We have an ion mang, manganese 2 plus and an atom vanadium, and the question it asked a couple things. First of all, are they isoelectronic? And then which of the two species has the largest radius? So let's consider the isoelectronic portion first. A lot of times people incorrectly assume that if the number of electrons are the same, then the atoms and ions have to be isoelectronic. And if we look at vanadium and I find it on the periodic table here, vanadium. It has 23 protons, okay? So let's say, vanadium has 23 protons. And since it's the atom, it's going to have 23 electrons. Now manganese 2 plus, okay. If we look at our periodic table, here's manganese. It has 25 protons. So if it has 25 protons, and it has a 2 plus charge, we're going to lose two of those, no, we're not going to lose two protons. We are going to lose two electrons, so we have an excess of 2 plus charge. So we're going to have 23 electrons. So these are iso, these are, have the same number of electrons. But just because something has the same number of electrons, it doesn't mean they are necessarily isoelectronic. Because isoelectronic means they the have same electron configuration and that's the next step we have to take. Do these have the same electron configuration? Well, let's start with manganese and let's do the electron configuration of the atom first. As we look at our periodic table and find manganese, it's going to be the noble gas that comes before it and that is argon. And then it's 4s2 3d, one, two, three, four, five. So that is manganese, let's write that down. Argon 4s2 3d5. So manganese with a 2 plus charge, it's not the same as vanadium, we're going to move these to electrons. So it's going to be argon 3d5. Now for vanadium as we find vanadium in our periodic table, here it is, vanadium. Noble gas that comes before is argon. Again, it's 4s2 and we're working our way over to vanadium. We hit the 3d block, it's 3d3. So argon 4s2 3d3. And the question is, are these exactly the same electron configuration? No. So they are not isoelectronic. Now the set part of this has, which of the two species has the largest radius? Would it be manganese or would it be vanadium? Well, it's the manganese with a 2 plus charge. Okay? And then it's vanadium. They have the same number of electrons, but we know that the manganese has got two more protons pulling in the same number of elections. So, I'll be able to pull them in more tightly. Not only that, but the vanadium has got electrons in a shell that's further away than the 3d. So it's got two things going against it in terms of size. It's got a valence shell, it's further away. Farthest out for this guy is the d subshell or the 3, n equals 3. This one has got electrons in the n equals 4. Plus the manganese has got more protons. So a higher nuclear charge pulling those electrons out in. So the vanadium is larger, and the manganese 2 plus is smaller. When you have an isoelectronic series, but this is not isoelectronic. But when we see isoelectronic series in the lecture, we note that the higher the positive charge, the smaller it's going to be. This is still holding true here. So even though they're not isoelectronic, they do have the same number of electrons and the more protons you have, the smaller the radius will be.