Understanding Atomic and Ionic Radii

Hello students, welcome back to the tetrahedron chemistry classes. So, guys in today's class I am going to discuss very simple aspects of periodic properties which you have already studied in your class 11th. And see the topic which actually I am going to take today is first is actually your atomic radii. So, what is the meaning of the atomic radii? So, it will not make any difference if you say the atomic radii or the atomic size, both are same. So, we will try to learn the concept actually, what this atomic radii means actually. For example, say you are having any atom. I am taking, say I am having say carbon. I am having this carbon which is having the atomic number of 6. If you write the electronic configuration then it is 2 comma 4. If you simply draw the picture of the atom of this carbon atom. So, in the center you see I am writing C here and this C you may consider as the nucleus of the carbon and this is the first shell. And this is the second shell of the carbon. You know, this is the first shell, which is K shell, and this is L shell. So, in the K shell, you are having the two electrons. Say, one electron is this one, and another electron is this one. And then, in the L shell, you are having another two electron, and you can fill those electron like that. Say, one, two. 3 and 4. So, this is the simplest picture of the carbon atom. Now, what is the atomic radii? So, atomic radii is nothing, but it is the distance actually this particular distance, which starts from the nucleus of the carbon and goes up to the outermost electron. So, this distance is basically your atomic radii. This distance is known as the atomic radii. So, by definition is what the distance between the nucleus and the outer most electron of an atom is called the atomic radii. And now say if you are having this atomic radii and suppose that you are having another species say you are having sodium ion Na positive. You are having the sodium positive you know the sodium is having the atomic number of 11. if it lost 1 electron that mean it will have the 8 electron. So, the configuration would be just like that 2 comma 8. So, now, again the same thing say this is the nucleus of the sodium and this is your first shell which is your K shell and this is your L shell. So, your K shell is having 2 electron again and then you are having. second L shell and this shell is also having the 8 electron 1, 2, 3, 4, 5, 6, 7, 8 and this is actually positively charged. This is sodium positive. This is iron. Basically, it is cation. You know the species which are having the positive charge on it. They are known as the cation. So, if you want to know the ionic radii of this cation, so what you will do? You will take the distance between the nucleus of this sodium ion and this outermost electron. You may take this outermost electron, you may take this outermost electron. See, out-of-weight electron, you can take any of one actually. So, in an ion, the ionic radii is the distance between the nucleus and the outermost electron, outermost electron, the electron which is present on the outermost shell. And say now if you have another thing, say for example, you are having fluoride F negative, you know F negative, fluorine is having the atomic number of 9. Now, it is having 1 negative over there. So, it will have the total 10 electrons. Again, the configuration would remain same, that is 2, 8. So, if you want to draw this one, say this is F negative, this is the nucleus of the fluorine. So, this is K shell and this is the L shell and again you can fill the electron on it 1 and 2 and remaining 8 electrons 1, 2, 3, 4, 5, 6, 7, 8. So this is anion. This is what anion. The species which are having negative charge over there they are known as the anion. So if you want to know the ionic radii of this anion so what you will do you will take the distance from the nucleus to the outermost. electrons, right? And that distance would be your ionic radii, right? This is your ionic radii and this is your ionic radii. So, this is the concept of the atomic radii and ionic radii. When you consider the atom, then it would be the atomic radii. If you consider the ion, then it would be the ionic radii and ionic radii can be of two types, okay? See, you may have the cation, you may have the anion, right? This is the basic simple concept actually. But this is not enough to know. This is not enough to know. Why this is not enough? You know, we cannot isolate atom, right? Isolation of atom is very, very difficult. We cannot isolate. We can't isolate atom or ion, okay? So, we cannot isolate atom or ion. And when we cannot isolate atom or ion, then how we can go for the how we can know all these things. So, for this what actually we do actually right. So, we actually take the different kinds of the radii. So, what different kinds of the radii we will take? We will discuss one by one. Say first I am taking the atomic radii and here in that case this atomic radii I am calling it as covalent radii, covalent radii. So, when we say the covalent radii it simply means the molecule is covalently bonded. Basically, this covalent radii is defined for the nonmetals. This you should know, defined for the nonmetals. Nonmetal means you may have the chlorine, you may have the fluorine, all these things, you may have the nitrogen because they form the covalent bond between them. Say I am taking this example. of chlorine actually right. So, what will happen actually say this is the chlorine and this is the chlorine and this is the total bond distance this is the bond distance and this bond distance is basically your 198 picometer this bond distance is 98 picometer which is known as the bond length. So, if you want to know the radii of your chlorine atomic radii of the chlorine So, what you will do actually in that case? You will write say for example, I am writing RCl and that would be your bond distance between Cl and Cl divided by 2. What is the meaning of that? I will take 198 and divide it by 2 getting this value of 99 picometer. So, this 99 picometer is the covalent radii of the chlorine. So, what is the general formula actually to calculate this one? And this formula actually I have given here, you see r equals to d by 2, where d is what? The bond length or the bond distance. So, see why this happens actually? Because say this is the chlorine, this is another chlorine and we cannot isolate a single chlorine. So, we will take this molecule actually. So, this distance from one nucleus to other nucleus, this is actually the total bond length and we when we divide this total bond length by 2 actually, if we bisect in that manner, in that manner. So, this particular distance, this particular distance the single one it is known as the covalent radii. So, see so what would be the definition? One half of the bond distance bonded together by a covalent bond is known as the covalent radii. This is simply, this is very, very simple. But the problem is that this is quite simple when we have the homonuclear diatomic molecules. These all are homonuclear diatomic molecules, homonuclear diatomic. So, what is the meaning of the homonuclear diatomic? Diatomic means two atoms are involved just like that and homo means both are of identical kind. But the problem is that what is the problem when you have the different kind of the species say for example you are having HBR. So, this is another covalent compound and you know every see in your polarization and the Fasan's rule I have already explained every covalent bond will have some ionic corrector. This is something very very important every covalent bond will have some ionic corrector and this ionic corrector would be significant when we have the heteronuclear diatomic molecules. So, in that case actually what will happen due to this ionic corrector is that the ionic corrector will be the bond length actually is not just the half of the bond. See, your covalent radii is not just the half of the bond length actually when we have the homonuclear, heteronuclear diatomic species because they have some ionic character. Due to the ionic character, actually the bond length decreases. When the bond length decreases, what will happen? The ionic radii also decreases. So, for this actually, what we do generally, say we can take Covalent radii, I am writing it as A, R, A, B. So, you can consider this A, you can consider this B. This is how you can write. So, for this, you have a formula which was given by some expert actually, right? And that formula is here R A plus rb minus 0.09 chai A minus chai B. This is something very, very important. So, this is the formula given by certain expert. Unfortunately, I did not remember that particular name. But it is not good actually. We should remember the name of the experts who contributed in the field. Sorry for that. So, this is the formula. So, R a is the radii of atom a, R b is the radii of the atom b, 0.09 is your constant and chi a is the electronegativity of atom a and chi b is the electronegativity of the atom b. So, this is how you can calculate. But later on this formula actually also modified by certain expert and fortunately I remembered that name. right. Potterfied actually Potterfied or Potterfied name of the expert is P-O-T-E-R-F-I-E-D. He actually changed this formula to certain other formula R-A-B that is equals to R-A plus R-B minus 0.07 times. chi A minus chi B square. So, if you have been given these things, these parameters, then you can calculate the radii of any atom actually, which you have given. So, these things actually certain way, these things are very, very important. So, the conclusion is that, what is the conclusion? Due to the ionic character present in the heteronuclear diatomic molecules. which we have studied in the Fasan's rule. The bond length actually the length the bond length is the shorter than the sum of the covalent radii of the two individual atoms. So, you will remember this particular point if you are comparing Br Br then obviously this would be different if you comparing H H then these two would be different. So, these are the things which you which you should know actually. So, this is the concept of the covalent radii when you have the covalent bond but another type of the radii is very common right and that that is your say okay unfortunately this picture is not quite good so please okay i have increased the size okay so next actually i am going to discuss is wonderwall's radii So, see initially we have seen the covalent radii and in this particular picture if you see this part is actually your covalent radii, covalent it is actually the distance, covalent distance. or total bond distance and this part is actually which is shown by the black is the covalent radii. Now, if you want to know the concept of the covalent radii then you should know the important thing. See these vulnerable forces are the secondary forces. Wonder wall forces are secondary forces. They are not actually primary bond, they are actually secondary forces. What is the meaning of the secondary forces? There is no involvement of the electrons in it actually, right? They depend on the surface area. Wonder wall forces depends on the surface area and when you are talking about the wonder wall forces, now it simply means you are talking about the noble gases. Simply it is defined for the. gases, this is something very, very important. You may take the noble gases and also for the same non-metallic elements. which you should know. So, what is the meaning of that? Say for example, this is one molecule diatomic and this is another molecule which is also a diatomic, right? And they are having the interaction between them, but there is no bond in between them. So, if you want to know the radii, the Van der Waal radii, so what you will do? You will actually take the distance of this one and distance two actually nearest atoms you will take and you will measure the distance between them right and if you take the half of this if you take the half of this then this distance would be your wonderwall radii so this is quite different actually you see if you if you are talking about the covalent radii it simply means this is the bond distance okay and this half actually is your covalent radii but in case of the wonderwall radii these atoms are not connected actually they are separated somewhere and which I have shown you here actually. So, this distance actually which I am highlighting here you see this distance. This actually this hole is your covalent sorry Wonderwall diameter and if you take the half of this which is this one this actually your Wonderwall radii. This is something very very important which you should know. So, what is the definition? One half of the distance between the two nuclei of the two non-bonded and identical neighboring atoms of the adjacent molecules in the solid state. So, what is the meaning of what is the meaning say this is actually in the solid state this sample is in the solid state and in this solid in solid state you are having this molecule you are having the another molecule okay and these two nuclei actually are not bonded together by any chemical bond. But they are adjacent to each other and we are taking the half of the distance between the two neighboring adjacent atom in the solid state. That would be your Wonderwall radii. I hope this is clear to you. And remember one thing, since there is no bonding involved in it, so the important thing is that your Wonderwall radii actually will always be lower than, say I can write here, Wonder wall radii is less than covalent radii. So, I am writing here covalent radii. So, it is actually smaller. No, it is not a smaller, very sorry, I made a mistake. Since there is no involvement of any bond, it should be actually greater. So, you can see here, it should be greater actually, right? So, wonder wall radii is always greater than the covalent radii and the example is this say you are having a hydrogen molecule okay so for this hydrogen molecule if i remember correctly covalent radii is 37 picometer so i am writing cr cr stands for the covalent radii okay i should write radii here and if you go for the van der waal radii then it would be quite large somewhere around 120 picometer. So, this is something very, very important which you should know actually. I hope this is clear to you. Now, we will see the factors affecting the covalent radii. How the, see there is no, not much of importance in describing the periodic variation of Wonderwall radii. But of course, we will discuss the factors affecting covalent radii. So, I can write factors affecting covalent radii. So, they should be only 1D radii. So, what are the factors actually? This is something very, very important. So, point number 1, number of shells, number of shells is directly proportional to the atomic radii, atomic radii. Of course, the covalent one. So, what is the meaning of that? Say for example, you are comparing carbon with your chlorine. Chlorine is 17. So, you can write 2, 8 and 7 electronic configuration and for carbon you will write 2 and 4. These are the different species. So, here in that case, this is your K shell, this is your L shell, this is your M shell. And for this, this is your K shell, M shell. So, here number of shells are larger actually, right. So, the chlorine should have actually the higher covalent radii or the atomic radii compared to the carbon. However, there are certain things actually which actually you need to consider, okay. So, what actually I do? To make it a little more clear, I am not actually writing a particular name of the atom. I can write say A having the atomic number of 6 and B having the atomic number of 7. So, higher the shell, higher would be the golden trade. This is something very, very important. So, why I have omitted that carbon and chlorine? Because they may have the opposite relation, because periodic variation is something else actually. We will see later on. So, what is the second factor? Second factor is the effective nuclear charge. So, guys, you have already studied the concept of the effective nuclear charge. And then you have also calculated Slater's rules and all shielding constant with the help of the Slater's rule. So, you are very familiar with the effective nuclear charge. So, effective nuclear charge is inversely proportional to the atomic radii, inversely proportional to the atomic radii. So, what is the meaning of that? If effective nuclear charge is high, then the atomic radii would be less. It simply means that whenever if you have the higher effective nuclear charge that mean that. The positive charge is more in the nucleus and when the positive charge is more in the nucleus, it will attract the electron towards itself strongly. Consequently, the electron cloud gets actually decreased. That is why the atomic radii decreases. This is something very, very important. And third point, which is another very important point, bond multiplicity. is inversely proportional to the atomic radii. What is the meaning of that? You may have the single bond, you may have the double bond, you may have the triple bond. So, when bond order increases, then atomic size decreases. So, here you see this is bond order which is increases, then definitely your atomic size I am writing ar atomic radii it is decreases it is decreases. So, these are the factors which you actually consider which you generally consider when you actually when you are talking about this your atomic radii or the ionic radii. Now next thing that is say periodic variation periodic variation of atomic radii. So, what is the meaning of the periodic variation? When you move along the row, that means from left to right in the periodic table, then your atomic radii decreases. And when you go downwards, then your atomic radii decrease. increases. So, it is just like that you are having that carbon, nitrogen, oxygen, fluorine. So, it is 6, it is 7, it is 8, it is 9. So, obviously, you see Carbon will have the higher size when compared to the nitrogen. Nitrogen will have the higher size when compared to the oxygen. And fluorine will have the lower size. Why this happens actually? See, the reason is quite obvious. When you move across the period, effective nuclear charge increases. So, across the period, effective nuclear charge increases. So, how we can explain this thing? See, guys, this is quite simple actually. Say, for example, I am writing. say i am writing carbon here it is 6 that is you see 1s2 and 2s2 i can write in that manner and 2p2 okay then i am writing the nitrogen 7 it is 1s2 2s2 and 2p3 so in that case 7 protons are there In that case, six protons are there in the nucleus. So, you see the extra electron in case of the nitrogen is added to the same shell because it is your L shell. It is also your L shell. okay okay this is k this is k shell and these two are l shell right so the extra electron is added in the k shell that means the distance is not actually increases but the positive charge increases in the nucleus this increases the effective nuclear charge and when the effective nuclear charge increases it attracts the electron clouds towards itself right and consequently the electron cloud contracts and the size decreases that's why this is the periodic variation. Now, you can take another example. Say for example, you are having lithium here. After lithium, you are having the sodium. Lithium is 3, sodium is 11. If you write the electronic configuration, then it would be just like that. 1 is 2, 2 is 1. For sodium, it is 1 is 2, 2 is 2. 2 p 6 and 3 s 1. So, when you actually go down the group, so here you see the principal quantum number is 2 actually it is L shell, but here it is M shell. So, when shell increases, the radii increases, which you have already studied. So, this is how you can explain the thing. So, this is your atomic radii. This is your atomic radii. Now, the second last thing which is left in this particular lecture, the concept of the ionic radii, concept of the ionic radii. So, this is something very, very important. So, you should remember. Cation is always smaller than parent atom. Cation is always smaller than parent atom. What is the meaning of that? Say you are having the sodium 11. So, you are having say 2, 8 and 1 and then you are having the sodium positive. You know the how sodium positive is formed? See the 11 when it loses 1 electron it will form the Na positive. When it is formed the Na positive it is having the only 10 electrons. So, when it is having the 10 electrons it is 2 and 8. So, here you can see here this. is your K shell, this is your L shell, this is your M shell. In that case, this is K shell, this is L shell. So, when you remove an electron from an atom, one of the cell actually gets disappear. So, when it disappears, obviously, your number of cells decreases. When number of cells decreases, definitely the atomic or the ionic radii also decreases. That is why the cation is always smaller than their parent atom, which is something very, very important, which you should know. And similarly, if you go for the anions say for example, so I am writing here anions are always bigger than their. parent atom which is something very very important okay so what is the meaning of that it simply means if you are having say chlorine 17 so what you will have you will have 2 8 and 7 and if you are having the chloride ion chloride means how chloride will form chlorine 17 when it will accept 1 electron. So, it will form the chloride negative it will have the total 18 electron is not it. So, when it is having the 18 electrons, so configuration would be 2, 8, 8. So, in that case, you see the number of electron increases. However, the C shell is quite fine. This is K, this is L, this is M shell. This is also K, this is L, this is M. But now you see the protons are same. In that case, 17 protons are there. In that case also 17 protons are there. But in that case, you are having the 18 electrons. In that case, you are having the 17 electrons. So, whenever the number of electrons increases and protons remain same, that means the attraction, force of attractions actually would be smaller because negative charge increases. So, consequently, what happens? The electronic repulsion would occur. And due to this repulsion, the electron cloud expands. When electron cloud expands, we say that the chlor the anion will always have the bigger size than their parent atom so whether you can uh you can explain in that manner that mean uh on adding the extra electron it is acquiring the noble gas configuration so electronic repulsion actually would occur due to this repulsion the cloud expands this is the one way of explaining second way is just like that number of protons in both the species right number of protons whether in this species or in this species are same but here in the anion the number of electrons actually are higher So, 17 electrons cannot actually attract these 18 electrons more effectively as they are as they were actually attracting the 17 electrons. So, consequently the electron cloud expands which actually increases the size of the size of the anion. So, periodic variations are same again if you move across the period. So, decreases your ionic radii decreases. And On down the group ionic radii increases. So, what is the meaning of that? See if we are taking about say your say chloride ion and your fluoride ion. So, obviously, fluoride would be smaller and when you take your say lithium sorry lithium not lithium positive we can we can take the lithium positive also. So, Just like that, say for example, you are having say nitrogen negative, 2 negative or nitrogen 3 negative. So, in that case, what we can do, we can skip this example. It can actually. can cause the confusion, but you should remember this thing actually, right? When we go down the group actually, so what we can take? We can take say oxygen 2 negative and we can take sulphur 2 negative. So, you know this actually oxygen is having the atomic number of 8 and this sulfur is having the atomic number of 16 and if you add 2 electrons to it that will be making S2 negative it would be 18 electron and if you add add 2 electrons to it, it would be 10 electrons. So, number of electrons actually are higher here. So, shells actually are higher. So, for 18 actually you will have 2, 8 and 8 that is K, L and M. So, shells are increasing. So, radii will also increase. In that case 8, 2 comma 6, sorry 2 comma 8 that is K shell and L shell. Shells are increasing. less, so the radii decreases, right? So, down the group, radii increases and across the period, ionic radii actually here decreases. So, this is the concept of the ionic radii. So, I have given you a much more detail of these, right? These are quite sufficient for your BTEC first year examination as well as for other examination also. Okay, guys. So, that is it for today.

So, we will try to learn the concept actually, what this atomic radii means actually. For example, say you are having any atom. I am taking, say I am having say carbon. I am having this carbon which is having the atomic number of 6. If you write the electronic configuration then it is 2 comma 4. If you simply draw the picture of the atom of this carbon atom.

So, in the center you see I am writing C here and this C you may consider as the nucleus of the carbon and this is the first shell. And this is the second shell of the carbon. You know, this is the first shell, which is K shell, and this is L shell.

So, in the K shell, you are having the two electrons. Say, one electron is this one, and another electron is this one. And then, in the L shell, you are having another two electron, and you can fill those electron like that.

Say, one, two. 3 and 4. So, this is the simplest picture of the carbon atom. Now, what is the atomic radii? So, atomic radii is nothing, but it is the distance actually this particular distance, which starts from the nucleus of the carbon and goes up to the outermost electron. So, this distance is basically your atomic radii.

This distance is known as the atomic radii. So, by definition is what the distance between the nucleus and the outer most electron of an atom is called the atomic radii. And now say if you are having this atomic radii and suppose that you are having another species say you are having sodium ion Na positive.

You are having the sodium positive you know the sodium is having the atomic number of 11. if it lost 1 electron that mean it will have the 8 electron. So, the configuration would be just like that 2 comma 8. So, now, again the same thing say this is the nucleus of the sodium and this is your first shell which is your K shell and this is your L shell. So, your K shell is having 2 electron again and then you are having. second L shell and this shell is also having the 8 electron 1, 2, 3, 4, 5, 6, 7, 8 and this is actually positively charged.

This is sodium positive. This is iron. Basically, it is cation.

You know the species which are having the positive charge on it. They are known as the cation. So, if you want to know the ionic radii of this cation, so what you will do? You will take the distance between the nucleus of this sodium ion and this outermost electron. You may take this outermost electron, you may take this outermost electron.

See, out-of-weight electron, you can take any of one actually. So, in an ion, the ionic radii is the distance between the nucleus and the outermost electron, outermost electron, the electron which is present on the outermost shell. And say now if you have another thing, say for example, you are having fluoride F negative, you know F negative, fluorine is having the atomic number of 9. Now, it is having 1 negative over there.

So, it will have the total 10 electrons. Again, the configuration would remain same, that is 2, 8. So, if you want to draw this one, say this is F negative, this is the nucleus of the fluorine. So, this is K shell and this is the L shell and again you can fill the electron on it 1 and 2 and remaining 8 electrons 1, 2, 3, 4, 5, 6, 7, 8. So this is anion.

This is what anion. The species which are having negative charge over there they are known as the anion. So if you want to know the ionic radii of this anion so what you will do you will take the distance from the nucleus to the outermost.

electrons, right? And that distance would be your ionic radii, right? This is your ionic radii and this is your ionic radii.

So, this is the concept of the atomic radii and ionic radii. When you consider the atom, then it would be the atomic radii. If you consider the ion, then it would be the ionic radii and ionic radii can be of two types, okay?

See, you may have the cation, you may have the anion, right? This is the basic simple concept actually. But this is not enough to know. This is not enough to know.

Why this is not enough? You know, we cannot isolate atom, right? Isolation of atom is very, very difficult.

We cannot isolate. We can't isolate atom or ion, okay? So, we cannot isolate atom or ion. And when we cannot isolate atom or ion, then how we can go for the how we can know all these things.

So, for this what actually we do actually right. So, we actually take the different kinds of the radii. So, what different kinds of the radii we will take?

We will discuss one by one. Say first I am taking the atomic radii and here in that case this atomic radii I am calling it as covalent radii, covalent radii. So, when we say the covalent radii it simply means the molecule is covalently bonded. Basically, this covalent radii is defined for the nonmetals. This you should know, defined for the nonmetals.

Nonmetal means you may have the chlorine, you may have the fluorine, all these things, you may have the nitrogen because they form the covalent bond between them. Say I am taking this example. of chlorine actually right.

So, what will happen actually say this is the chlorine and this is the chlorine and this is the total bond distance this is the bond distance and this bond distance is basically your 198 picometer this bond distance is 98 picometer which is known as the bond length. So, if you want to know the radii of your chlorine atomic radii of the chlorine So, what you will do actually in that case? You will write say for example, I am writing RCl and that would be your bond distance between Cl and Cl divided by 2. What is the meaning of that?

I will take 198 and divide it by 2 getting this value of 99 picometer. So, this 99 picometer is the covalent radii of the chlorine. So, what is the general formula actually to calculate this one?

And this formula actually I have given here, you see r equals to d by 2, where d is what? The bond length or the bond distance. So, see why this happens actually? Because say this is the chlorine, this is another chlorine and we cannot isolate a single chlorine.

So, we will take this molecule actually. So, this distance from one nucleus to other nucleus, this is actually the total bond length and we when we divide this total bond length by 2 actually, if we bisect in that manner, in that manner. So, this particular distance, this particular distance the single one it is known as the covalent radii. So, see so what would be the definition?

One half of the bond distance bonded together by a covalent bond is known as the covalent radii. This is simply, this is very, very simple. But the problem is that this is quite simple when we have the homonuclear diatomic molecules.

These all are homonuclear diatomic molecules, homonuclear diatomic. So, what is the meaning of the homonuclear diatomic? Diatomic means two atoms are involved just like that and homo means both are of identical kind. But the problem is that what is the problem when you have the different kind of the species say for example you are having HBR. So, this is another covalent compound and you know every see in your polarization and the Fasan's rule I have already explained every covalent bond will have some ionic corrector.

This is something very very important every covalent bond will have some ionic corrector and this ionic corrector would be significant when we have the heteronuclear diatomic molecules. So, in that case actually what will happen due to this ionic corrector is that the ionic corrector will be the bond length actually is not just the half of the bond. See, your covalent radii is not just the half of the bond length actually when we have the homonuclear, heteronuclear diatomic species because they have some ionic character. Due to the ionic character, actually the bond length decreases.

When the bond length decreases, what will happen? The ionic radii also decreases. So, for this actually, what we do generally, say we can take Covalent radii, I am writing it as A, R, A, B. So, you can consider this A, you can consider this B.

This is how you can write. So, for this, you have a formula which was given by some expert actually, right? And that formula is here R A plus rb minus 0.09 chai A minus chai B. This is something very, very important. So, this is the formula given by certain expert.

Unfortunately, I did not remember that particular name. But it is not good actually. We should remember the name of the experts who contributed in the field. Sorry for that.

So, this is the formula. So, R a is the radii of atom a, R b is the radii of the atom b, 0.09 is your constant and chi a is the electronegativity of atom a and chi b is the electronegativity of the atom b. So, this is how you can calculate.

But later on this formula actually also modified by certain expert and fortunately I remembered that name. right. Potterfied actually Potterfied or Potterfied name of the expert is P-O-T-E-R-F-I-E-D.

He actually changed this formula to certain other formula R-A-B that is equals to R-A plus R-B minus 0.07 times. chi A minus chi B square. So, if you have been given these things, these parameters, then you can calculate the radii of any atom actually, which you have given.

So, these things actually certain way, these things are very, very important. So, the conclusion is that, what is the conclusion? Due to the ionic character present in the heteronuclear diatomic molecules.

which we have studied in the Fasan's rule. The bond length actually the length the bond length is the shorter than the sum of the covalent radii of the two individual atoms. So, you will remember this particular point if you are comparing Br Br then obviously this would be different if you comparing H H then these two would be different.

So, these are the things which you which you should know actually. So, this is the concept of the covalent radii when you have the covalent bond but another type of the radii is very common right and that that is your say okay unfortunately this picture is not quite good so please okay i have increased the size okay so next actually i am going to discuss is wonderwall's radii So, see initially we have seen the covalent radii and in this particular picture if you see this part is actually your covalent radii, covalent it is actually the distance, covalent distance. or total bond distance and this part is actually which is shown by the black is the covalent radii.

Now, if you want to know the concept of the covalent radii then you should know the important thing. See these vulnerable forces are the secondary forces. Wonder wall forces are secondary forces.

They are not actually primary bond, they are actually secondary forces. What is the meaning of the secondary forces? There is no involvement of the electrons in it actually, right? They depend on the surface area.

Wonder wall forces depends on the surface area and when you are talking about the wonder wall forces, now it simply means you are talking about the noble gases. Simply it is defined for the. gases, this is something very, very important. You may take the noble gases and also for the same non-metallic elements. which you should know.

So, what is the meaning of that? Say for example, this is one molecule diatomic and this is another molecule which is also a diatomic, right? And they are having the interaction between them, but there is no bond in between them. So, if you want to know the radii, the Van der Waal radii, so what you will do?

You will actually take the distance of this one and distance two actually nearest atoms you will take and you will measure the distance between them right and if you take the half of this if you take the half of this then this distance would be your wonderwall radii so this is quite different actually you see if you if you are talking about the covalent radii it simply means this is the bond distance okay and this half actually is your covalent radii but in case of the wonderwall radii these atoms are not connected actually they are separated somewhere and which I have shown you here actually. So, this distance actually which I am highlighting here you see this distance. This actually this hole is your covalent sorry Wonderwall diameter and if you take the half of this which is this one this actually your Wonderwall radii. This is something very very important which you should know.

So, what is the definition? One half of the distance between the two nuclei of the two non-bonded and identical neighboring atoms of the adjacent molecules in the solid state. So, what is the meaning of what is the meaning say this is actually in the solid state this sample is in the solid state and in this solid in solid state you are having this molecule you are having the another molecule okay and these two nuclei actually are not bonded together by any chemical bond.

But they are adjacent to each other and we are taking the half of the distance between the two neighboring adjacent atom in the solid state. That would be your Wonderwall radii. I hope this is clear to you.

And remember one thing, since there is no bonding involved in it, so the important thing is that your Wonderwall radii actually will always be lower than, say I can write here, Wonder wall radii is less than covalent radii. So, I am writing here covalent radii. So, it is actually smaller. No, it is not a smaller, very sorry, I made a mistake. Since there is no involvement of any bond, it should be actually greater.

So, you can see here, it should be greater actually, right? So, wonder wall radii is always greater than the covalent radii and the example is this say you are having a hydrogen molecule okay so for this hydrogen molecule if i remember correctly covalent radii is 37 picometer so i am writing cr cr stands for the covalent radii okay i should write radii here and if you go for the van der waal radii then it would be quite large somewhere around 120 picometer. So, this is something very, very important which you should know actually. I hope this is clear to you.

Now, we will see the factors affecting the covalent radii. How the, see there is no, not much of importance in describing the periodic variation of Wonderwall radii. But of course, we will discuss the factors affecting covalent radii.

So, I can write factors affecting covalent radii. So, they should be only 1D radii. So, what are the factors actually?

This is something very, very important. So, point number 1, number of shells, number of shells is directly proportional to the atomic radii, atomic radii. Of course, the covalent one. So, what is the meaning of that?

Say for example, you are comparing carbon with your chlorine. Chlorine is 17. So, you can write 2, 8 and 7 electronic configuration and for carbon you will write 2 and 4. These are the different species. So, here in that case, this is your K shell, this is your L shell, this is your M shell. And for this, this is your K shell, M shell.

So, here number of shells are larger actually, right. So, the chlorine should have actually the higher covalent radii or the atomic radii compared to the carbon. However, there are certain things actually which actually you need to consider, okay.

So, what actually I do? To make it a little more clear, I am not actually writing a particular name of the atom. I can write say A having the atomic number of 6 and B having the atomic number of 7. So, higher the shell, higher would be the golden trade.

This is something very, very important. So, why I have omitted that carbon and chlorine? Because they may have the opposite relation, because periodic variation is something else actually.

We will see later on. So, what is the second factor? Second factor is the effective nuclear charge.

So, guys, you have already studied the concept of the effective nuclear charge. And then you have also calculated Slater's rules and all shielding constant with the help of the Slater's rule. So, you are very familiar with the effective nuclear charge.

So, effective nuclear charge is inversely proportional to the atomic radii, inversely proportional to the atomic radii. So, what is the meaning of that? If effective nuclear charge is high, then the atomic radii would be less. It simply means that whenever if you have the higher effective nuclear charge that mean that.

The positive charge is more in the nucleus and when the positive charge is more in the nucleus, it will attract the electron towards itself strongly. Consequently, the electron cloud gets actually decreased. That is why the atomic radii decreases.

This is something very, very important. And third point, which is another very important point, bond multiplicity. is inversely proportional to the atomic radii.

What is the meaning of that? You may have the single bond, you may have the double bond, you may have the triple bond. So, when bond order increases, then atomic size decreases.

So, here you see this is bond order which is increases, then definitely your atomic size I am writing ar atomic radii it is decreases it is decreases. So, these are the factors which you actually consider which you generally consider when you actually when you are talking about this your atomic radii or the ionic radii. Now next thing that is say periodic variation periodic variation of atomic radii. So, what is the meaning of the periodic variation?

When you move along the row, that means from left to right in the periodic table, then your atomic radii decreases. And when you go downwards, then your atomic radii decrease. increases. So, it is just like that you are having that carbon, nitrogen, oxygen, fluorine. So, it is 6, it is 7, it is 8, it is 9. So, obviously, you see Carbon will have the higher size when compared to the nitrogen.

Nitrogen will have the higher size when compared to the oxygen. And fluorine will have the lower size. Why this happens actually?

See, the reason is quite obvious. When you move across the period, effective nuclear charge increases. So, across the period, effective nuclear charge increases. So, how we can explain this thing?

See, guys, this is quite simple actually. Say, for example, I am writing. say i am writing carbon here it is 6 that is you see 1s2 and 2s2 i can write in that manner and 2p2 okay then i am writing the nitrogen 7 it is 1s2 2s2 and 2p3 so in that case 7 protons are there In that case, six protons are there in the nucleus. So, you see the extra electron in case of the nitrogen is added to the same shell because it is your L shell. It is also your L shell.

okay okay this is k this is k shell and these two are l shell right so the extra electron is added in the k shell that means the distance is not actually increases but the positive charge increases in the nucleus this increases the effective nuclear charge and when the effective nuclear charge increases it attracts the electron clouds towards itself right and consequently the electron cloud contracts and the size decreases that's why this is the periodic variation. Now, you can take another example. Say for example, you are having lithium here. After lithium, you are having the sodium. Lithium is 3, sodium is 11. If you write the electronic configuration, then it would be just like that.

1 is 2, 2 is 1. For sodium, it is 1 is 2, 2 is 2. 2 p 6 and 3 s 1. So, when you actually go down the group, so here you see the principal quantum number is 2 actually it is L shell, but here it is M shell. So, when shell increases, the radii increases, which you have already studied. So, this is how you can explain the thing. So, this is your atomic radii.

This is your atomic radii. Now, the second last thing which is left in this particular lecture, the concept of the ionic radii, concept of the ionic radii. So, this is something very, very important.

So, you should remember. Cation is always smaller than parent atom. Cation is always smaller than parent atom.

What is the meaning of that? Say you are having the sodium 11. So, you are having say 2, 8 and 1 and then you are having the sodium positive. You know the how sodium positive is formed?

See the 11 when it loses 1 electron it will form the Na positive. When it is formed the Na positive it is having the only 10 electrons. So, when it is having the 10 electrons it is 2 and 8. So, here you can see here this.

is your K shell, this is your L shell, this is your M shell. In that case, this is K shell, this is L shell. So, when you remove an electron from an atom, one of the cell actually gets disappear. So, when it disappears, obviously, your number of cells decreases. When number of cells decreases, definitely the atomic or the ionic radii also decreases.

That is why the cation is always smaller than their parent atom, which is something very, very important, which you should know. And similarly, if you go for the anions say for example, so I am writing here anions are always bigger than their. parent atom which is something very very important okay so what is the meaning of that it simply means if you are having say chlorine 17 so what you will have you will have 2 8 and 7 and if you are having the chloride ion chloride means how chloride will form chlorine 17 when it will accept 1 electron. So, it will form the chloride negative it will have the total 18 electron is not it. So, when it is having the 18 electrons, so configuration would be 2, 8, 8. So, in that case, you see the number of electron increases.

However, the C shell is quite fine. This is K, this is L, this is M shell. This is also K, this is L, this is M.

But now you see the protons are same. In that case, 17 protons are there. In that case also 17 protons are there. But in that case, you are having the 18 electrons.

In that case, you are having the 17 electrons. So, whenever the number of electrons increases and protons remain same, that means the attraction, force of attractions actually would be smaller because negative charge increases. So, consequently, what happens?

The electronic repulsion would occur. And due to this repulsion, the electron cloud expands. When electron cloud expands, we say that the chlor the anion will always have the bigger size than their parent atom so whether you can uh you can explain in that manner that mean uh on adding the extra electron it is acquiring the noble gas configuration so electronic repulsion actually would occur due to this repulsion the cloud expands this is the one way of explaining second way is just like that number of protons in both the species right number of protons whether in this species or in this species are same but here in the anion the number of electrons actually are higher So, 17 electrons cannot actually attract these 18 electrons more effectively as they are as they were actually attracting the 17 electrons.

So, consequently the electron cloud expands which actually increases the size of the size of the anion. So, periodic variations are same again if you move across the period. So, decreases your ionic radii decreases.

And On down the group ionic radii increases. So, what is the meaning of that? See if we are taking about say your say chloride ion and your fluoride ion. So, obviously, fluoride would be smaller and when you take your say lithium sorry lithium not lithium positive we can we can take the lithium positive also. So, Just like that, say for example, you are having say nitrogen negative, 2 negative or nitrogen 3 negative.

So, in that case, what we can do, we can skip this example. It can actually. can cause the confusion, but you should remember this thing actually, right?

When we go down the group actually, so what we can take? We can take say oxygen 2 negative and we can take sulphur 2 negative. So, you know this actually oxygen is having the atomic number of 8 and this sulfur is having the atomic number of 16 and if you add 2 electrons to it that will be making S2 negative it would be 18 electron and if you add add 2 electrons to it, it would be 10 electrons.

So, number of electrons actually are higher here. So, shells actually are higher. So, for 18 actually you will have 2, 8 and 8 that is K, L and M.

So, shells are increasing. So, radii will also increase. In that case 8, 2 comma 6, sorry 2 comma 8 that is K shell and L shell. Shells are increasing.

less, so the radii decreases, right? So, down the group, radii increases and across the period, ionic radii actually here decreases. So, this is the concept of the ionic radii.

So, I have given you a much more detail of these, right? These are quite sufficient for your BTEC first year examination as well as for other examination also. Okay, guys.

So, that is it for today.

Transcript for:Understanding Atomic and Ionic Radii

Transcript for:
Understanding Atomic and Ionic Radii