 Hello, good evening All of you please type in your name Let me know who are there Shugosh is there all of you please type in your name Shugosh, Neha, Sri Ramya. Okay So today we are going to start Not start. We are going to revise atomic structure today Very you know the basic chapter but important Okay, so in this chapter atomic structure We are going to study about the structure of atom as the name itself suggests right Okay, so this is just a revision class Okay, so we will discuss all the important topics here, but not all the topics right So we'll discuss only important topics Which is useful for problem-solving Okay, so like the very basic thing we have in a structure of math model, which is nothing but the the first thing where we have is the discovery of electron proton and neutron, okay So we know the atoms are made up of very various subatomic particles Right, so atoms made up of subatomic particles for example, like electron proton Neutron, okay, mainly these three subatomic particles we discussed right But apart from this we have meson also positron and other Subatomic particles also, but mainly we'll discuss what really we'll talk about electron proton and Neutron, okay, these three are the main subatomic particles that we discussed. Okay, so first of all Since any atom if you say Right any atom is neutral, right? It is neutral. There's no charge Suppose if I say carbon atom see there is no charge on carbon atom So it is neutral in nature Similarly nitrogen phosphorus anyone if you take it is neutral in nature, right? So before discussing this structure of an atom first of all we have to Understood or we have to know that there are Various subatomic particles from which the atoms have been made right So how do we get this subatomic particles for that? We have various different discovery like we have discovery of of electron proton and neutron It is given in NCRT also. I'm not going to discuss this experimental thing again. Okay. We can read it out. Okay So electrons are negatively charged Right protons are positively charged and neutrons are what neutrons are neutral Right, so when you draw an atom the structure of an atom atom are assumed to be spherical in shape So this is an atom and this is the nucleus Right, how do we get the? Nucleus discovery of nucleus also we have one thing that is another for model. Okay, so in the nucleus we have proton and neutron present and in the orbital electron revolves around the nucleus like this only the Subatomic particles are arranged Right, so the arrangement of subatomic what happens here when we have this electron proton and neutron when we came to know That there are various subatomic particles present within an atom then we started what we started To understand that how this subatomic particles are arranged within an atom, right? So what is the arrangement of subatomic particles we have how this subatomic particles are placed or arranged within an atom Okay, so in this course we get different atomic models Different atomic models here we get okay, so what are the different atomic models we have there are Models like Thomson model rather Ford model board model all these models we have right So we have Thompson model Rutherford model and Then in the last we have Boards model boards model and one more we have wave mechanical model Okay, so this Rutherford model because of this model only or because of Rutherford only we have an experiment here Also that we known as discovery of nucleus so nucleus Discovered by Rutherford only okay discovery of nucleus we have here only in which there is an experiment with gold Fine and all you must have done all those things. I'm not going to again this Discuss those experimental thing here But discovery of nucleus is done by Rutherford and then the most important model because all these models are given by the scientist called Thompson and Rutherford, but these models will have some I had some what? Drawbacks, okay, there are few drawbacks in Thompson model There are few drawbacks in the report model. So finally what happens? We have discarded all these models. Okay, and then Boards was one of the scientists He has also given his own model of atoms and that we call it as Boards model. This model is comparatively more accurate Okay, or right also, but the only thing here at constraint here It is what in in in case of Boards model that it is applicable for It is applicable for only one electron system One electron System one electron system means what the atoms must have one electron for in case of hydrogen Hydrogen atomic number is one one electron right for carbon. Sorry for lithium Lithium atomic number is what three. So this is not applicable for Boards model, right? So whatever the formula we get in Boards model that is only applicable for one electron system, right? So li for li it is not valid But when I write li plus 2 it has one electron. So for li plus 2 it is valid Okay, so like this there are few constraints we have in Boards model that you have to keep in mind That's why you must have solved some question in which whenever we have the application of Boards model They always give you one electron system Right, they always give you one electron system So in this Boards model will come back or we'll finish this Boards model here only then we'll move to the dual nature of light Okay, so what is a Boards model? There are a few You know, there are a few postulates of Boards model. We have right So if you want to write it down all those postulates, you can follow my notes Okay, those who are new who have joined late they you can ask your friends for that notes You can get all those postulates. Okay, so I'm not dictating those postulates here But I'm giving you one or two few important postulates of Boards model Okay, that is important for you to understand, right? So what this Boards Atomic model or the postates of Boards model is It says that one of the important point here. It is what that out of infinite orbit. See first of all Whenever you have an atom, okay Whenever you have an atom this atom has one nucleus. Okay Yeah, that is also one model correct apple pie putting it's right sugar So this is one orbit around the nucleus and this is another orbit Next orbit the next orbit like the meaning of this is what? in an atom there are in an atom There are infinite orbit presence infinite orbit presence and that point of time when we were discussing this Boards model at that point of time We have this understanding. We had this understanding that atoms contains infinite number of orbits And in these orbits electron resides Electron resides in these orbits, right? But later on I'll tell you but there is nothing called orbit within an atom Right when you write down orbit orbit is actually wrong Okay, but electron in which the electron resides we call it as orbital not orbit Okay, so what is orbit and orbital that we'll discuss later on But around an atom like around the nucleus of an atom. There are infinite number of orbit right now. We do not know about Like till here when we were discussing when we were talking about Boards model Here now we do not have any information about orbital Okay, we only know one thing that there is orbit present and in this orbit electron resides Okay, but actually later on you will come to know that there is nothing called orbit in an atom but electron resides in a you know in a Space three-dimensional space and that we call it as orbital not orbit. Okay, so we'll come to that later on Okay, so what Boards one of the important costumers of Boards is what out of infinite number of orbits around the nucleus electron can devolve Only in those orbit in which its angular momentum is integral multiple of h by 2 pi So what Boards suggest that the angular momentum of electron Should be equals to integral multiple of h by 2 pi Right, so electron Devolves only in those orbit in which the angular momentum of the electron This is the mass of the electron velocity of the electron and r is the radius of that orbit Right this distance is the radius of that orbit Right, so m v r must be equals to n h by 2 pi where n is an integer. This is one important postulates of board which which Was proven later on. Okay, this this actually this equation or this relation has been observed by Boards Experimentally, okay, there is no, you know supporting, you know argument behind this relation Okay, given by Boards But he observed one fact that electron decides or revolve only in those orbit Where the angular momentum is n h by 2 pi later on will have the proof of this also Okay, we'll discuss that. Okay Right now since we have different orbits present Correct. So in one particular orbit electron has Definite amount of energy Right when you give some energy to this electron electron may jump to the higher energy Level or a higher orbital Understood. So in one orbit definite amount of energy We have when you supply some energy to that electron electron will jump to the higher orbit and hence like this only the electron Um switches orbit over here Similarly, if suppose if this is one orbit we have I'm just writing down like this to make you understand And here we have energies like this Or bits right or different energy level also we can say each of these orbit will have certain energy, right? So that energy level I am writing down like this. Okay, suppose the electron is here now You assume the electron Is here in this orbit Right now when you supply energy to this electron with the you know irradiation of light Then with this energy electron will jump into the Higher energy level. Okay. Suppose. This is one joule. This is two joule This is four joule and this is ten joule I I have taken this value randomly to make you understand when the electron is in this energy level Its energy must be two joule Right when you go when you give energy to this electron so that the energy becomes four joule it will jump into this Uh orbit again again. You give energy it will jump over here if the energy is ten joule But whenever the electron resides in this orbital orbit energy will be ten joule here It is four two and one. Okay. Similarly when the electron loses energy Then it will come down to the lower orbit or lower energy level. So both way it is correct Okay, this is again one of the postulates of bore model we have okay Now you see one thing here. Also, you can understand that why the you know Both model is applicable only for one electron system. Okay so what one again one important observation here we have our postulates that What bore says that Since the electron is revolving in one of these orbit Right electron is revolving like this. So you must have started in circular motion when one object is moving in circular path Like this right there must be some you know The then the object must have The centripetal force which is equals to what? mv square by R v is the velocity of that object And r is the radius in which the object is moving radius is up to a path Right. So when the object so what happens here since the electron also moving in this orbital So this electron also must have the necessary amount of centripetal force towards the nucleus or center Right. So what is the you know, what is how this electron gets this centripetal force here? Right, that's the point. So if you see when you observe this atom Right with atomic number z Right. So charge present in the nucleus will be z e And one electron if you observe here it is moving in this orbit of radius r One electron here moving in this orbit of radius r Right. So this is moving like this Correct. And since this nucleus is positively charged and this electron is negatively charged. So we have here Centripetal force of Electrostatic force of attraction Okay, the charge in the nucleus is z e and here the charge is e the force applied by these two opposite charge Will be k q 1 q 2 by r square. What is this formula? I'll tell you suppose one charge is here And another charge is present here at q 2 which is q 2 the distances are between these two Right and both are of opposite nature Right. So since both charges are of opposite nature. So we have what we have electrostatic force of attraction between these two Right. So that electrostatic force of attraction is given by this formula Where k is a constant q 1 q 2 by r square r is the distance between the two charge Right the same formula if you try to apply here, right one electron that is q 1 is e and q 2 is z e So the electrostatic force of attraction here it is f is equals to k e into z e q 1 q 2 by r square Right now this force of attraction is what towards the center. So obviously this is the agent we have which supply the necessary amount of centripetal force which is m v square by r Right. So one equation of board model is this m v r is equals to n h by 2 pi another equation is this which is k z e square by r is equals to m v square Okay, this is the second relation Now when you solve these two equation you will get velocity in certain orbit and radius in certain orbit, okay So this derivation this derivation is not required for your question, right for your For the question you get but these formulas are important of r and v that you will get Okay, I'll write down the formula also Now the point is like I said that board model is applicable only for one electron system When I say one electron system it means the atom must contain only one electron White is not valid for more than one electron system, right? So the point here you see here that we are considering this attraction force And that is what we are equating towards the with the centripetal force, right? Now you assume this case Suppose we have more than one electron system and electrons are present here in inner orbital also Inner orbit also, right? So since this is electron negatively charged This is electron negatively charged. So this electron and this electron will repel each other This electron and this electron will also repel each other This electron and this nucleus will attract Right and this electron this nucleus will also attract. So you see there are how many there are so many forces present here Right now this force we have to solve According to the vector law and we have to get the net force towards the nucleus in this direction Right, so hence when we have more than one electron system So there are many different forces involved into this and that's why this calculation becomes very difficult And hence it is not applicable Okay, that calculation is beyond our scope to understand at this level. Okay So that's why the poor atomic model is you know is bonded to only for One electron system That's the reason we have here because this equation becomes very difficult now and it will be difficult to solve So when you solve these two equation coming back to the formula here When you solve these two equation, you will get the radius r and the velocity v So the formula of radius that you get here Is equals to radius r n n means in nth orbit Right the formula of r n is equals to 0.5 to 9 n square by z This formula you have to memorize once you know this formula you can solve the question. Okay second the velocity formula in nth Orbit that is v n is equals to 2.18 into 10 to the power 6 z by n meter per second Take care of the unit also here. We have meter per second and here we have angstrom right now Few things which is important here n is the nth orbit So for first orbit n value will be one for both i'm talking about for first where orbit n is equals to 1 Second orbit n is equals to 2 and so on right now z is what z is the atomic number for both formula Atomic number and for hydrogen For hydrogen z value is 1 right for lithium z value is 3 But remember one thing all this formula is not applicable for lithium. It is applicable for what li plus 2 Right, so for li plus 2 will be atomic number will not change But when we write li plus 2 it has only one electron and hence the formula is applicable for this Right, so like this we do now Our n value r1 if I try to find out. Okay radius of um radius of hydrogen atom in first orbit That will or r0 will write okay radius of hydrogen atom in first orbit That will be 0.5 to 9 n value is 1 Square since it is hydrogen. So it is also 1 so r0 is nothing but 0.5 to 9 This right so this we can write this relation as radius in nth orbit is equals to the radius in the first orbit Into n square by set Right, so this is the formula We get now one question you write down here Find the ratio of of the radius of radius of hydrogen and Li 2 plus iron in second and third orbit Respectively Tell me the answer of this question Should there's getting 2 is to 3? 4 is to 3 Others tell me the answer See ramiya is getting 4 is to 3 Okay, I'll solve this quickly See what we have to find out Radius of hydrogen atom in second orbit So I'll write down r2 That will be equals to r0 2 square And since this is for hydrogen so that value is what 1 Right, this is for hydrogen Now radius are in third orbit For li plus 2 That will be equals to again r0 3 square Z for li 2 plus will be 3 So 1 is this and 2 We have to find out 1 is to 2 That will be equals to r2 for hydrogen divided by r3 for li plus 2 r0 r0 will get cancelled. So we'll get 4 by 3 and this is the Answer here Right, so you don't have to Understand or You know Understand the derivation that for Bohr's model You just have to memorize this formula for radius and this formula for velocity in nth orbit Right now coming back to the next thick concept here Suppose the electron Suppose the electron is moving in nth orbit Here you see one electron we have here And this is moving in nth orbit the velocity in nth orbit is vn And the radius for nth orbit is rn Right now since the electron is moving continuously So obviously this electron will have some Kinetic kinetic energy because the electron has mass also and it has velocity also Right So what is the kinetic energy we can write for this electron in this orbital? The kinetic energy of this electron will be half The mass of the electron me and velocity in this orbit that is vn Square electron mass we already know Right 9.1 Indra minus 31 kg So when you substitute m here Or when you substitute vn here that formula we have already calculated We will get kinetic energy Right Similarly we can also find out the potential energy also One thing let you just let me know when the two charge is present at a distance r You will study this in electrostat In physics Right q1 q2 at a distance r So we have discussed the Electrostatic force of attraction which is nothing but f is equals to k q1 q2 by r square At this time only both this charge will have some potential And the potential energy here we can write that is k into q1 q2 by r not r square When you write r square it becomes what it becomes force r is only Potential energy Right now half mv square you see since we know from the Bohr's postulate that the Electrostatic or The centripetal force we have mv square by rn is equals to what we can write k q1 q2 by rn square Right so here me vn square is equals to what k q1 q2 by rn That is nothing but the kinetic energy is equals to half Into k q1 q2 by rn little bit. We are discussing the derivation also Potential energy of the electron is this now this Nucleus has charged z e and this is e so potential energy here it will be what k z e into e by rn square So this becomes what k z e square divided by rn Okay, total energy if I try to find out that will be the sum of kinetic plus potential energy You're talking about the energy of electron why rn What is the dot dot brinda rn2 In the question in the question you are talking about brinda. Oh here it should be rn only not square Is it right? Yeah, correct. This one by mistake. I have written it's rn only fine I hope it's clear now It's rn not rn square Correct, so you see the total energy will be what the sum of this and this okay So when you add these two the total energy you will get here Will be equals to kinetic energy is half k z e square by rn Plus potential energy is z e square by Okay, now Here one thing You have to understand What is that that the potential energy is negative? Potential energy is negative here You will study this in Electrostat physics Minus k q and q2 by this for the formula is minus here This is force the potential energy is minus here. It will be minus here, right? Actually, what happens? One thing you must understand here That the electron It is nucleus and this is at the infinite distance here. We have electron So the energy of electron at infinite distance from the nucleus is assumed to be zero Right, so when you are taking this electron close to the nucleus Okay, you have to do some work in this if you want to shift this electron from here to here or here Or here close to the nucleus you have to do some work on it And that work will be stored in this electron and that's why the potential energy is assumed to be what negative Right, so potential energy of the electron is negative Right minus k q and q2 by r square will write So when you put this negative charge here also Here also and you solve this you'll get minus k z e square by 2 r n Now k z e square by r n is nothing but potential energy. You see k z e square by r n So total energy is what it is it is half of potential energy Half of potential energy because potential energy itself is negative now if you compare this potential energy and kinetic energy relation Okay, kinetic energy is what kinetic energy is equals to Is equals to minus half of potential energy because kinetic energy is positive Right, so when you relate all these things you will get the total energy is equals to minus Plus half of potential energy and then potential energy is this kinetic energy is this so that will be minus half of kinetic energy that is also that is also one of the relation we have correct so now the point is Potential energy is k z e square by r n This is a constant. We have z values atomic number. We know for hydrogen atom e value We'll also have r and we have already calculated. Okay, so when you substitute all these known term the formula of The energy In nth orbital, you'll get minus 13.6 z square by n square electron volt Okay Total energy is negative. You must take care of potential energy In nth orbital is equals to twice of this minus 27.2 z square by n square electron volt kinetic energy Is equals to minus total energy that will be 13.6 Z square by n square electron volt So the energy relation we can write total energy is equals to minus of kinetic energy is equals to minus of kinetic energy is equals to potential energy By This is the relation we have minus this way, right? So this is the relation we have One more like this. These are the three formulas in electron volt. The unit is electron volt. This formula is important Okay, another formula in another unit. We have total energy can be given as 2.18 into 10 to the power minus 18 z square by n square Joule per atom This is the another formula we have Right, so important point here. Sometimes you have to find out the ratio of energy in second and third orbit Okay, so this formula will be what in second and third orbit for the same atom Since we know from these formula that the energy is directly proportional to what z square by n square So for the same atom what we can write For the same atom z value is what's equal. So energy is directly proportional to inversely proportional to n square So when we have to find out e2 by e3 of the same atom Of the same atom here Then what we can write n Of three square divided by n two square or we can write three square by two square Which is nine by four Okay, this is how we calculate this formula. Sometimes it is useful But the most important thing is what energy is directly proportional to z square by n square This is the most important relation we have next to write down dual nature of light light has dual characteristics Right, that is The first nature of this we have wave nature And the second one we have particle nature wave nature and particle nature Right, so to understand the wave nature we have various term that we use And the first term we have is wavelength. It is represented by lambda Okay, just again, okay So now wavelength is what since we are talking about a wave here So generally the wave Propagates like this you see Wave propagates like this, okay Now in this you see All these peaks, okay this peak this peak and further also This peak we call it as crest And these points are trough GH only not T crest and trough, okay so The distance between The two consecutive crest or trough is known as one wavelength So this distance here Is lambda for this wave Or we can also take this distance This is also one wavelength that is lambda So the definition of wavelength is what it is the distance between Two consecutive crest or trough First thing is this This way you can define Another definition is what you are starting the wave is starting from here So you start from here Right and at what point what next point The direction of the wave is same with same phase. Okay, you see the wave is going like this started like this Here also the wave is going like this. So these two are parallel here. So from here to here We say there is one wavelength again from this to this direction We have another second wavelength then third then fourth like this So this distance is also one wavelength here Any way you can define the wavelength of light The next term that we use here is frequency Frequency frequency can be donated by small f or new Small f or new It is what frequency is the number of wave produces per unit time number of wave Produces per unit time. So new should be equals to one by T Where t is the time period right now suppose if the Wave is propagating with a velocity v right so time period to travel In one wavelength will be given as new is equals to one by Time is what distance by velocity that is lambda by v And then we can write new is equals to v by lambda So for electromagnetic wave or em wave For em wave, we know all these em wave travels with the same velocity So v is constant Okay for em wave velocity is constant. So we can write new into lambda Is equals to constant So for our electromagnetic wave If the frequency is more then wavelength will be less and vice versa Okay third term we have here that is time period t capital t This is given as t is equals to lambda by v. Just now I have discussed t is equals to lambda by v V is the velocity of the wave lambda is the wavelength One important term here. Also. We have that is wave number lambda bar new bar, sorry new bar wave number wave number is nothing but the inverse of the wavelength Right, so its unit will be meter inverse So these are the few basic of terms that we use in wave nature of light in for any wave actually, okay So this formula you must remember formula based question they asked generally Okay, the next thing we'll discuss and this one is important particle nature Is it clear till here? Okay, now you see To understand the particle nature first of all you have to understand that What are the properties of light? That could not be explained through wave nature Right, for example There are certain properties or phenomenon Okay, which could not be explained Phenomenon of light which could not be explained on wave nature. The first phenomenon is what? It is the nature of emission of radiation nature of emission of radiation By hot body Which is nothing but the black body radiation second thing is what? emission of electrons emission of electrons from metal surface metal surface when light strikes at it so first of all with all the light electrons does not come out Okay, first thing is that light must have certain range of frequency Okay, so what is that we'll discuss in photoelectric effect now only we'll discuss Okay, so i'm not going in detail now into this Now first of all you see If you have an iron rod Okay, if you have an iron rod, Fe rod And when you heat this When you heat this iron rod Then what happens? If you see or if you observe there will be change in color Okay, first first of all the color is The color is dull red slightly red it is Then as the temperature increases color becomes More red it becomes more red Then it becomes white And then it becomes blue at higher temperature You keep on increasing the temperature of this iron rod the color changes like this Okay, so now when the color changes if you see for all this color The Vibg you must know V-I-B-G Y-O-R Here you see if you're going from red to violet The frequency increases and wavelength decreases Right So now if you see this pattern dull red red white and blue It means The frequency keep on increasing right in this Keep on increasing So why this different different energy and with frequency also we know there are energy associated with it So why different different energies are coming out when you heat this iron rod? Okay, so this phenomenon is also not observed or explained by the wave theory of light Okay, now later on plank Was one of the scientists was a scientist who explained this particular phenomenon and then we call it as the plank Quantum theory it is Okay, it is solved by plank and it is given as plank Quantum theory and what is this plank quantum theory? It says that The atom molecules can emit or absorb energy Only in discrete quantities Okay, what is plank quantum? This is very important. Okay, you try to understand it very clearly Atoms or molecules molecules emit or absorb energy energy only in discrete manner Means what the energy present here is not continuous energy is not Continuous This is what we have Uh explained by the plank continuous means what energy is not present in continuous See when you see the light, okay If you have a light source and when you strike lights from that light source on a surface You see what you see the light strikes like this. Okay, it goes and it strikes on a surface So when I say discrete means what because light source, whatever you have here the light source, right? this will You know Produce light like this and this light is looking like okay It is to continuous then what is the meaning of discrete here? It looks like continuous, but it is not continuous. There are infinite number of particles present into this suppose we have one particle like this Then we have another particle Then we have another particle It's like this So it looks like this But actually there are infinite number of back-to-back particles present in the light and these particles only strike Strikes one by one onto the surface Okay Now the point is coming back to this. This is nothing but the particle nature Okay, because a light energy is not continuous. It is available in discrete manner or in packets It is available in packets. Okay Each packets will have certain amount of energy and when it strikes to the surface any surface One packet will strike at a time and the energy associated with that particular packet that will only exchange Okay, that's the thing So this is what the particle nature of light on this nature only the photoelectric effect has been explained Okay, so what is that? Let me tell you okay So photoelectric effect is what if you have First you write down the heading here photo Electric effect have you studied this photoelectric effect? What is photoelectric effect tell me? Any one of you What is photoelectric effect when light strikes at the metal surface? There is a rise of electron. It happens always Sugosh See okay, so you know the basic definition of photoelectric effect. Okay So can you tell me? What happens When the frequency of Incident radiation increases Whatever light we are striking at the metal surface and photoelectric effect is taking place When we increase the frequency of that incident light, what happens then? Can you answer this? Shruti Shiramya Sugosh What happens when the frequency of incident light increases? What happens? when the frequency Of incident light increases suppose you are striking on the metal surface with one particular light of a certain frequency and photoelectric effect is taking place What happens when you increase the frequency of light now you see Here you have to understand the concept first of all See The metal surface is this This is the metal surface we have Now since it is a metal surface. So it must have some electrons in it right There are some electrons present onto this metal surface now electrons Of which atom the atom which means the metal has been made Okay, so when you have electrons so for each atom if you consider there are infinite number of atoms present here And for each atom if you are considering one atom One atom will have spherical shape like this Right, it has some nucleus one nucleus and it will have one electron also here And this electron is associated with this nucleus by electrostatic attraction force. Yes or no tell me Yes I am talking about one single atom over here I have magnified the one single atom here like this number of photo electrons increases Okay, you see Is it clear this electron is associated with this nucleus? Fine Yes or no Is it clear all this electron will be associated with the nucleus like this fine Now in photoelectric effect your definition is correct when the light of certain frequency It strikes at the metal surface electrons comes out. That is photoelectric effect, right? So when this electron has to come out Right, then what have what you have to do you have to break this Force of attraction. Yes or no when you break this force of attraction then only the electron will get free and it will come out Correct now to break this Force of attraction and to overcome this force of attraction. We are supplying energy to this electron with the help of an light Of new frequency so h nu is the energy associated with it We know energy e is equals to what with new frequency e is equals to h nu is the energy associated with the new frequency correct So when you are striking with a frequency that is incident frequencies new in Right, then the energy associated with the incident frequency is h nu in So when I say you are striking with a light of frequency nu It means we are striking with the energy of h nu right So when this energy is taken up by this electron This will overcome the attraction pull over here and the electron comes out and this electron which are coming out We call it as photo electrons Right, this is photoelectric effect Now this is what given in the book right, but The actual thing you have to understand here to solve the question If you want to solve the question for j you have to understand the actual what happens here See we are going to understand this photoelectric effect in two different uh segment one is Uh observation Right And other one is explanation Now both this segment or both this uh phase of this concept is given by two different scientists Okay, first of all this phenomenon Phenomenon of what photoelectric effect electron which is coming out it is observed by a scientist called henry herds h e r t z Okay, so what he did actually he has taken a metal sheet Okay, and in that metal sheet he strikes with a light of certain frequency Right, he strikes with a light of certain frequency on it What he observed That there is no emission of electrons. Okay, listen to me very carefully Right when the light of certain and all these things was doing by herds, right? He strike the Metal plate with a certain frequency of light and nothing observed right no electrons comes out then what happens He increases the intensity of light intensity of light means what you are striking With uh once of Light like this now when you increase the intensity it means you are increasing the light like this more intense light we have now Right intensity you must have you must watch tv, right in tv You see yeah, when there are options of changing color right contrast and all So when you are changing the color you are changing the frequency of light When you are increasing the brightness you are increasing the intensity of light That's what the difference between frequency and intensity Right, so what hurts did he strikes the metal plate with a certain frequency of light Nothing came out then he increases the intensity of light then also nothing happened Okay, with large intensity also nothing happened So again he what he did he has changed the light he has taken different frequency of light Again, he is tried at the metal surface. Nothing came out intensity increases. He increases the intensity again And then also nothing came out here, right? He he actually kept on repeating this experiment with several different frequency of light Okay, finally what we observe for a given uh, you know a metal a light with certain frequency new Right the electrons came out in this Uh in this experiment right, but what he observed that this light with which the electron is coming out The intensity of this light is quite less than the intensity. He has already used Right, then he got confused like how it happened because that time the conception is Was that more intensity means more energy of light, okay Since he is using the more energy previously electron was not coming out And he has changed the intensity then with it changed the frequency then and with lower intensity also the electron was coming out So he started thinking that how it is possible We were using the large intensity means more energy previously electron was not coming out and with less intensity on Only the electron is coming out. However, the frequency is more Right, then what he since he has or he had observed all this thing Then he said what that the energy of the light wave is depends only on the frequency of light It has nothing to do with the intensity of light Right, but he did not understand this he could not explain this fact like why it is happening But since he observed this thing he then he Then he published his paper like what the energy is Energy energy depends depends upon frequency not on intensity And then every other scientist in that era they started, you know Like embarrassing him since he could not explain this fact, right? Then he was like that this experiment is wrong You have done something some mistake into this and all and he did not have any answer Since he could not explain this Then later on The explanation of this fact since this fact was correct and this fact was Explained by a scientist called Einstein. You must have heard his name Right and this Einstein has taken the help of plan quantum theory to explain the concept to explain this phenomena Understood. So what Einstein said that that the Energy of a light wave is not continuous, but it is available in discrete manner Right. So when you say that the energy suppose a light is this Suppose this is the light wave we have So the Einstein explanation you try to understand none of the second part of this concept Einstein explanation was what in this light wave there are infinite number of you know Photons are present like this It is not continuous like just now I said that energy is present in discrete manner like this So there are infinite photons are present in this light wave like this And this right and when when we say that energy E is equals to h nu E is equals to h nu This is the energy of one photon E is equals to h nu This is the energy of one photon not all the photon present in the light wave Okay So if you have n number of photons present here then the total energy will be E is equals to n h nu correct This is what the discrete manner we have not continuous Okay, it is something like suppose you have a light source and when you strike the light On the metal surface then what happens this Photon the first photon will strike at the metal surface first And whatever the energy this photon has it will give to the electron Right and if this energy is sufficient to overcome this attraction force the electron will come out Otherwise the electron will not come out Did you understand this? Is it clear? Tell me till here is it clear Right So this is what the meaning of discrete manner we have not continuous. Okay So it is something like it is something like if I take one example of Suppose you have a like, you know gun which is ak-47 suppose Right and with this gun you are striking at a target Then what happens with this gun one by one the bullet comes back to back correct First bullet will strike then second bullet will strike then third fourth Fifth like this. It's not like all the bullet strikes at the same time Fine. So first of all the first bullet will strike Whatever the energy this bullet has it will transfer to the target Then the second then the third and fourth like this correct similar way photons also strike with the Metal plate. Okay. You have a light source Right light source. You just you know Replace by ak-47 the same example. I'm taking here Since this is a light source here. We have bullet but here. We have photons right photons are the particles of light Okay, so with the light source Thousands or infinite number of photons came out back to back And at a time one photon only strike at the middle surface then the second photon then third fourth fifth like this Okay, this is how the light strikes with any object. Okay one point is this now another point What is the problem or like? What Was the thing which actually happened happening with hers when it says that when the intensity of light, suppose it is increasing Right intensity means what if you initially suppose you have 10 photon When you increase the intensity this 10 becomes 50 Photon further you increase 50 becomes 100 photon But will that energy of photon changes in this case? During this course when you are increasing the intensity of light Number of photon is changing But the energy of photon is changing or not the energy of photon is changing or not tell me When the hurt when hurt was increasing the intensity of light does it affect the energy of photon single photon Yes, or no, tell me what happened doubt Tell me the answer No, right So the point is when suppose if hers has taken one incident one light with certain See strikes at the middle surface electron did not come out Then he increased the intensity but point is when he increased the intensity He is only increasing the number of photon No, I am I am talking about when See what happening with hurts initially He is strike with the metal surface with a light of certain frequency Electron was not coming out what he did he increased the intensity of light So the point is when he was increasing the intensity of light it means The number of photon is increasing Intensity means what the number of photon there is more Photon we have now But the energy of photon is same initially it was h nu when the number of photon was 10 Now when it is 50 again the foot energy of each photon is h nu only when it is 100 energy of each photon is h nu only Right the point is since energy is not changing So the and this energy was not sufficient for the electron to come out. That's why The electron was not coming out initially So when the energy is not sufficient no matter whatever the number of photon you take whether it is thousand or lakhs of photon If the energy of one photon is not sufficient electron will not come out at all Why because one photon will strike at a time First this one will strike then this one then this one means at a time only one photon can exchange energy with the electrons Right, so when the Hertz was increasing intensity of light. He was actually increasing The number of photon number of photon increases, but energy of Each photon Is same energy is not changing Right, so if right, so this is the one thing when intensity increases now Suppose this is the metal we have And in the metal electrons are associated with some energy with this nucleus right and we are Striking with a light of frequency nu in So the energy given to this metal is what? H nu in in stands for incident incident frequency So this is the incident energy we have now if this nu in With this if the photoelectric effect is taking place What is the use of this energy with which we are with which we are striking at the surface? some of the energy will go Into to will go to will be used in overcome Will use to overcome the attraction pull of the Attraction pull of the electron Right, so this electron is associated with the nucleus with some force Right, so the energy that you are giving in some part of it Will be used to overcome this attraction pull and that energy we call it as work function represented by five Right, and whatever the energy left with which the electrons With which the electrons will come out right and hence this electron will have certain value of kinetic energy We call it as ke max So this energy which is giving in is used in two different way One is to overcome that traction pull and the other one is in the kinetic energy of the electron ke max Right, this is what it is given in the book Right now, suppose if the energy given here is just sufficient So that it will only overcome the attraction pull and electron is not moving out Right, so in that case when The kinetic energy Of the electron will be zero Right and in this case the incident frequency must be equals to the threshold Right, what is the meaning of this when the frequency that you are giving in It is when it is equal to the threshold frequency At that point of time the electron will not come out. It will just overcome the attraction pull So in that case kinetic energy will be zero since the electron is not moving out But it is free to move now 0.0001 kinetic energy incident light you increase energy you increase electron will move with some kinetic energy Here i am taking one condition that the incident frequency is such that It just overcome the attraction pull no kinetic energy there So when you substitute these two here, you'll get h new not is equals to phi Which is the work function of the metal plus zero So phi is nothing but h new not this is the work function of the metal given It is constant for a given metal For a metal for every metal this will be constant may have different different value, but it will be constant Right, so when I substitute this here this becomes h new in Is equals to h new not plus ke max This is what the equation given in the book if you see photoelectric effect They have just given this equation and they said it is the phenomenon of emission of electron when a light of certain frequency Strikes at the metal surface Correct now here you see if the incident light new in first case I am discussing last two case we'll discuss if the incident light Is greater equal to the threshold frequency Right, then in this case what happens? To photoelectric effect to take place the incident frequency must be more than or equal to the threshold frequency in this case First condition I am taking if Incident frequency we are increasing further Then what happens? See try to understand here When new in is increasing the incident energy will increase right Phi will is constant for a metal This will not change But when you increase the incident light, obviously that will increase the kinetic energy of electrons Right, so an incident frequency increases the kinetic energy of photo electrons increases right Number of photo electron will be same number of photo electron Will not change right second case what Now when this condition is true and we are increasing the intensity of light If intensity increases If intensity increases, which means what number of photon increases Number of photon increases. We are not changing the energy. So the kinetic energy will be same of photo electron kinetic energy will not change, but the number of photo electrons increases or decreases What happens number of photo electrons increases or decreases number of photo electrons increases or decreases increases yes So number of photo electrons increases because we are having more photon now Okay, so one photon can emit only one electron. So initially the number of photons was 10 So 10 electron was coming out now. We have increased the intensity to this 10 becomes 50 suppose So now the 50 electrons will come out Okay, so just you remember one thing if you increase the intensity of light If you increase the intensity then the number of photons So number of photon increases and then the number of photo electrons also increases But the kinetic energy will not change because the energy is not changing here Right energy of the incident light, but when you are increasing the incident light So the energy of the incident light is increasing Right, so the kinetic energy with which the photo electrons is coming out will will increase But number of photo electrons will not change Correct. Is it clear? Understood. Okay, so these are the numerical question you will get On this equation Okay on these two concept you'll get some theoretical question Okay, so I have taken the case of increasing if you decrease in what happens They may ask you like this, but if you have got the concept you can solve any of these questions right actually It's no you cannot say like that the point is that Einstein has explained this fact Okay, it is true always Okay, whether Einstein suppose if Einstein did not explain this would not have explained this Then maybe some other scientists will be explained this will maybe will other scientists will explain this right but the point is The fact that we get here or the actual explanation that we get here that is because of Einstein Right, but it is true in all the cases Yes, tell me What is it clear can we move ahead? Next we'll see that is Broggy hypothesis What is Lyman series barma series and all Lyman barma passion bracket fund series You know all these things The Broggy hypothesis again this D Broggy Is the name of the scientist? Okay And what he Okay, we'll discuss that also after this okay after this we'll discuss that also Lyman barman, you know, it's just the basic Okay, I'll give you a little bit of it also We'll discuss first this Okay, so D Broggy is the name of the scientist. Okay, what he proposed in 1924 In 1924 D Broggy proposed that the electron proton And even atoms even atoms Well in motion in motions possess wave properties So any object what D Broggy suggests that any object when it is in motion it will have some wave properties Okay, and If I use the if you use the two different relation of according to Planck's equation what we can write e is equals to h nu And nu is equals to c by lambda So e is equals to h c by lambda Einstein mass energy equation is what e is equals to mc square So when you club these two so what we can write at c by lambda Is equals to mc square and lambda is equals to h by m c so for any particle For any particle particle of mass m moving with the velocity v with a velocity v It will have the wave nature and the wavelength associated with it is given by lambda is equals to h by m into v Any object suppose Even if we are moving also We will have the wave properties also Right according to this relation mass and velocity Right, suppose a bike is moving of mass m is moving with the velocity v Then this also will have the wave properties or wavelength of that wave will be lambda is equals to h by m v Now the point here it is what that this lambda Or wavelength of the wave associated with any object is inversely proportional to its mass Right, so when mass increases wavelength decreases, that's why what we say for heavier object For a heavier object length is very small Since it is inversely proportional And hence we neglect it hence We neglect it Now the point is any object in motion will have the wave properties and This value of wavelength will be associated with that particular object Okay Now since it is inversely proportional to mass with heavier object lambda is very small and hence we neglect this And so as mass increases wavelength decreases All right, now this is one formula, but there are two three different expressions of this we have Right suppose if the kinetic energy of the mass is given suppose the kinetic energy of any object is given k So how do we write down the formula now you see kinetic energy is equals to what half m v square Multiply m by both side you'll get 2 m k left hand side and here we have m square v square m square v square so m v is equals to what root over of 2 m k so this I can substitute here So lambda becomes h by root over of 2 m k where k is the kinetic energy you must take care of this thing This is very important relation. We have if kinetic energy and mass is given you can use this formula directly Right one more important relation will have here That will see If a charged particle q this formula you write it down if a charged particle q moving under a potential difference Moving under a potential difference v. This is capital v Then the kinetic energy of that charged particle can be given as q into v V is the potential difference Okay, this formula you must remember kinetic energy is q into v and we also know kinetic energy is equals to half m v square This v remember this v is the velocity capital v is the potential difference. Okay, don't get confused with it Okay, again if you find out m v over here, it will be 2 m q into potential v root over of it So again lambda becomes what h divided by root over of 2 m q potential v. This is again the another representation So when charge and potential is given we will use this formula if kinetic energy is given We'll use the previous one and with momentum Or math and math and velocity is given. We'll use the first formula lambda is equals to h by m v Is it clear? You must mention there that v capital v is the potential difference Next one is the interpretation of of hydrogen spectra Draw these lines and see these are the energy levels These are the energy levels in the hydrogen atom. We have different different orbits So different different energy levels, right? This is n is equals to one first energy level n is equals to two n is equals to three n is equals to four six seven and okay now suppose in all these energy level electron may jump to the first energy level from second Let me draw this diagram i'll explain Now you see what happens. This is the first energy level and the electron may jump to the first energy level From any other higher energy level all these All these lines means the electron is coming from second to one third to one four to one fifth to one six to one seven to one like this many possibilities we have Okay, so whenever the electron Jumps from Suppose this is the higher energy level we have and this is the lower energy level Suppose what happens if I explain you by with this two energy diagram since we have different energy levels present Now see if the electron is here And it is coming back to the lower energy level like this. This is what I have drawn in a straight line here So obviously here the energy is more and here the energy is less When you go one thing you must remember when you go away from the nucleus the energy increases of the electron The point is what when you are going away from the nucleus the energy of the electron increases Right, so here we have higher energy And lower energy when the electron jumps to the high to low energy It will radiate energy in the form of It it will emit energy in the form of radiation and that radiation we have certain wavelength Right the point here. It is what suppose electron is in third energy level and it is going back to the second energy level So this energy difference Or this energy will come out in the form of radiation That has a definite wavelength called lambda So e3 minus e2 is equals to 1 by lambda. So this is what happens over here When the electron jumps to the first energy level From any other high energy level The series will get here because you see from 2 to 1 will get certain value of lambda 3 to 1 again Some value of lambda 4 to 1 lambda 5 to 1 lambda like this will get a series of wavelength Okay, so whenever the electron jumps to The n is equals to 1 orbit then the series we get here. We call it as Lyman series Right means what from any other higher energy orbital if the electron jumps to n is equals to first orbit Then the series of wavelength that we get that we call it as Lyman series Second thing is what if the electron jumps to the second energy orbital Similarly the series we get we call it as barmer series If the electron comes to the third energy orbital We call it as Pastron series p s c h e l If n is equals to 4 it is bracket And for fifth it is fund series Did you understand what is lyman series? What is barmer series? Bracket fund Yes or no Understand tell me We'll take a break after this next important thing here. It is what Sometimes they ask you to find out Maximum or minimum wavelength in all these series in any one of these series like Lyman barman pastron and all So first thing here you see When you have Lyman series One formula you have to memorize here that is 1 by lambda Is equals to r into 1 by f square minus 1 by n i square n f is the final orbit where the electron jumps Okay final orbit where the electron jumps And i is the initial orbit where the electron was present initially Right means what if the electron jumps from 2 to 1 Then n f is 1 But n i is 2 Okay now you see Lyman series this formula we are going to use for all these series to find out maximum or minimum wavelength First of all you tell me one thing In the previous slide you see this and you tell me For Lyman series For Lyman series What is the value of n f What is the value of n f For Lyman series. What is the value of n f f is 1 per barmer super barmer nf is 2 3 4 and 5 Right for Lyman series. What are the possible value of n i? Lyman series if you understand Lyman similarly you can do all these for the other one For Lyman series. What is the possible value of n i? Sorry, uh n i Lyman series. What are the possible value of n i only 2? Or any other value possible see? Electrons may jump to first orbit From any of this orbit right So n i value can be 2 also 3 4 5 6 7 8 till infinity Any other value possible for n i yes that is right. So now you see For Lyman series if I write down the value of n f here n f is fixed We cannot change this one, but n i can be any value from 2 to infinity 2 3 4 to 5 and so on till infinity because we have infinite number of orbits Right, so you see you have this n f value you have possible value of n i Okay, so what is the value of lambda suppose lambda max you have to find out So for maximum value of lambda what should be the value of n i out of all this see our value is fixed constant n f is also fixed one we can only change this n i And with respect to this value of n i only we have a range of wavelength we'll get which is lambda minimum and lambda maximum So lambda max if you have to find out so for lambda maximum, what should be the value of n i out of these all these value? tell me lambda max n i should be minimum and that is 2 right Yeah So you have this value n f and n i So lambda max if you calculate In terms of r You'll get lambda max is equals to 4 by 3 r And lambda minimum if you calculate for this lambda minimum n i value should be infinity maximum That will be 1 by r See one thing you remember here For all these whether you have limelabarmer pastor bracket fund whatever whatever it is Whenever lambda max if you have to find out so we'll take the minimum possible value of n i reverse Right lambda minimum if you have to find out then we'll take the maximum value of n i why you see this You see here If this lambda is maximum then 1 by lambda is minimum When 1 by lambda is minimum it means all these terms this term is minimum Now when this is minimum To make this term minimum we have to subtract the maximum possible term over here Maximum possible value we have to subtract so 1 by n i square should be maximum right So 1 by to make to make this term maximum n i should be what n i should be minimum That is how we do but one thing just you remember For maximum wavelength We'll take minimum value of n i for minimum wavelength will take maximum value of n i You see we have a range of wavelength from 1 by r to 4 by 3 r So this wavelength when you substitute the value of r when we substitute the value of r The wavelength that you get here that lies in ultraviolet reason and this is important you must remember Okay, I'll write down here in the previous slide For lineman series The wavelength lies in ultraviolet reason For bummer it will be invisible. This is the only series where the visible range is there And for all the other one it is infrared This is infrared This is also infrared And this is also infrared Okay, so this is lineman bummer pressure back to that front series in this sometimes they ask you to find out Lambda max and lambda minimum in any of these series lineman bummer and all right And this reason also you must remember ultraviolet visible and all infrared. Is it clear? Did you understand till here? Tell me first fine. So we'll take a break now. Okay. It's six 35 so we'll start the class at 650 now Okay, we'll start the class at 650 again From here only we'll start we'll start Heisenberg after this Okay, so we'll start with Heisenberg at 650 Take a break now Hello, can we start? That's right wave equation probability of funding nodal planes all those are please. Okay Are you there? Can we start now? Okay, uh So we'll we'll we'll start with uh A schrodinger only fine Because Schrodinger wave equation in the last if I go with the sequence. I don't think I can you know Okay, then we'll do this Okay, just we'll finish Heisenberg and then we'll do schrodinger schrodinger. Okay So, uh, you see this Heisenberg uncertainty principle She should see nothing but Shivani Shivani from Well, I'm all right. Okay. Good. Okay. So Heisenberg uncertainty principle It states that it is impossible to measure the current position or current position and momentum simultaneously with absolute accuracy and certainty Okay, so you see what happens Heisenberg is the name of the scientist He suggests or he proposed that it is impossible to measure the current position and momentum of an electron simultaneously with absolute accuracy or certainty. Okay, then he has given the possible relation of the position Uncertainty in position and uncertainty in momentum and the product of these two is found to be greater than or equal to h by four pi Okay, where del x is the uncertainty in position and del p is the uncertainty in momentum. Okay So since momentum we have so del x and momentum we can write m delta v greater equal to h by four pi Since mass cannot change mass will be constant of an object So del x into delta v greater equal to h by four pi m Okay, so on this you will get a direct question either uncertainty of momentum or position is given And you will find out the other one. Okay del x you remember it is the uncertainty in position Del p is the uncertainty in momentum del v is the uncertainty in velocity Okay, so this is what the statement given by Heisenberg Now when this principle comes came into the picture Then what happens till now before this principle till now we were Trying to find out the position of an electron because what we have already discussed that electron keeps on moving in a definite orbit around the nucleus in a definite path Right, so since electron is moving here in this path So can we find out the position at what position the electron is and when the electron is here What is the velocity of the electron at this particular position? This is what we were trying to find out But when Heisenberg came with this principle We have come to this conclusion that it is impossible to find out the uncertainty in position of an You know electron or any subatomic particles hence after this After this what happens The concept of Electron revolving around the different orbit Where its position and velocity are exactly known see what happens according from Bohr's atomic theory We know the position of electrons right that we can say whether the electron is in First orbit or second orbit or third orbit right this position of electron was known and in all these positions We know the velocity of the electron also because we have the Formula of radius we have the formula of velocity Right, so what happens when Heisenberg principle came into the picture the concept of electron revolving around different orbit Where its position and velocity are exactly known Was replaced by the probability of finding an electron in a particular space or volume Correct. So after this Heisenberg uncertainty principle the concept has been completely changed Now we are now we started talking about the probability of finding an electron in a given reason Okay, so here we get the concepts of orbital Okay, and after this orbital We'll talk about orbital orbit is nothing actually exist Okay, so orbital the definition of orbital is what it is the three dimensional space or volume Where the probability of finding an electron is maximum Right three dimensional space Or volume where the probability of Where the probability of finding an electron is maximum Is maximum so after this we will not talk about orbit, but where the electron resides That we call it as orbital not orbits orbit is nothing actually Okay, now when we have to Get the shape of this orbital Okay shape of the orbital is nothing but the path at which the electron moves Okay, so to find out the shape of the orbital we have An equation and that we call it as Schrodinger wave equation Schrodinger wave equation Okay, Schrodinger wave equation now Schrodinger wave equation. There are few you know terms here we use Those terms are first of all it is psi psi is It is wave function wave function or amplitude function Wave function or amplitude function. Okay, psi square Is the probability density function probability density function, which can also be defined as probability per unit volume So when I multiply this psi square with volume Will get the probability of an electron Okay, what is wave function amplitude function? You don't think about it. It is not in our Slip us it. Okay. Don't think about it. It's not required now Okay, now the Now the Schrodinger wave equation is given by this dou square psi by dou x square plus dou square psi by dou y square Plus dou square psi by dou z square is Equals to minus 4 pi square by lambda square into psi This is Schrodinger wave equation Okay, now when you solve this Schrodinger wave equation, you will get the value of psi Okay in terms of x y and z Okay in terms of x y and z now the good thing is since the question the equation looks so difficult Okay, the point is the solution of this Schrodinger wave equation again is not there in our sliver Okay, so we do not have to solve this Schrodinger wave equation You will not get any question on the solution of this Schrodinger wave equation What we have to understand over here that when you solve this you will get psi in terms of in terms of in terms of x y and z so psi we can say it is a function of x y and z Okay, psi is a function of x y and z it is something like this so when you uh See you must have seen the equation of circle, right? Or uh, suppose if you have uh, you know, it is a differential equation Suppose if I write down the differential equation like this dy by dx is equals to suppose m So when you solve this differential equation, we will say what y is equals to mx plus c will get c is any constant Right, so when you get this equation It means you can say that the equation is of Is for a straight line Right linear equation Gives you a straight line Similarly, when you write down this equation x square plus y square is equals to r. This is a circle When you write down x square plus y square plus z square is equals to r. This is a sphere Right, so these are some geometrical equations. We have which we use in coordinate geometry To represent uh to understand the what kind of shape or you know Uh Geometry we have here circle straight line in the sphere So the point is when you solve this equation and solution is not there in the uh, uh, syllabus So you will get four set of solution Okay, four set of solution the first set of solution is spherical First solution Is spherical Right and how it is spherical Maybe when you solve this you will get a equation something like this which represents and is Which represents a sphere Right and that's why it is uh Is spherical second set of solution that you get here that will be Dumbbell shape Third set of solution is double dumbbell and the fourth set of solution we have that is leaf like structure leaf like structure Okay, a spherical shape is nothing but s orbital Dumbbell shape is p Double dumbbell is d and this is f orbital Right, so the point is Schrodinger wave equation You don't have to worry about it because the only thing you have to understand here from schrodinger wave equation only Will get the shape of the orbital whether it is spherical double dumbbell dumbbell or leaf like structure Understood this now in this one you see From schrodinger wave equation will got some result here That initially what we were saying that the electron revolves around the nucleus in a circular path Right, this is what we were discussing from board at all board model and all but here what we get here the shape may be spherical Maybe double double double double double double anything right the first conclusion of schrodinger wave equation is what? electron revolves this is the conclusion of schrodinger wave equation electron revolves around the nucleus in a path Which may or may not be circular? Okay path can be anything may or may not be circular In this we have major energy shell and can be one two three four Right each major energy shell may have sub shell and each orbital Each orbital Can accommodate? maximum two electrons maximum two electrons Okay, now in this if you have major energy shell and i'll just draw this table and is the major energy shell Then we have shell Orbital and the number of electrons Okay, so n can be what n can be one two three four One two three Four first major energy shell may have only s orbital second will have s n p third will have s p and d and fourth will have s p d and f In s shell. We have only s orbital in s and p. We have s p cell. We have px py pz orbital Similarly in d also will have five f also will have seven more orbitals. I'm not writing down all those. Okay number of electron is what? One orbital can have two electrons number of electrons is two We have one two three four orbitals eight electrons right Here we have how many electrons possible 18 And then in the last we have 32 See one thing you must keep in mind maximum number of electrons Present in n shell that is given by two n square where n is the number of Principal Shell right principal shell that we have that is nothing but n Okay You see if for n is equals to one the number of electrons is two if n is equals to two You substitute two here. You will get eight accordingly. You'll get this 18 and 32 Okay, after this we have quantum number, okay So quantum number we will discuss in next class. We'll discuss now nodal surface will it be fine Will it be fine if we discuss nodal surface since you are you are only saying Otherwise we'll discuss quantum number first Nodal surface What is nodal surface? nodal surface Is the surface where the probability of finding an electron is zero Where there is no electron present Right, so first of all the definition of nodal surface is what It is the surface at which at which the probability of Finding an electron Is zero To solve the question. You should only know these two things. There are two types of nodal surface one is Spherical node We also call it as radial is spherical or radial node And the next one is non-spherical Or angular node Number of radial node the formula you should keep in mind n minus l minus one And the number of angular node is l Where n and l are the Quantum number and is the principal quantum number and l is the What is l? l is the Angular quantum number or azimuthal quantum number Okay, and and l are the quantum number, you know, what is the value of l for different orbitals? You must know this thing for spd and f the value of l is zero one two and three These value you must remember for different orbitals spd and f the value of l is zero one two three So if I write down three s Right for three s orbital the l value is zero because it is s orbital. That's the meaning we have here right number of nodes if the question is Total number of nodes will be the sum of radial plus angular, which is n minus l minus one plus l n minus One is the total number of nodes Yeah, l value is zero to n minus one correct Now when you know these two formulas You can actually solve the questions of nodal plane nodal surface with this formula. You can find it out Okay, these two three formulas. Okay, but if you want to understand it Accurately, okay exactly what the thing is suppose if I ask you what is the nodal plane For one s orbital You have to find out the nodal plane for one s orbital First of all one s if I write what is the value of n and l here tell me What is the value of l l l? One and zero since it is one s you see since it is one s so n value is one And for s l value is zero so one and zero so when you know this and and and and and and and and l value You can substitute into this number of radial node will be one minus zero minus one that is zero And angular node is again the value of l which is zero. So there is no node present into this Okay, so if you draw the structure the draw the you know The graph here Okay, this is the graph. This is the probability of finding an electron. Okay, and which is given by a psi square into four pi r square dr And this is the distance from the nucleus. This is the distance from the nucleus You see psi square is probability density function Okay, and when this is multiplied by volume, this gives you what the probability So you you try to understand this term four pi r square is the surface area of this sphere Right, and when you multiply this by dr. So this is also meter. This is meter square So meter square into meter square becomes meter cube. It means this term is nothing but the volume So psi square into four pi r square dr when you integrate this this gives you the probability of finding an electron Okay, so when you draw the structure here for one s orbital. I'm talking about there is no nodal plane into this so the diagram of this will be Like this here at the nucleus. There is no electron, right? So it is zero probability then at some point of time the probability of finding an electron will be maximum Then it will decrease but it will never touch the x axis since it is zero When it touches the x axis it means the probability is zero when the probability of electron is zero It means there is one nodal plane, but since there is no nodal plane This graph will not touch the x axis Did you understand this graph as you as you start moving away from the nucleus at some point of time Will you have the electron present So there the probability of finding an electron will be maximum and then the probability will decrease but it will never touch the x axis So the graph will be like this. Is it clear? Now the same thing we have to do for two s orbital Again the number of radial node for two s orbital It is two minus zero minus one is equals to one Angular node is what? Angular node is zero since l is zero Right, so one radial node we have here. It means at one point at at some distance from the nucleus The probability of finding an electron will be zero So when you draw the graph the axis will be same like we have discussed earlier So when you draw the graph again from nucleus The probability of finding an electron increases And then it will decrease it will touch the x axis once because there is one radial node Right, and then again the probability of finding an electron will increase goes to a maximum value Again, it will decrease but again it will not touch the x axis So this is what the distance from the nucleus where the node is present Right, suppose this distance is r1 from the nucleus Right r1 from the nucleus so we have nucleus here and around this we have a spherical node Because there is a radial node radio a spherical node. It is That's why the shape is spherical here right at a distance. What at a distance r1 from the nucleus Right, so this is the nodal surface for For 2s orbital Is it clear now? Okay, similarly I will not do this if you try to find out 3s orbital The graph of 3s will be what since radial node will be 2 here So graph of 3s will be like this it will touch the x axis twice and then it will not touch So this is the x axis we have and last it will not touch Okay, so one node here another node here spherical node clear So like this will find out the node. Okay, only you have to use the formula Remember one thing these graphs is for your understanding. Okay, they will not ask you these things in the exam Okay, rarely they ask but if the graph is like this This is the probability and this is the distance from the nucleus when they have Drawn the graph like this they may ask you this in the reverse way also Suppose the graph this is given and they'll ask you which orbital it is Okay, since when the graph is this it means we have only one node Okay, and one node is what one node is spherical node Right, so one node is possible only for 2s orbital Right, so according to the option you can also do this or with graph also you can do this Is it clear fine, so you just have to keep those formula in mind and then you can solve the questions But there are a few factual questions. We have that you should know According for this nodal plane only that I'll give you okay for 3d orbital you write down for 3d orbital for 3d orbital number of radial node is 0 n minus l minus 1 number of radial node is 0 But angular node is 2 Okay, d orbital angular node is 2 Right, so if you have since we have 3d so we can have d x y d y z d z x any orbital possible Right, so if you have d x y orbital, so its nodal plane will be y z and z x If you have d z its nodal plane will be y x and z x If you have z x then nodal plane will be x y and z y the other two One note you write down here. This you must memorize for d z square orbital there is no There is No nodal plane There is no plane here, right, but the angular nodes the angular nodes are in The shape of cone shape of cone For d z square orbital this question they have asked in need exam Okay, so you must remember this for d z square. There is no nodal plane But the nodal surface or angular node the shape of angular node is in the shape of cone Understood fine. So this is it for nodal surface, okay Only thing you have to keep in mind is formula and these are the few facts. I have given you already Okay, right. So in this chapter, we are left with only this Some rules are there who's to learn on right and then Quantum number, okay, so that we'll discuss in next class. Okay Next class will will have some, you know revision class for 11th class. Okay So we'll discuss in the next class and then we'll discuss some other chapters also Fine, if you have any specific doubt, you can text me And you must solve few questions based on this. Otherwise you will forget again all these concepts that we have discussed today Right, so solve some questions on this if you have any doubt you can text me Okay, so we'll wind up the class here only Okay for next class, I'll send you the schedule whenever it is Fine, is it clear? Okay. Bye. Bye. We'll see you soon