 Okay, can we start now see the next the concept we are going to study is molecular orbital theory. So first of all we will try to understand that what is the use of this theory and why do we need this? Tell me what is the structure or Lewis structure of oxygen molecule O2? The Lewis structure of oxygen molecule if you draw it is O bonded with another oxygen with a double bond and each oxygen atom has two lone pair on it, has two lone pair on it, okay? So according to this structure you see the oxygen molecule is paramagnetic or diamagnetic because all the electrons are paired, okay? So according to this structure to this, okay? But experimentally it has been observed that that oxygen is paramagnetic in nature. It is slightly attracted towards the magnetic field so it is in nature, okay? This is the experimental fact. Obviously there is something which is missing in this theory when we do the sharing of orbital or VBT theory that we have, okay? Now to explain this the behavior of this oxygen molecule, the exact behavior we have got or we got the new theory of bonding that is molecular orbital theory, molecular orbital theory. Now this, what is this molecular orbital theory? When I ask you to draw the electronic configuration of carbon, okay, you will write what? 1S2, 2S2, 2P1, okay? So this is for an element. If you remember the electronic configuration we draw only for an element, right? Not for a molecule, okay? But if you consider a molecule like suppose any general example I will take AB molecule, right? So in this we have two nucleus basically. One is the nucleus of A and another one is the nucleus of B. This B will have certain number of electrons and A will also have certain number of electrons. The electrons of B when these two are close enough in a bonding state, the electrons of B is attracted towards the nucleus of B and the nucleus of A and the electrons of A is also attracted towards the nucleus of B and the nucleus of A, right? So what we can say in this, in a molecule the electrons are considered to be associated with all the nuclei in the molecule, right? So when you take any molecules, so in a molecule, trons considered to be associated with all nuclei, whatever the nucleus present there with all the nuclei, the electrons are associated. Like in atoms we say like carbon atom we are talking about, we say the electrons are present in atomic orbital, atomic orbital. In molecules we say what? That the electrons are present in molecular orbital, molecular orbital. And this molecular orbital are forms by forms by the combination of combination of atomic orbitals, combination of atomic orbitals, right? Now if you talk about the combination of atomic orbital, there are two different ways for atomic orbitals to combine. There are two ways of, two possible ways of combining the atomic orbital. The first one is linear combination of, linear combination of atomic orbital and the second one is united atom method, united atom method. This united atom method is not in our syllabus, okay? So this is not in our syllabus, we have to study only linear combination of atomic orbital. Now you see in this linear combination of atomic orbitals, when suppose the two atoms we have A and B, A and B are combining and forms AB, a molecule, right? So this A and B when combines, so it has its own wave amplitude function that is psi A. This is the wave function of atom A and this is the wave function of atom B. And when this combines, it forms psi AB, that is the wave function of the molecule AB, right? So this kind of combination when A and B are combines, because the orbitals are nothing but the path of the electron, right? We can say if we say the electrons is in P orbital, it means what? The electron is moving in this path continuously. That's why we are calling it as P orbital double shift. S orbital means electron is moving into this path continuously, spherical shape, right? Here also like that. So the wave orbital is nothing but the path of the electron, right? And since electrons are moving, so they have wave function also with it, because when electrons move, there are, you know, waves associated with it. That is you must have studied a deep loggy wave length, right? Lambda is equals to h by mv. Means what? When m mass of velocity is moving with velocity, m mass of an object moving with velocity v, then this is the wavelength produced by that particular object. Now, since wavelength is inversely proportional to mass, so for a higher object, the wavelength is negligible and hence we neglect that. But the particles like electrons, subatomic particles like electrons, this wavelength is quite significant and we cannot neglect that, okay? Because mass is very small for these kinds of subatomic particles. So when electrons move, there are some waves associated with this with a particular wavelength, okay? So when the two orbitals, atomic orbitals are combining together, so they are nothing but their waves are combining, okay? So when we have wave, so wave can have same phase also, same phase. Or different phase also, right? Phase may be same or may be different also, both possibility we have. So when the same phase orbital combines, they form bonding molecular orbital, BMO. When opposite phase orbital combines, they form anti-bonding molecular orbital AB MO, right? So if I write down this psi AB, that will be equals to N into CA into psi A plus CB into psi B. N is the normalizing factor and CA-CB are constant. You don't have to worry with all this, what is CA and CB. We don't require this also, even in solving the questions to solve these questions. So this is not for our purpose, it is just I have written here, right? So when the bonding molecular orbital forms, when the wave or the orbital combines with the same phase, then bonding molecular orbital forms, so for that the psi AB of the molecule, the wave function of the molecule will be the sum of the wave function of the individual orbital, psi A psi B, right? But when anti-bonding molecular orbital forms, so obviously the phase is different now, so that wave function of each orbital will get subtracted, okay? Psi A minus psi B, okay? Right, this is how the two wave forms, okay? Anti-bonding molecular orbital, we write down star mark here. This star mark represents anti-bonding molecular orbital, right? If you see the energy diagram of this, anti-bonding and bonding molecular orbital, the anti-bonding molecular orbital has higher energy than bonding molecular orbital comparatively. This is energy diagram and this is the axis we have, okay? Now here you see, we can have SS combination, SP combination, PP combination and there are many things. When same phase combines, bonding molecular orbital forms, when different phase combines, anti-bonding molecular orbital forms, right? So here you see the next thing here, which is important shape of orbital I can draw, but that is not important, so I am not doing that one, okay? Only thing you see when 1S, 1S orbital is combining, we are getting two different orbital here since SNS combining, so we will have a sigma bond first, right? So for that we will write sigma 1S when same phase and sigma star 1S when opposite phase. This is anti-bonding molecular orbital, AB, MO and bonding molecular orbital. So we have basically both possibilities depending on the phase of these two orbital, okay? Similarly, when 2S, 2S orbital combines, it again forms sigma 2S and sigma star 2S, anti-bonding. When 2PX, 2PX orbital combines, it forms pi 2PX and pi star 2PY. 2PY, 2PY combines, pi 2PY and pi star 2PZ, sorry 2PY. And the last one is when 2PZ and 2PZ combines, this gives sigma 2PZ and sigma star 2PY. You see in some of the book they have written here, sigma 2PX, sigma star 2PY, sorry it is X only, X. Sigma 2PX, sigma star 2PX and pi 2PY, pi star 2PY, pi 2PZ, pi star 2PZ. So any one of these you can take along, see actually when sigma when forms, when the overlapping takes place along the inter-nuclear axis, which is along the inter-nuclear axis, right? Then only sigma forms. Generally assumption is what will take PZ along the inter-nuclear axis, so sigma will write with PZ only. But if you write with here sigma and here if you write on pi here, then also it is not wrong, okay? You will get the same answer. So that is not the concern we have. But if you have to write on better, if you write sigma with PZ and pi with PX and PY, okay? So when these orbital forms, so these are the orbitals present in any molecule, in any molecule. Like when we draw the electronic configuration of an element, we should have the energy order of those orbitals present in an atom. So similarly here also we should have the energy of these orbitals and according to the energy only, the electron will fill into this orbital from lower to higher energy orbital. Like we have done in electronic configuration, N plus L rule we have done over there, right? Lower energy orbital will fill first and then higher, the next higher and the next higher like that will go. So here also the same thing, but for that you should know the energy order of these orbitals, okay? So that is the experimental order we have, okay? There are some, you know, logic behind this, but that is again beyond our syllabus. So we are not discussing that. If the number of electrons in a molecule, number of electrons is less than equal to 14, right? Then the energy of these orbitals, which has anti-bonding and bonding molecule orbitals is given as this. Sigma 1s, then we have sigma star 1s, sigma 2s, sigma star 2s, then we have pi 2py, pi 2px, then sigma 2pz, sigma 2pz. N is greater than 14, the value of N greater than 14 and less than equal to 20. Then the order is this, sigma 1s, sigma star 1s, sigma 2s, sigma star 2s, then we have sigma 2pz, pi 2py, pi 2px, then we have pi star 2py, pi star 2px, sigma star 2pz, sigma star 2pz. Here also, if you write down, we have pi star 2ppi, pi star 2px, and then sigma star 2pz. This is the order of orbital we have. Now, these two orbitals, see, these orbitals are degenerate orbitals, these two, these two, these two, and here also, these are degenerate orbitals. Degenerate orbitals means what? Degenerate orbitals means equal energy orbital. Energy will be equal, right? Equal energy orbitals, so when you fill these two orbitals with electron, they follow Hans' rule. This orbital follows Hans' rule, this one, this one, this one follows Hans' rule, okay? So now, if I take the example of oxygen, which has 16 electrons, which has 16 electrons, so 16 electrons will be there in this range, right? So this is the orbital we have. Now, we'll substitute or we'll try to distribute the 16 electron into these orbitals, which has bonding also and anti-bonding also. So one of these orbitals can have maximum two electrons only, which is true for this case also. This sigma 1s can take two electrons, then two we have here, 4, 6, 8, 10. Since these two are degenerate orbitals, so 11, 12, then 13, 14, 15, and then 16. We cannot put two and two here first, like 2, 4, 6, 8, 10, 12, 14 we cannot do, 13, 14, 15, 16 like this. Or 11, 12, 13, 14, then 15, then 16, okay? You see here, there are two unpaired electrons present and because of this only, the oxygen is paramagnetic in nature, magnetic in nature, okay? Now we have one again bond order formula here. It is the number of electron in bonding molecular orbital minus number of electron in anti-bonding molecular orbital, this divided by two, right? So for this one, if you calculate the bond order of O2 here, that will be all these are anti-bonding, anti-bonding, anti-bonding and anti-bonding, right? 2, 4, 6, 10, 10 electron in bonding, 2, 4, 6 electron anti-bonding divided by 2, 10 minus 6 by 2, 4, so it is 2 only. So 2 is the bond order of oxygen molecule, right? If you calculate O2 minus, O2 minus will have 17 electron, so now this one extra electron, 16 we have already done, so one extra electron will go into any of these orbital, right? So number of electrons in anti-bonding orbital will increase by one, okay? So bond order if you calculate for this O2 minus will be 10 minus 7 by 2, that will be 1.5. What with O2 2 minus bond order electrons will be 18, so that will be what? 10 minus 8 by 2, that will be 1, okay? So like this we can calculate the bond order and this is the molecular orbital theory we have. What is the bond order of H2? HE2, H2 plus, tell me, what is the bond order of H2, HE2, H2 plus and N2? HE2 is 0, H2 is 1, H2 is 1, H2 plus is half, what about N2? N2 should be 3, yeah? So we also know the number of bond present in H2 molecule is 1, so bond order is 1. HE2 does not exist at all, H is the noble gas, so it's a monatomic gas. HE exists, HE2 does not exist, there is no bond into this, so it is 0. H2 plus you can find out you are getting half, maybe it is correct. N2 we know N triple bond N is the molecular formula we have, so number of bond order will be 3, number of bond is 3 into this, okay? In this also they have asked question many times in JMAs, okay, regarding the stability of these compounds, okay? They have asked this question, like one question you see that they have asked in JMAs, actually three questions we have, I'll give you all these three questions, last three questions I think we have 10 minutes, okay? So right on the first question, in which of the following pairs of molecules are ions, which of the following pairs of molecules are ions, the species does not exist, okay? Which of these species does not exist, that's the question we have. So first option we have H2 plus HE2 2 minus H2 minus HE2 2 minus H2 plus H2 minus HE2 2 plus, which of these following pair does not exist, this was asked in JMAs, option D, what about others? Don't think you calculate simply bond order, if the molecule does not exist, bond order should be 0, that's a simple thing. HE2 you see, option C, HE2, HE2 does not exist, we know that, okay? You check for H2 plus, sorry H2 plus, option C you check first, bond order should be 0, if the molecule does not exist, bond order should be 0, find out the bond order and tell me the answer. I think C should be correct, see H2 plus, H2 plus, how many electron this H2 plus has, one electron, total 2 plus 1 charge 2 minus 1 equals to 1, so bond and this will be sigma s1 then, only one electron, I don't think for this bond order is 0, bond order will be 1 minus 0 by 2, so we are getting half for this, okay, C is not correct I guess, what about H2 minus, 2 electron and then 1 for the minus charge 2 plus 1 3, so it will be sigma 1 s2, then sigma star 1 s1, this is also not 0, right, bond order of H2 minus will be 2 minus 1 by 2, that is 1 by 2, I think the option is wrong, yeah let me check something, yeah the option is wrong, some mistake is there, this should be H2 2 plus, then it will be 0, okay, see for H2 will be 0, just now we have calculated, it does not exist that it is monotomic gas, if you write on H2 2 plus then you see, H2 2 plus should be what, how many electrons total we have, total 0 electrons, right 2 minus 2, so that's why this does not exist, bond order is also 0, so this does not exist, option C will be correct if we have H2 2 plus, the option was wrong, yeah according to the given option initially that I have given here, with this H2 plus, only H2 does not exist, all other molecule exist, so if this question will be correct, if you write H2 2 plus here, okay, so basically if this kind of question they ask, you have to find out the bond order of the molecule, if it is 0 then molecule does not exist, okay, now one question they have asked on this only, which of these molecule exhibit diamagnetic behavior, diamagnetic behavior options are C2 N2 O2 and S2, which of these molecules are diamagnetic behavior, tell me, maybe more than one correct, okay C2 is correct, what about N2, C2 and N2, what about O2, O2 is paramagnetic just now we have done, okay, see O2 and N, O2 we just now we have done, O2 is paramagnetic, correct, you don't have to check S2 also, because these two belongs to the same group, if this is paramagnetic, this is also paramagnetic, right, so these two you can rule out easily, these two you have to draw the electronic configuration of from molecular orbital theory, sigma 1 is sigma star 1 is like that, and then you have to check whether the electrons are paired or unpaired, so when you draw the configuration of these two, you'll get all electrons paired, so C2 and N2 both are correct in this, right, O2 and S2 will be paramagnetic, understood, one more question, last one, the question is the stability of the species Li2, you have to find out the stability order of this, Li2, Li2 minus then Li2 plus, stability order of this you have to find out, all these three questions they have asked in GE mains, okay, molecular orbital theory, tell me what is the order, Li2 then Li2 minus then Li2 plus, Li2 plus and minus, see Li2 has greatest stability, okay, see first of all the option if you see I did not give you the option, in the option there is only one option into this, Li2 has maximum stability, right, only one option we have, so with that you can easily find out, okay, so when Li2 is maximum then answer will be correct, okay, so Li2 has greatest stability then we have Li2 plus and then we have Li2 minus, okay, so I am here to check your calculation, see, just you have to find out the number of electrons in this which is 3 plus 3, 6 electrons, okay, there will be sigma 1s2, sigma star 1s2, then sigma 2s2, bond order will be 4 minus 2 by 2, that will be 1, Li2 minus will have 7 electrons, so sigma 1s2, sigma star 1s2, sigma 2s2, sigma star 2s1, so bond order will be what, 4 minus 3 by 2, that will be 1 by 2, right, Li2 plus, that will have 5 electrons, so sigma 1s2, sigma star 1s2, sigma 2s1 with 3 minus 2 by, 1 by 2 I am getting, oh sorry, it has 3 into 2, 5 now, 3, 2, 5, 7, 2, 4, 6, 7, 4 minus 3 by 2, see one thing here, see one thing, Li2 has maximum bond order, so obviously Li2 will have maximum stability, right, now when Li2 minus and Li2 plus you compare, the number of the bond order is same, right, but in Li2 plus there is only 2 electron in anti-bonding orbital, but here we have 3 electrons in anti-bonding orbital, so if more number of electrons present in anti-bonding orbital, its stability will be less, right, so the order will be Li2, then Li2 plus and then Li minus, okay, so that's the answer we have into this, understood, so this kind of question they ask in molecular orbital theory, all questions you can solve, previous year question you see, they have asked this question only, only bond order formula you have to find out, there are many questions they have asked in JEMNs and then other exams also, so you can go through with that, so today we'll stop here only, okay, next class we'll see what will start probably Tottenberg's and all we'll do next class, okay, you understood this, okay, solve some question onto this, okay, so that you as only archives you solve, previous year question that would be better, okay, hello, thank you all, we'll see you next class.