 The edge length of the edge length of a FCC unit cell is 508.508 picometer. Edge length of a FCC unit cell is 508 picometer. The radius of cation is 110 picometer. Find the radius of an ion. Edge length is 508 FCC unit cell. The radius of cation is 110 picometer. What is the radius of an ion? What is the answer? FCC unit cell, right? So in FCC unit cell, all the atoms are anions. Along the phase diagonal, we have anions present, right? And cations are present here. See this diagram. Anions, anions, and here we have cation, right? What we can write? This distance is what? 2 into R plus plus R minus is equals to 8. A is given 508. So 508 by 2 is what? R plus R minus is 254. So R minus is what? 254 minus 110. 144, right? 144 is the answer, right? Option A. Next question you write down. Just you need to know the position of ions. Anionic solid A plus B minus and ionic solid A plus B minus crystallizes as an FCC structure. As an FCC structure, the ions along the phase diagonal, the ions along the phase diagonal has been removed. Has been removed. What is the formula of the lattice? AB FCC unit cell adapts another phase diagonal. So phase diagonal, all anions we have to remove. Phase diagonal, B A plus and B minus we have, okay? So B minus, A plus and B minus if you see, right? And we know anions occupy CCP arrangement, right? Like any CL. CL minus occupies ACV arrangement. B minus present at corners plus phase center, okay? So when all the atoms along the phase diagonal has been removed, it means we have 2B at the corner and one phase center. 3B we are removing. Two from the corner, one from the phase center. So 6 corner atoms left. 6 into 1 by 8 and 5 into 1 by 2. That is B. So this will be what? 26 by 8. So this is 13 by 4. B. A occupies octahedral void. That won't change. A is 4. A4 B 13 by 4. A16 B 13. Correct? Okay. Now see, we have an FCC unit cell, okay? AD atoms are arranged in this. Now all atoms along a diode has been removed. All atoms along a diode has been removed. What is the formula of the unit cell? Diode is two-fold exosymmetry. It is a line which passes through the crystal, okay? And when you rotate the crystal along this line, the same appearance appears twice. That is a diode. See, last class I have discussed the axis of symmetry. In this we have discussed three things. Two-fold, three-fold and four-fold exosymmetry. Two-fold exosymmetry is a line which passes through the center of the cube, right? And when you rotate the crystal along this line, as I rotate here, the same appearance appears twice in one complete rotation, okay? So this line is a two-fold exosymmetry. This will be rotated once. So you will get the same appearance on 180. You will get the same appearance on 180 again. The same appearance appears twice in one complete rotation. That is why this line is a diode, okay? So the question is the atoms along this line has been removed, all atoms, okay? So what is the formula of the unit cell? A plus, B minus. B? Four. B four. How about A five, B eight? Yeah, A five, B eight. A five, B eight. See, along this line, what are atoms we are removing? We are removing one H-center atom, okay? One body-center atom. And again, one H-center atom, okay? And H-center page, we have octahedral void. So cations present in the octahedral void. So we have A present here. Here, too, we have A. Because body-center may be octahedral void over or here may be octahedral void over. So three A we are removing, okay? Three A we are removing. Two at the H-center and one from the body-center. So number of A is what? We have ten edges, ten into one by four. Okay? Or body-center to the left. So you will have a five by two. You will have a four. So A to five by two, B. A five, B, okay? So the question is atoms along four fold axes of symmetry has been removed. Four fold axes. Four fold axes, what will happen? Opposite face-centers. Opposite face-centers, okay? Body-center plus opposite face-center. A, B. Done? Yes. So along this line, two face-center and one body-center, okay? So B is at the face-center and corner. So corner we have eight into one by eight and face-center we have four left. Four into one by two. So one plus two, three. A is what? A is twelve into one by four because body-center is removed. So plus zero, so it is three. So answer is A, B. Done? A, B. The last one, when we remove the atoms from three fold axes of symmetry. This line. Three fold axes of symmetry. Only. Alright. We have tetrahedral void also here but atoms are not present there. That does not make any difference. I don't know. Is it A-19, B-12? No? Done? See along this line we are removing two corner atoms and one body-center. Corner atom, B is present. B is what? B is six into one by eight plus six into half. So it is three plus forty-four plus thirty by eight. So it is fifteen by four, right? A is twelve into one by four. That is three. A-three, B-15 by four, right? So A-12, B-15, correct? A-4, B-5. You must know this line is three fold axes of symmetry. This is four fold and this is two fold axes of symmetry. One more thing you must take care of. Along this three fold axes of symmetry we have two tetrahedral voids also present. So if any atoms are present in the tetrahedral void that also you have to remove. In this question it is not there. Next write down magnetic properties. Write down every substance has some magnetic properties associated with it. Every substance has some magnetic properties associated with it. Electron itself behaves as a small magnet. On the basis of magnetic properties the compounds are classified into following categories. The first one, paramagnetic. This is because of unpaired electron weakly attracted towards the magnetic field. This is because of unpaired electron and it is weakly attracted towards the magnetic field. Examples of paramagnetic compounds are O2, VO, CuO, P5. All these are paramagnetic substances. Diamagnetic. All electrons are paired weakly repelled by the magnetic field. Examples are benzene, KCl, NaCl, etc. The third one is ferromagnetic substance. No magnetic substance. These are the solids which are strongly attracted by external magnetic field and they do not lose their magnetism. Definition based question they ask on this. They do not lose their magnetism when the external field is removed. Examples are nickel, Fe Ni, Cr O2. Cr O2 we use in audio videotapes because it is permanent effect. So, audio videotapes we use this. Next I will just write down. It arises due to the spontaneous alignment of magnetic moments. Spontaneous alignment of magnetic moment due to unpaired electron in the same direction. Next slide. The unpaired electrons of one atom interacts strongly with the unpaired electron of the other atom and they align themselves in a very small reason called domain. In same direction. Small reason in same direction called domain. All the electrons unpaired electrons are aligned in the same direction. In a very small reason called domain. So, this is ferromagnetic substance. The important thing here is that they do not lose their magnetism when external magnetic field is removed. That is the difference. Fourth one. Next slide. Fourth one is antiferromagnetic solids. Antiferromagnetic solids. The solids which are expected to show paramagneticism or ferromagneticism. Paramagneticism or ferromagneticism. On the basis of the unpaired electron present. On the basis of the unpaired electron present. But actually they have zero net magnetic moment. But actually they have zero net magnetic moment. Or called antiferromagnetic substance. Antiferromagnetic substance. MnO, MnO2, Cr2O3 etc. Why they are antiferromagnetic substance? Because electrons are aligned in opposite direction like this. Here all electrons are aligned in the same direction. But here we have alternate. One is upward, other one is downward. So, these two cancel out the magnetic moment of each other. That is why they have net zero magnetic moment. This is antiferromagnetic substance. So, paramagnetism and ferromagnetic substance are those which is attracted towards the magnetic field. They have unpaired electron present. Here also we have unpaired electron. But they aligned in such a way that they cancel out the magnetic moment of each other. And hence they have zero magnetic moment. Net magnetic moment is zero. Examples are this MnO, MnO2, Cr2O3 etc. Next one write down. Ferry magnetic solids. Ferry magnetic solids. These are the solids which are expected to show very large magnetism, very large magnetism due to presence of unpaired electrons. But they have a smaller value of net magnetic moment. This is due to the random alignment of electron. Random alignment of electron. Examples write down Mg204, Fe304 etc. Random alignment of electron. So, there is no order arrangement here. Suppose one is up, one is down. Then again two electrons on this side. Random arrangement of electron. So, suppose these two cancels out the magnetic moment. These two cancels out magnetic moment. And if you have some more arrangement like this. These two cancels out. But these two electrons and this electron gives a net magnetic moment. We have unpaired electron present. So, we have unpaired electron. Random arrangement gives a smaller value of net magnetic moment. Here we have maximum magnetic moment. And here we have zero magnetic moment. Example Fe304, Mg204 are the examples we have here. Now in this there is a term. We call it as effect of temperature. Effect of temperature. This alignment of electron you must remember here in these three numbers. What kind of alignment we have? Write down effect of temperature. All ferromagnetic, antiferromagnetic and ferrimagnetic substance. All ferrimagnetic, ferrimagnetic and antiferrimagnetic substance has property to become, has property to show paramagnetic behavior on heating. On heating. The next slide. The temperature at which these solids behaves as paramagnetic solids are called curie temperature. CuRie, curie temperature. So, for ion the curie temperature is 103 for nickel it is 650 Kelvin. For Fe304, 850 Kelvin. Fe304 this question they have asked once. At what temperature this behaves as a paramagnetic solids? Curie temperature is 850 Kelvin for Fe304. This temperature you must remember. Definition only important.