Exceptions and Exchange Energy

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Chromium has twenty four electrons. Fill them by the Aufbau rule from the last lesson, and you get the argon core, then three d four, four s two. Four s fills first, because it is lower in energy, right? But the real chromium atom says: three d five, four s one. One electron leaves the lower four s, and climbs up into three d. Why would it do that? Strange, isn't it? Keep this puzzle in your mind; by the end of this lesson, you will crack it yourself. And look, JEE questions can ask you to write these configurations, explain their stability, or count exchange pairs. So, let's begin.

0:43Extra stability: half-filled and filled subshells

So, here is the big rule of today. Half-filled and completely filled subshells have extra stability. Half-filled means every orbital of the subshell has one electron; completely filled means every orbital has two. Clear? But why are they special? There are two reasons. Reason one: the charge distribution is symmetric. Every orbital of the subshell holds the same number of electrons, so the charge is spread evenly, all around. Balanced, and so stable. Reason two is the important one: exchange energy. Now, what is exchange energy? Listen carefully. Degenerate orbitals are orbitals with the same energy, like the five three d orbitals, okay? Now, when electrons in these orbitals have parallel spins, that is, spins in the same direction, they can exchange places with each other. And every such pair that can exchange lowers the energy of the atom. Lower energy means more stable. So, more exchange pairs, more stability. Simple, right?

1:47Counting exchange pairs

Now, how do we count these pairs? With k parallel spins, the number of exchange pairs is k times, in brackets, k minus one, all over two. Why? Each of the k electrons can pair with the other k minus one, but that counts every pair twice, so we divide by two. Got it? Now a quick one. Take d five. The small five up top is the number of electrons, okay? Five electrons in the d orbitals, all spins parallel. Five electrons, so five exchange pairs, right? No, no, careful! We count pairs, not electrons. Put k equal to five: five times four, over two. Ten exchange pairs! Ten pairs, and each one lowers the energy. That is why a half-filled d subshell is so stable. With me?

2:34The exceptions to remember

Now the list every JEE student must know. First, chromium. The twenty four in round brackets is its atomic number. The argon symbol in square brackets means the argon core, all the electrons of argon, written short. Then three d five, four s one: a half-filled three d. Clear? Next, copper, atomic number twenty nine. Same idea. Which subshell do you think copper wants to complete? Yes, three d! Copper is the argon core, then three d ten, four s one. So a completely filled three d, and just one electron in four s, okay? Now, the same patterns, one period lower. Molybdenum is four d five, five s one, just like chromium. And silver is four d ten, five s one, just like copper. Exactly the same. Also gold: five d ten, six s one. And palladium, the special one: four d ten, five s zero. Zero! Palladium keeps no electron at all in five s, and its four d is completely filled. Careful here, students often miss this one. And one from the lanthanoids: gadolinium. Four f seven, five d one, six s two. Seven electrons in the seven f orbitals: a half-filled four f. The same story again, right?

3:57Example 1: why chromium is 3d5 4s1, not 3d4 4s2

So, remember our puzzle from the start? Let's finish it. Use exchange pairs to explain why chromium is three d five, four s one, and not three d four, four s two. Pause the video, and try it first. Done? Okay, let's check. First, the Aufbau guess: three d four. Four parallel spins, so k is four. Four times three, over two: six exchange pairs. And the real chromium, three d five? You already know this number. Yes, ten! Five times four, over two. So, six pairs against ten pairs. The half-filled three d clearly wins. So, two things work together here. The gain in exchange energy, plus the symmetric half-filled subshell. The plus sign just means and, okay? Together, they outweigh the small energy needed to move one electron from four s to three d. The arrow means from four s, into three d. And there it is, puzzle solved! That electron climbs up because the atom gets much more back in exchange energy and symmetry.

5:04Example 2: exchange pairs in N 2p3 and O 2p4

Now a slightly harder one, JEE level. Count the two p exchange pairs of nitrogen, two p three, and of oxygen, two p four, with three spins up and one down. Pause and try. Hint: only parallel spins can exchange. Done? Okay, nitrogen first. Two p three: by Hund's rule, three electrons, all spins parallel. So k is three. Three times two, over two: three pairs. Easy. Now oxygen, with four electrons in two p. So k is four: four times three, over two, six pairs, right? More than nitrogen? No, no, careful! This is the JEE trap. Only parallel spins can exchange. The three up spins give three times two, over two: three pairs. And the one down spin? It has no partner with the same spin. So the total is still three. Nitrogen three, oxygen three. Okay? But oxygen has one more problem. Its fourth electron is paired with another electron, and the two repel each other strongly. And that is one reason why the first ionisation energy of oxygen is lower than that of nitrogen. The sign between them means less than, okay? See, the exchange pairs are equal, three and three, so it is this extra repulsion that makes the difference!

6:27Quick revision: k(k-1)/2 pairs and the exceptions

So, quick revision. Half-filled and completely filled subshells have extra stability. With k parallel spins, there are k times k minus one, over two exchange pairs, and only parallel spins count. And learn the exceptions: chromium, copper, molybdenum, silver, gold, palladium and gadolinium. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!