 In this video, we're going to solve a few problems on atomic radius. Atomic radius is basically the measure of size of an atom and it is usually the distance between the nucleus to the outermost electron. Now the problem here is that electrons are not really found in well-defined parts like this, you know, not like orbits they are. They're actually found in orbitals which is basically a probability distribution of where maximum electron density is. So if we were to visualize that, how shall I make that look like one moment? Yeah, it would look something like this. Okay, so if we assume this is the area where there is maximum probability of finding an electron, we still don't have a problem solved because the electron could be here. So do we calculate the atomic radius as the distance from nucleus to this electron or the distance from nucleus to, let's say, this electron. So it is clearly different, right? Since we do not have a well-defined boundary, there are various non-equivalent definitions of atomic radius. Okay, to give you an example, let's look at covalent radius. Covalent radius refers to the size of an atom that is a part of a covalent bond because here the two atoms share an electron pair. So the covalent radius here would be half the inter-nuclear distance between the bonded atoms. On the other hand, if you look at van der Waals radius, this refers to the closest distance the two atoms can approach or come towards each other without actually forming a bond. So the van der Waals radius would be half the distance between the nuclei in this case of non-bonad atoms. Now, if you talk about ionic radius, ions are formed when an electron is removed from a neutral atom or when an electron is added to a neutral atom. Now, in the case of these ions, we can find out the ionic radii by measuring the distance between the cation and anion in what we call as ionic crystals. And interestingly, the ionic radii also exhibits similar trend as the atomic radii. So basically what I'm trying to say here is that the definition of atomic radius varies depending on what we are looking at. Are we looking at bonded atoms or non-bonad atoms or are we looking at metallic radii and so on. Alright, so that's about a brief recap on atomic radius. Let's now jump on to our questions. Okay, so let's look at the first question which says, which among the following has the largest size? Li plus, B2 plus and B3 plus are the ions that are given to us. So we have three ions, all of them are isoelectronic with each other, which means they have the same number of electrons. Okay, so let's look at lithium. The atomic number of lithium is 3, which means it has 3 protons and 3 electrons, right? But lithium plus ion has lost an electron and that means this is not 3 electrons, here we have only 2 electrons. Alright, let's look at the next one which is beryllium. Beryllium has atomic number 4, which means it has 4 protons and 4 electrons. But beryllium 2 plus ion has lost 2 electrons from the neutral atom. So that means the number of electrons in B2 plus ion would be, again, 2 electrons. And lastly when you look at boron, ion that we have is B3 plus ion. So B3 plus ion means it has lost 3 electrons and that means the total number of electrons in this ion is just 2. And if you compare them, we can see that even though they have the same number of electrons, they have different number of protons. As a result, the ions have different nuclear charge. More number of protons means stronger pull on the electrons and this makes the ions even smaller. Since boron has the maximum number of protons, this ion would shrink the most and lithium has the least number of protons and therefore would be the largest ion. So if we arrange the ions in the increasing order of their size, the order would be B3 plus less than B2 plus less than Li plus. That is, lithium ion has the largest size. Okay, so let's look at the second question. Here we are supposed to identify the correct relationship between the two ions given here based on their ionic size. So one is a fluoride ion and one is a sodium ion. So that is one is an anion and one is a cation. So this is similar to a previous question, but here we have two different types of ions. Now the atomic number of fluorine is 9. It has 9 protons again and 9 electrons. But in the case of F minus ion, we don't have 9 electrons. We actually have 10 electrons. Similarly, if you look at sodium, sodium has an atomic number of 11. That means it again has 11 protons and 11 electrons. But Na plus ion has one electron less than the neutral atom. So that means here we have a total of 10 electrons. Now, even though they're isoelectronic because Na plus has more number of protons, the electrons experience greater nuclear attraction and as a result, the ion has a smaller size as compared to fluoride ion. And now you can also look at it in a different perspective. You see when fluorine gains an extra electron to become fluoride ion, there is also extra repulsion between the electrons. Now this electron-electron repulsion pushes the electrons further apart, causing the electron cloud to expand and as a result, the anions have larger size. On the other hand, Na plus has just lost an electron and that means it experiences less electron-electron repulsion. Based on this, we can see that the correct relationship between the two given ions is option A where F minus is greater than Na plus ions. So let's look at the last question. It says that ionic radii of A plus and B minus ions are nearly the same. Then what would be the atomic radius of the neutral atoms A and B? So here we have A plus and B minus ions having the same ionic size. And we need to figure out which among these values would correctly describe the atomic radii of the neutral atom A and B, okay? So by now we have kind of figured out a general trend that the size of the cation is always smaller than its neutral atom and size of the anion is always greater than the neutral atom. Now this again comes down to the two factors, which is the effective nuclear charge and electron-electron repulsion. You see, compared to the neutral atom, its cation has already lost an electron, which means now the cation has more number of protons than there are electrons and as a result, the ionic size decreases. If the neutral atom sizes this, then the size of the cation would be less than that. And there's already something we know. If P by E ratio increases, then the size decreases. And in the case of anions, here we have fewer number of protons than there are number of electrons. And in addition to it, the extra electron that is added increases the electron-electron repulsion between the electrons in the balance shield. And this causes the electron clouds to spread and increase the size of the anion. So the anion size would be this compared to the neutral atom. So based on this, we can figure out the relationship here. Now the neutral atom should have greater size than the cation. So atomic size of A would be greater than A plus and the neutral atom here should have a smaller size as compared to its anion and this would be the relation. Now the only option that satisfies this condition, as you can see here, is option B. So if the ions have 134 picometer as their ionic size, then the neutral atom A should have a size that is greater than the cation, which is 196 picometer. And the neutral atom B should have smaller size than its anion, which is 72 picometers.