less than 1 because now you have more z than n. So it needs to be pushed towards the line of stability. Over here, maybe it is less than 1.5, the ratio. It needs to be pushed towards the line of stability. And how can that be done? You need to get rid of some protons. You need to go back. You need to get rid of some protons and increase some neutrons. So that the ratio of n by z is again appropriate and the nucleus, after undergoing the decay, is pushed towards the line of stability. These are called beta plus emitters where a proton changes to a neutron and a positron is emitted in the process. Here the ratio, the ratio of n by z is increasing because the number of neutrons are increasing. It's increasing by 1 and the number of protons are decreasing by 1. Let's take an example of copper. So you have this copper which after undergoing beta plus decay, it forms nickel and a positron is emitted. We can look at the ratio n by z. So initially 6429, if we calculate the ratio of n by z, number of neutrons would be 64 minus 29, that is 35, 35 divided by 29, that would be 1.2. And in this case, the ratio becomes 1.28. So the ratio increases, it increases slightly and the nucleus of nickel would be more stable than the nucleus of this isotope of copper. So the ratio is slightly increased, the unstable nucleus undergoes decay and the product, the product that is formed is slightly pushed towards the line of stability. Now for atoms with a topping number more than 83, this is the last stable nucleus. For all the atoms beyond this, they are too large. They are just too large, they want to get rid of some protons very quick, very soon. So what happens over there is alpha decay. Alpha decay is the process which emits an alpha particle, a helium nucleus with two protons and two neutrons. Because these atoms are so large, they get rid of some protons and also some neutrons, two protons and two neutrons right away. So the ratio becomes n minus two divided by z minus two. Two neutrons and two protons are emitted right away. And as a result of this emission, this, these unstable nuclei, they are pushed in this direction. Let's see how the ratio really changes. Let's see if the ratio increases or decreases. Let's take an example for that. First, to make some space. Okay, let's take an example of uranium. So you have uranium undergoing alpha decay to make thorium 23490 and an alpha particle is emitted. So if we calculate the n by z ratio, here it is 238 minus 92 divided by 92 and here it is 234 minus 90 divided by 90. So the ratio over here, this is 1.58 and the ratio here is 1.6. Now the ratio slightly increases. That's what happens in alpha decay. The ratio slightly increases. The ratio of n by z increases, only slightly. But you might be wondering, why is that happening? We want to keep the ratio closer to 1.5, 1.56. That's, it's closer to 1.58. Why are we increasing the ratio? The only reason for that is because the nucleus is so large, it immediately needs to get rid of some protons. That's the quickest way for it to become slightly stable. That's the quickest way for it to become, for it to move towards stability. But this decay does not end here. It's highly possible that then this thorium, this thorium nucleus undergoes a beta minus decay to form 234 protactinium. And now if you check the ratio, now the ratio goes from 1.6. If you figure out the ratio for this, 234 minus 91 divided by 91, this is 1.58. The ratio is such that the atom would lie on this line of stability. So many atoms that undergo alpha decay do not just stop there at alpha decay. They do undergo some other forms of decay so that the ratio, so the ratio is such that the atom, that the final product lies on the line of stability. But for very large nuclei with atomic number more than 83, they get rid of some extra protons by just undergoing alpha decay first.