 Hello. Good evening, guys. Okay. So, guys, today we are going to start a new chapter. And that is atomic structure. Last class, we have finished general organic chemistry. Okay. This is the second chapter of physical chemistry. Okay. First chapter is some basic concepts we have discussed. That is the second part of that. And as more concept two, we'll discuss after periodic properties. Okay. So, atomic structure. In this chapter, we are going to study about atoms. Okay, we know already the definition of atoms. Okay. What are the various subatomic particles we have? They are discovery. All these things we are going to understand in this chapter. Okay. Like we all know, atom is given by a Greek word that word atom is given by a Greek word that is atom use. Okay. It is a Greek word. And this means this means indivisible. This means indivisible means what which we cannot divide, because earlier the understanding didn't get your study. What book you're talking about or notebook you're talking about. Right. Okay. The general organic chemistry is the part of organic chemistry. So it would be better if you use a different notebook for this. Okay. You should have one notebook for physical, one for organic, another one for inorganic. Okay. So this is better if you write a different notebook. Okay. Atom use means indivisible. Right. Which cannot be divided further because earlier the understanding was what atoms are the smallest particle, which we cannot divide further. Okay. That is what the understanding regarding the atom we have. Okay. The theory of atom is given by a scientist called John Dalton. In between 1803 by John Dalton and this theory was given during this time, 1803 to 1808. These things you don't have to memorize. Okay. So this theory, we call it as Dalton's atomic theory. Dalton atomic theory. Okay. So today this chapter is mainly about the theory. Okay. Because there are so many theoretical things that we need to understand before going into the numerical part. Okay. So we'll take the reference of classical physics also here. Right. So this today's session mostly it is all about the theoretical aspect of all these things that we have. Okay. This theory, we call it as Dalton's atomic theory. What is Dalton's atomic theory? There are a few postulates of this. Write it down on a few. At all particles in this world, we call it as Dalton's atomic theory. Okay. This theory, we call it as Dalton's atomic theory. What is Dalton's atomic theory? There are a few postulates of this. Write it down on a few. At all particles in this world, all particles in this world are made up of in this world are are made up of made up of very small elements called particles elements called atoms. Means everything is made up of atoms. Okay. There are so many atoms present in anyone in any compound. Right. So there are like, you know, the basic unit for any matter is atom. That is what John Dalton said. Second point. Atoms of different element has different properties. Atoms of different element has different different element has different properties. Okay, like the atoms of carbon has its own property. Atoms of nitrogen oxygen has its own property different. Okay. Atoms cannot be created or destroyed cannot be created or destroyed, which was obviously wrong. This postulate this theory of atom was wrong. When various sub atomic particles like electron proton electron discovered. Right. So John Dalton said that atoms cannot be created or destroyed, but this theory, this theory was proved to be wrong. When various sub atomic particles, particles like electron proton neutron, etc. discovered. Okay. Copy down these points. Atoms cannot be created or destroyed but this theory was proved to be wrong. When various sub atomic particles like electron proton neutron, other particles are meson positron discovered. Okay. Done. Okay. Now you write down discovery of sub atomic particles discovery of sub atomic particles. Okay. The first one we have the first one is electron. Right. The discovery of electron. There is an experiment. And this experiment we call it as cathode ray, cathode ray experiment. Okay. The experiment related questions. They won't ask much, but I'll just discuss the the experimental setup and other things over here. Okay. So this is the experimental setup we have experimental setup is this one you see here. This is a discharge to the cylindrical glass tube. It is a discharge to okay you don't have to draw this it is not that important. Okay. And I would suggest that if you want to draw you can draw it later. Okay, because we are already, you know, our syllabus is already lagging behind from the other batches. That's why I'm taking this reference so that I can save time in drawing this. So what I'm suggesting you try to understand this now. Okay, it is given in your book and CRT you can draw it from there also later on if you want. You don't need the diagram. They won't ask you to draw the diagram. Okay, it is not that tough. You can understand it easily. Right. So what happens here, we take a cylindrical glass tube. This is a discharge to the cylindrical glass to that you have it is the discharge to So what happens in discharge to it contains two electrode on it. These are the electrodes. Okay, this one and this one. This is electrode that is cathode and this one is anode cathode. This one is anode. This electrode connected to a high voltage source from this. We use a vacuum pump to maintain low pressure in the tube, low pressure in the tube, approximately 10 to the power minus four atmospheric. We use here in this cube, right, and this is stars to is filled at with an any gas over here. We remove all the air and we fill any gas into the stars to When you allow when you connect this with a very high voltage source, we see an invisible ray, right an invisible ray coming from the cathode electrode towards the anode electrode. This is invisible ray and since it is coming out of cathode, we call it as cathode ray. This side, it is ZNS fluorescent screen we have here. It is coated with the ZNS screen. Okay, so this is starts glowing actually when you connect this an external source, this part starts glowing, which confirms that that something some invisible ray is moving from cathode to anode side. And when it strikes on this side, it starts glowing. Right, so this invisible ray, we call it it as cathode ray. It's called cathode ray. This entire experiment I'm not dictating you, I would suggest you request you to after the class, you just read out these things in the book and CRT. Okay, you will understand it. Okay, not much important, but yes, go through once. Okay, this is called cathode ray. Now this cathode ray has some properties. Okay, we'll discuss those properties by write down the properties of properties you write down on that experiment I have told you that there is a discharge to connected with a to end with an electrode electrode is connected with an external source of battery. When we connect this with a battery, a very an invisible ray comes from cathode plate. Hence we call this cathode ray travels towards anode in a straight line. Okay, write down the property first one cathode rays, cathode rays travels, travels along a straight line travels along a straight line and forms shadow of any obstacle, obstacle or object. Okay, now what we do if you place here, a positive plate this side and this side, this side if you place a positive plate we observe that this ray bend towards this positive play if you played this this side, okay it moves like this. Since it is attracted towards the positive plate, it means this is negatively charged. Okay, slide down the second point. These this ray or cathode ray write down cathode ray is a stream of negative charged particles called electrons. Okay, next point write down consist of negative charged particle called electron next point it produces it produces mechanical effect it produces mechanical effect this means what suppose that cathode ray we have a fan blade. We have a fan blade. Suppose here we have a fan blade. Which is this one right and suppose the cathode ray if you strikes on this fan blade in this direction. These are the cathode ray we have suppose. We have this fan blade with this cathode ray so what we observe all these are experimental facts we have actually. Okay, so this is cathode ray. So when it is strikes to this fan blade, we observe that this fan blade starts rotating in this sense. Okay, means what this provide some energy to this fan blade and hence it is starts rotating in this direction. Okay, this is mechanical effect. Okay, it produces or it imparts energy to any object. This is mechanical effect. Okay, fourth point to write down the last point the behavior of cathode ray is same for all gases. The behavior of cathode ray is same for all gases. Why it is same for all gases means what whatever gas we use in this discharge to here we have gas present whatever gas you use here the property of cathode ray is same. It won't change. Why because electrons are electrons only whether it is present in hydrogen carbon dioxide oxygen nitrogen, right the property of electron won't change with different different gases. Correct. So hence, since it is the stream of negative charged particle called electron, hence with the change in gas, the property won't change for cathode ray. Okay, so these are the properties of cathode cathode is properties important. Okay, you must keep that in. Now, after this experiment what happens is this we call it as cathode ray experiment and the ray here comes out from cathode we call it as cathode. Okay, after this experiment, after this experiment, we came to this conclusion that within an atom, there is a negative charged particle present. Okay, so since we know that the atom is electrically neutral and if there is any negative charged particle, it means there must be some positive charged particle which neutralizes the negative charged particle and makes the atom overall. What neutral because we know atom overall is neutral. If negative charged particle is present. This means we must have some positive charged particle present, which makes the atom neutral over. Correct. So this gives us an idea that within an atom, there must be some negative positive charged particles present and hence the scientists that that point of time, they started looking for the another sub atomic particles, which must be positively charged. And in this way only they have you know come to this conclusion that a positive charged particles called proton exist within an atom also. Okay, so for that also we have the similar kind of experiment. Okay, the second point to write down the discovery of proton. So you look at this diagram here exactly same. The only difference here that we take a perforated cathode. It is exactly same just one change we have here and the change is this that the cathode we have we take it as perforated cathode like this the holes what they're so what they observe the moment where the anode sorry the cathode ray comes out from this you know cathode plate. So first of all you see this, this particular plate is cathode this the perforated one is cathode it is written over here and it is connected to the battery this side. This is cathode written over here. So here we have perforated cathode that is the only difference we have in the two experiments. Right, and this is an anode and the ray comes out from perforated cathode it is cathode ray which we have discussed you know in the last experiment and what they observe the moment cathode ray comes out from this you know cathode plate. The same time only some positive ray also moves in the opposite direction of this cathode ray ok means cathode ray travels towards the positive charge electrode. So this positive ray moves towards the opposite of the cathode ray because it is positively charged and it is negatively charged right if this moves towards the positive plate this will go away from the positive. Ok so this ray since it is coming out since it is coming from this direction to this direction from anode to cathode this positive ray we also call it as anode ray from this side to this side anode to cathode hence it is anode ray. Since it is moving away from the positive plate hence it is the anode ray is positively charged positively charged ok the property of this is what you write down the properties anode ray anode ray consist of anode ray consist of a positive charged particle positive charged particles called proton. Ok called protons next point proton is the smallest and lightest positive charged particles protons are the lightest and smallest positive charged particles and proton is nothing but H plus proton is H plus ok. Since it is lightest and lightest and smallest positive charged ion H plus ok next point the behavior of anode ray the behavior of anode ray the behavior of anode ray is different for different gases. The behavior of anode ray is different for different different gases next one like cathode ray next one like cathode ray it is also deflected by electric and magnetic field like cathode ray it is deflected by electric and magnetic field. Any charged you know don't write this any charged particle if it is present in any wave or any ray correct it will always be deflected by electric and magnetic because electric magnetic field produce attraction or repulsive force on any charged particles depending upon the charged present on it ok. So like this we came to know about this fact that within an atom like we have electrons and protons present ok now what happens after this the third point is the discovery of neutron neutron ok so neutron is what it is a neutral particle neutral particle it is neither positive charged nor negative charged ok. So what happens with this electron and proton we already know this fact that neutron plays a role in defining the atomic mass of that particular atom right because it is present in the nucleus this fact we know already right. So if you do not know about this neutron obviously you cannot get the correct value of atomic mass of various atoms so what happens there are various scientists they came to this conclusion that with the help of only proton and electron the atomic mass of different atom could not be explained that point of time ok. If there were any proton like only proton and electron present then atomic mass of different atoms could not explain properly ok there will be some you know error or difference ok. Then Rutherford in 1920 suggested that in an atom there must be a third type of fundamental particles present which should be electrically neutral and possess mass equal to the mass of proton. So Rutherford suggested this that there must be some third type of neutral subatomic particles or fundamental particles present in the should present in the atom. This proposal was given by Rutherford in 1920 right later on James Chadwick later on James Chadwick in 1932 James Chadwick in 1932 discovered electron sorry neutron. So how do we discover this what he did actually he took beryllium atomic number mass number and this beryllium is attacked by alpha particle that is helium 4 and 2. So we say what beryllium is bombarded with alpha particle beryllium is bombarded with alpha particle and we get a nucleus of carbon and a fundamental particle also eliminates in this which is neutron which is neutron. So this is the discovery of neutron we have this nucleus is this reaction is nuclear reaction ok nuclear reaction ok so this nuclear reaction the nucleus are involved in this that's why we are getting a different nucleus here. Yes alpha particle is H E plus right alpha particle is H E plus that generates from helium only that's why we have written helium over there to make you understand H E 2 plus in fact so actually what happens this helium you can write it down it converts into H E 2 plus plus 2 electron. So this is actually alpha particle which comes out from this and to write down the reaction we use this one because it generates from this ok so this is how we came to this point that within an atom there are various fundamental particles or subatomic particles present and they are electron proton neutron mainly. Ok so like this we discovered electron proton and pop it this down a few now you see till now what we know that after this we have an atom right and within this atom there are various subatomic particles present various subatomic particles present. Ok but how they are arranged means where are electrons present here where protons there are neutrons so how this subatomic particles are arranged within an atom that we do not know. Ok so once they came to this point that where there are various subatomic particles present within an atom then how they are arranged within an atom that they started looking for. Ok and the arrangement of subatomic particles within an atom is given by different different scientists and all these attempt were made these attempts we call it as atomic models. Ok so what are the various atomic models we have atomic models I hope you understand that atomic models are what these are the various theory given by the different different scientists in order to explain the distribution of subatomic particles within an atom or arrangement of the subatomic particles within an atom. This we call it as various atomic models. Ok so before going into that few points that we should know here that for electron electron proton and neutron the mass of electron you should know and that is 9.1 into 10 to the power minus 31 kg. The charge on electron you know 1.6 10 to the power minus 19 coulomb, coulomb stands C. The mass of proton is 1.697 into 10 to the power minus 27 kg. The charge on proton is equals to the charge on electron and that is 1.6 10 to the power minus 19 coulomb. If you write down here the charge is negative here it is positive magnitude is same. Ok the mass of proton neutron is equals to 1.697 10 to the power minus 27 kg and the charge on electron neutron is 0 because it is neutral that we already know. These value you should know. The other thing is what that electron is discovered by proton is discovered by Goldstein and neutron is Jim's Chadwick. This question actually they do not ask in the exam. What they ask sometimes they ask the charge by mass ratio of this, this and this means QE by ME. If you find out this the charge by mass ratio we also call it as a specific charge. The charge by mass ratio is a specific charge. Sometimes they ask you this question what is the charge by mass ratio of electron proton neutron order. Ok so it is 1.76 into 10 to the power 10 to the power 8 coulomb per gram. The charge by mass ratio of proton is 9.58 into 10 to the power 4 coulomb per gram. Obviously the mass of proton is more charge is same. So charge by mass ratio of proton is lesser than to that of electron. Ok and this charge by mass ratio is 0 we do not find that. Ok so what we can write if you see this comparison QP by MP that specific charge of proton is lesser than is lesser than to that of electron. This you must keep in mind. One more relation you see the mass of proton by mass of electron the ratio is 1837 approximately. So this also you remember. Ok all these things they ask sometimes directly. Ok now like I told you once we know all these subatomic particles present within an atom. But the question is how they are arranged within an atom. So to answer this question different different scientists they have given their own theory and all these theory we call it as atomic models. Ok so next heading you write down atomic model. Write down the atomic models explains the atomic model explains the arrangement of the arrangement of the various subatomic particles within an atom. Now what are the different atomic models we have. Ok the first model was given by JJ Thompson and we call it as Thompson model. What are the other name for this. Yes what are the other name for this. We have watermelon model watermelon model. And we also call it as plum pudding right plum pie pudding or plum pudding model. Ok so all these are the same name we have. According to this what Thompson suggests it's he's given his own theory and what he suggests that atom is an atom is a solid sphere positively charged solid sphere. I guess you have done all these things in your 10th grade. Ok so again I won't take much time into this. An atom is a positive charged solid sphere in 9th grade. Ok positive charged solid sphere in which the electrons are distributed in such a way in such a way that they experience minimum repulsion like this. Like this the distribution was there but this theory was not found to be was not found to be right. This theory was not found to get fit into other various investigations like alpha particle scattering experiment and hence this theory was discarded right. So write down quickly into this one according to this model according to this model. An atom positively charged positive charged solid sphere in which the electrons are embedded in such a way in such a way so that they experience minimum repulsion. Ok so later on what happened. This model this model discarded later on because it does not fit for the other experiments or investigations. Ok next one we have the second one that is that is rather Ford model rather Ford model is given by obviously rather Ford. No he did not take he did not talk anything about the position of neutrons right. Actually the moment the when he gave his own you know theory that time the neutron was not known. Ok that's why he did not talk about neutron but anyway that does not make any difference because the model was not correct so we have discarded it correct. So rather Ford model is given by the scientist called rather Ford and this model is given by you know by it is based on an experiment which we call it as the alpha particle scattering experiment. So this model is based on write down it is based on alpha particle scattering experiment alpha particle scattering experiment which we also call it as gold foil experiment. Both are same thing gold foil experiment. So what happens I'll show you the you know the diagram the you know the experimental setup of it. Ok you have to draw this this one you see we have a lead block here a radioactive substance which is allowed to pass through a hole here lead plate and this is thin gold foil this is thin gold foil. Ok so you don't have to worry about it just you see the alpha particle passes through this and it strikes at the gold foil here. So what is the observation we had here the observation is most of the alpha particles the passes through without any deviation they just passes through it without any deviation. Ok a few of them deviates by a very small angle you see this is the incident alpha particle this is the incident alpha particle. Ok so most of them passes through without any deflection they passes simply like this. Ok don't look at this now just you focus on here focus here some of them deviated by a very small angle and passes like this you see this is the figure we have right. Few of them deflects like this it comes back it reflects and comes back like this and there are very few which retraces their path means they goes like this it strikes and come back onto this path it comes back like this. It goes strikes and comes back like this so this is what it happens you see here this atom because we have thin gold foil so we have thousands of gold atoms present into this foil. So one of the atom is this we magnify one of the atom and this is this the atom of metal foil this one. So what happens when alpha particles beings of alpha particle strikes very few of them deflects like this and most of them you see they passes through this atom without any deflection. Say it is like this without any deflection so there are so many alpha particles which passes without any deflection this was the first observation. Second observation was what a very few of them deflects by a very small angle. I'll discuss this in just a second just a second so first observation was what most of the alpha particle passes through the gold foil without any deflection. A very few of them like few of them deviates by a very small angle and goes like this you can see this one and this one over here deviations. This one deviates like this by angle theta and this one deviates like this by angle theta. A very few of them retraces their path you see it goes here strikes at this point and comes back to those. This three observation we make. Why do you use gold foil here? The two things gold foils are first of all it's very thin we require a very thin foil over here the thickness if you see the thickness is around 0.0004 centimeter approximately. Because of this thick ribs very thin plus it is the gold foil is malleable also. Because of these two properties we use gold foil for this particular thing. So observation you write down here observation you write down first of this observation is the most of the alpha particle passed out without any deviation. There's no deviation. Most of the alpha particle passed out without any deviation. Okay, so what is the meaning of this when there is no deviation. It means there is no collision here which further means that within an atom most of the space is vacant that is the first conclusion drawn from this observation. So observation you have written most of the alpha particles passed out without any deviation next line which means which means which means most of the spaces within an atom. Most of the space within an atom is vacant most of the space within an atom is vacant. The second observation is what write down the second observation. The second observation some of the alpha particles some of the alpha particles deviates with a very small angle deviates with a very small angle deviates with a very small angle. It means what this means that there are some positive charged particles also present within an atom. There are some positive charged particles because alpha particle is positively charged h2 plus and when it gets deviates it means there are some positive charged particles also present within an atom. Write down. There are some positive charged particles present within an atom. Third point a very few of them retraced their path a very few of them retrace their path. This means what why the this is the very important one. Okay, this is the very important one. Why the particle retrace their path because the mass of the atom is concentrated in a very small reason. So mass is almost here present. So when it collides with the very heavy mass here it cannot penetrate it and it comes back to its original or following the original part it comes back. Right. So a very few of them retrace their path this means what this means the mass of an atom is concentrated within within a very small reason called. Nucleus. No this is not repulsion. This is because of mass the particle retrace their path is because of mass if repulsion is the criteria then it could deviate in different angle and go to the different angle. Charge can deviate it but since it retrace it path it is mainly because the mass that is concentrated in the nucleus. So this is the this is the very important you know observation and the result of Rutherford experiment that is gold foil experiment or alpha particle scattering experiment. The discovery of nucleus takes place from this we got to know that there is a very small reason within an atom it is present in which the mass of the atom is concentrated. And this is small reason later on is called as the nucleus of the okay now based on these observations and conclusion Rutherford given its own model and that we call it as Rutherford nuclear model. So write down the heading next Rutherford nuclear model Rutherford nuclear model write down the main postulates of Rutherford nuclear model. The first point electron revolve around revolve around a nucleus around a nucleus like planets like planets revolve around around the sun. Second one electron revolve in a circular path orbit electron revolve in a circular path called orbit. Next the force of attraction force of attraction between electrons and nucleus nucleus balance the centrifugal force on electron not attacks sorry. So this is the three postulates are three points given by Rutherford for its atomic model right these are the three points we have here now in this also we have a drawback. Right so what he said first of all you try to understand he said what that we have obviously we have a nucleus so we have an atom right and around an atom there are different orbits present like this. There are different orbits present and electron revolves in this orbits no he did not talk about the number of electrons in this orbit. Okay we just have electrons and there is a reason very small reason which is the center of these circular path this reason is the nucleus. This is nucleus and electron revolves around this nucleus in different different orbits like this this is what he said like planet revolves around the sun. Third point what he said because it is positively charged nucleus and this is electron so you must have some force of attraction. You know what is centrifugal force could you tell me what is centrifugal force centrifugal force is the force acts on an object in outward direction this one this force is centrifugal force right so this takes place in outward direction. The force that acts towards the center along the radius this force is centripetal force and this centripetal force keeps this object in this circular path. Yes this force which acts in the outward direction that is the centrifugal force which takes place which actually which acts on the object moving in a circular path. Now this is electron negatively charged and this is nucleus positively charged so we must have some force of attraction between the nucleus and the electron electrostatic force of attraction. So what he said this force of attraction balance the centrifugal force because the electron is revolving in a circular path like this this force balance this centrifugal force of attraction. That is what the third point we have for rather. Now we have a drawback in this points only what is that drawback I'll tell you. Okay, now the point is according to according to the electromagnetic theory, which is there in modern or this classical physics. What electromagnetic theories says okay I'm just giving you this information. Electromagnetic theory says whenever charged particle is moving under the influence of an attractive force right again I'm repeating this. Or you write it down right down here drawback and then you write down this. What is the drawback and how we discarded why we discarded this particular model also that you try to understand right down. According to electromagnetic theory according to electromagnetic theory when a charged particle when a charged particle moves under the influence of whenever a charged particle moves under the influence of attractive force. It loses energy continuously. It loses energy you write it down each of these points I'll just this point you write down I'll explain this what is happening. Okay, whenever a charged particle moves under the influence of attractive force it loses energy continuously in the form of electromagnetic radiation. It loses energy continuously in the form of electromagnetic radiation. It loses energy continuously in the form of electromagnetic radiation as the result as a result. The electrons as the as a result the electrons loses energy as a result electrons loses energy continuously in every turn loses energy continuously in every turn and comes closer and closer to the nucleus. It comes closer and closer to the nucleus nucleus following a spiral path. Electrons should loot energy in every turn and moves closer and closer to the nucleus following a spiral path. And finally it falls into the nucleus and finally it falls into the nucleus. Into the nucleus, which makes the atom unstable. Okay, following a spiral path and finally it falls into the nucleus and hence the atom becomes unstable. Next slide. Since the atom is quite stable. Since the atom is quite stable. Hence the stability of atom. Hence the stability of atom is not explained by this model. This is the drawback. Hence the stability of atom is not explained by, stability of atoms is not explained by this model. So this is the drawback we have here. The EM laws are not applicable to anyone. Who told you this? Ken Shook. From where did you get this? Tell me. What is an electromagnetic, this EM laws or what? Electromagnetic laws. What is electromagnetic laws? That's what I said. According to electromagnetic theory, any charged particle, it does not talk about that it is applicable for subatomic particles or not. It is just, it says any charged particle. Whenever in motion, right, whenever in motion under the influence of any attractive force, it loses energy continuously. Since electron has charge over here and it is moving around the nucleus and there is attraction force also here. Hence it should lose energy continuously, which is not happening here. Right. According to electromagnetic theory if you go, the electrons keeps on moving like this and since it is losing energy continuously. It won't be able to maintain the same path in every turn. It loses energy. Hence it should follow the spiral path like this and keeps on going and going and going and finally it should fall into the nucleus. According to the electromagnetic theory, this is the theory that we have. Now when electron falls into the nucleus, which makes the atom unstable because electrons does not fall into the nucleus. An atom we know it is quite stable. It is not like it is unstable substance atoms. Correct. So hence this is the drawback of Bohr's atomic. Sorry, this one rather for model. And because of this drawback only we discarded this model, discarded the model. Okay. So what is the drawback? The drawback is it could not explain why atoms are unstable. According to this rather for model, the atom must be unstable, but it is not the fact. The fact is what the atom is quite stable. Right. The second drawback is what this was the biggest blow for this particular theory. The second drawback is what that it could not explain. It could not explain the energy, the energy velocity of electron in an atom. Okay. These are the drawbacks. Hence, hence the model was discarded later on. Okay. So I said, guys, we'll take the reference of the classical physics to understand a few things here in this chapter. Okay. It's very theoretical initially. Later on, we'll have numerical problems into this, but to understand all these things you should, we have to take the reference of physics, the modern physics or classical physics that we have. Okay. You will see 12 in standard. The last, there is a chapter called modern physics. There again, you will study all these things, atoms, electrons. Right. So we are taking the reference of those particular things that you should know. Like what reference I have taken here? I have taken the reference of electromagnetic theory. What is electromagnetic theory? Any charged particle in motion under the influence of an attractive force, it should lose energy continuously. So this is the reference I have taken here to understand the drawback of the Rutherford model. Okay. These are the few models we have, the most important and the next model we have here, that is Bohr's model. Okay. But Bohr's model, like I said, to understand this, you should know various facts before this to understand the Bohr's model. Right. So first we'll discuss all those concepts and then we'll move into the Bohr's atomic model. Okay. So write down the discovery heading, write down discovery leading to Bohr's model. We'll try to understand here what are facts, what are important things we should know, which is important for us to understand the Bohr's model. So first thing we need to understand here is the dual nature of electromagnetic radiation. Write down into this electromagnetic radiations, electromagnetic radiation is nothing but electromagnetic radiations is nothing but electromagnetic waves. It generates, it generates whenever, whenever a charged particles, whenever a charged particles moves under any potential difference, any potential difference or in or in a magnetic or electric field. So electromagnetic radiations are this. It consists of various waves when we have a wave. So we have various wavelength and frequency. Like we have radio waves, UV rays, okay, visible rays we have, microwaves, okay, X rays we have, all these comes under electromagnetic radiations. Okay. Electromagnetic radiations, unlike sound wave, it does not require any medium to travel. Okay. One more point to write down here. Unlike sound waves, unlike sound wave, it does not require any medium. Unlike sound wave, it does not require any medium to travel. Okay. These are the one property. This is the one property of electromagnetic radiation, which is very important. And because of this property only, it is used by the satellites and other things that send pictures from the, you know, from the universe when they go over there. Like we use to see the various pictures of Mars. Okay. So since in vacuum, there is, there's no medium over there. Then also we are able to receive those messages, those pictures because we are using radiations, electromagnetic radiations over there. So it does not require any medium. That's the one thing. We are talking about the dual nature of electromagnetic radiation. So electromagnetic radiations, we are, we all are very sure with it that it has wave properties. These are waves. Example, I've given you microwaves, radio waves, X rays and all. Right. So these are waves. Right. So dual nature means what it has wave characteristics as well as particles, particle characteristics. Okay. So the characteristics we know, they shows diffraction, they shows interference. There are many different things we have, which confirms the wave characteristics of these radiations. Okay. What is particle characteristics? We'll discuss that later, but let us first understand, since these are waves also, so there are some terms associated with it, right, with the wave. Those terms will see first and then we'll move on to the next part. Next thing, right? So dual nature means, dual nature means wave nature as well as particle nature. Wave nature and particle nature. Wave nature is defined by the various phenomenon like we have diffraction, interference, all these things you will just, you will study in physics. Okay. Diffraction, interference. Diffraction is nothing but the bending of light. Right. Interference is the combination of two waves. Okay. So I'm not going to detail of all these. You'll study this in physics. Right. Diffraction and interference. Yes. Photoelectric effect actually, photoelectric effect confirms the particle nature. Right. Not wave nature, but particle nature. We'll discuss that. Okay. Photoelectric effect also. Okay. So the terms associated with a wave, right down, the first term is wavelength. Wavelength is represented by lambda. This is lambda. Okay. Wavelength. What is the definition of it? Write down. It is a minimum distance, minimum distance over which a wave can be created. Okay. Look at this. Okay. This is the wave. It travels like this. Now you see this. It originates from this point. Right. It originates from this point. And here the velocity is in this direction. So the other point where the velocity is again in the same direction parallel to this. Right. This one from here to here, it is one complete wave. One wave is this from here to here. This one is another way. Second wave is this, then we have third wave, fourth wave, fifth, sixth, seventh and all. Right. So it is the minimum distance over which a wave can be created. Right. So the distance or the minimum distance is this from this point to this point. This is a minimum distance. Right. So this distance is nothing but the wavelength of this wave that is represented by lambda, minimum distance. Again, from this point to this point, you see it is another wavelength. This distance is again lambda. Okay. That is the wavelength of the wave. This point, this peak and this peak, you see this distance is also is also one wavelength. Right. So this distance you see here from this point to this point, just a second, this distance is also wavelength that is one wavelength. Okay. This peak that we have here, this we call it as the crest of the curve, C-R-E-S-T. So this is crest. This is also crest. This is also crest. This one is trough. Trough. This one is also trough. Right. So we can define this wavelength as minimum distance over which a wave can be created. This is one definition. The other one is it is also the distance between two consecutive crest or two consecutive trough. Correct. So the next point to write down, it is also defined as wavelength. It is also defined as as the distance between two consecutive crest or this is the definition of wavelength. Correct. So wavelength, the unit is angstrom represented by this and one angstrom is equals to 10 to the power minus 10 meter. One nanometer is equals to 10 to the power minus nine meter. One micrometer is 10 to the power minus 12 meter. All these conversion you should know. So this is the unit we have. Mainly it is represented in angstrom. One angstrom 10 to the power minus 10 meter. Okay. So this is the term associated with any wave that is wavelength. Pop it down this. Yeah. Micrometer. Yeah. Correct. Correct. It is 10 to the power minus 6. One picometer is PM. Its picometer is 10 to the power minus 12 meter. Okay. Mainly we will use angstrom, nanometer and meter. That is it. This is the thing we should know. Now, the next term we have frequency. Frequency is represented by small f or new. This is not V. This is new. Okay. Small f or new definition you write down. It is defined by the number of wave produced per unit time. Number of wave produced per unit time. Okay. So frequency new is equals to 1 by T. We can write where T is the time period. Now the next term you see the third one. It is time period represented by T time period. It is the time required to complete one wave to complete one wave. Okay. So in one wave. The distance travel is the wavelength of that way. That is lambda. Right. So we can write time period T is equals to the distance travel. That is lambda divided by the velocity of the wave. This is V. So time is equals to distance by velocity. Okay. This is what we have here. So if we substitute this time over here. This T over here. So from this to new is equals to V by lambda. This is velocity. Right. So V is the velocity of wave. Right. It is given by generally it is the speed of light. That is what we use. Right. So it is three into 10 to the power eight meter per second. Right. So this is constant. This is constant. Right. So we can write the frequency into wavelength is constant here for this electromagnetic wave. Right. So as wavelength increases, frequency decreases and then frequency increases, wavelength decreases. This is the relation. So all these formula, you'll get formula based question on this. Easy question. So one more time we have here. This is wave number. New bar. This is wave number wave. Number is the number of waves produces per unit distance. Right. What we have here is the number of waves. So this is channels per unit. So the feedback output is based on. This is free of charge, Ms. unit distance, right? So we know with the distance of lambda, the number of wave produces is one that we know because we know in lambda distance one complete wave is there. So this distance we have one wave, so per unit distance we have right? So for one the number of wave is what? 1 by lambda correct? Hence the formula we have wave number new bar is equals to 1 by lambda, right? And the unit of wavelength, sorry this wave number is we can write meter inverse, the unit, meter inverse, okay? Unit I forgot to write in the terms that we have used previously. Time period you can use any unit of time. Frequency unit is second inverse or it is also written as urged. Done? Okay. Now one more thing here is electromagnetic spectrum, electromagnetic spectrum, okay? Write down, write down, write down the different types of electromagnetic radiation, the different types of electromagnetic radiation, the different types of electromagnetic radiation which differs with each other, which differs with each other in terms of their wavelength and frequency, right? Again I'm repeating this, there are different types of electromagnetic radiation which, which differs with each other in their, in terms of their wavelength and frequency. Next, write down, when we arrange these radiations, okay? When we arrange these radiations in ascending or descending order, in, in ascending or descending order of their wavelength or frequency, in ascending or descending order of their wavelength or frequency, then the spectrum forms is called electromagnetic spectrum. Then the spectrum forms are called electromagnetic spectrum, electromagnetic spectrum. Now copy this down. This is cosmic rays, UV rays, visible rays, visible wave we can also write infrared, microwave, radio wave, okay? Now when you go left to right here, left to right if you go, wavelength increases, frequency decreases. Right to left if you go, frequency increases, wavelength decreases. Just as I can let me finish this, okay? I'll repeat. This is, let me finish this, okay? Yellow and then orange and then red, okay? So if you look at this, this is V I D G Y O R, okay? Again you see red, red color, here you see it has maximum wavelength because again left to right, wavelength increases and while it has maximum frequency, right? From this point to this point, if you look at the wavelength, this is 400 nanometer and this is 760 nanometer. Means this wavelength, whatever wavelength falls in this range that we can see, this is a visible range we have. Copy this down. Yeah, Shradha tell me, what did you write the last point? Did you write the electromagnetic spectrum theory of it? Electromagnetic spectrum, did you have written? Did you write? Did you write this, the definition of it, what is electromagnetic spectrum? Sir, I am like in the, can you just start from the beginning because I don't know. Okay, I will start from the beginning of electromagnetic spectrum, correct? The different types of electromagnetic radiations, there are different types of electromagnetic radiations which differs with each other, which differs with each other in terms of their, in terms of their frequency and wavelength, in terms of their frequency and wavelength. When we arrange these frequency or wavelength, when we arrange this frequency or wavelength in either ascending or descending order, in either ascending or descending order, we get a spectrum which is known as electromagnetic spectrum, which is known as electromagnetic spectrum. After this Shradha, I have drawn this diagram that we have here. Thank you so much. Yeah, Shradha come again. Thank you so much sir. Okay, yeah. So yeah, yeah, just a second guys, just two minutes. Okay, I know this is very difficult to, you know, sit continuously like this because we are not doing any numericals. Numericals we can solve after some time, a few more things we have to discuss. So you don't have to, all of you don't have to memorize the wavelength of all these, but you should know at least this point that the visible reason, the wavelength falls in this range, 400 nanometer to 760 nanometer. This value you should know 400 to 760. The second point you should know, you all know this, I guess, Vibs Yo, right? So red has the maximum wavelength and that is the reason we use red light for all this traffic signal. So that we can see this from a long distance. Okay, so this is electromagnetic spectrum and this is all for wave nature of any electromagnetic, right? We'll take a break now and after the break, we'll start with the particle nature. Okay, so we'll resume the session at 620. Okay, take a break. Okay guys, 620 will resume. Okay, this will be on time. Okay, thank you. Hello. Shall we start with that? Okay. So we have this, we had discussed the wave theory of light, wave nature we have discussed. Now the next thing is, is the particle nature. Okay, particle nature. In this, we'll understand first, what is Planck's quantum theory? Planck's quantum theory. Write down, you write down this. No, no, no, it's not, it's not double three. It's different. Okay, write down the theory in this and then we'll discuss. It's very important. Okay, it's very important to understand. If you don't get it, you'll have difficulty in understanding photoelectricity. Okay, so concentrate here. Write down, write down the energy emitted or absorbed. Okay, the energy emitted or absorbed, the energy emitted or absorbed by a body, by a body is always in discontinuous manner, is always in discontinuous manner, means the energy available, means the energy available in the form of, available in the form of a small discrete packets, in the form of a small discrete packets, and these packets are called quantum. These packets are called quantum. I will explain this, first you finish this theory called quantum. Next line, in case of light, in case of light, the smallest packet of energy is called, right, the smallest packet of energy in case of light, it's called photon. But in general case, in general case, these packets are called quantum. It's called quantum. Next line, the energy of each quantum, the energy of each quantum is directly proportional to the frequency of the radiation. The energy of each quantum is directly proportional to the frequency of the radiation. Okay. Now, we try to understand this. Suppose we have a radiation, this is the radiation suppose we have, okay, any radiation, correct, any radiation. We say this radiation is of frequency new, for example, right. And according to plan quantum theory, the energy associated with this frequency or this radiation is E is directly proportional to new. This is what it is given in Planck's quantum theory. Okay. So if you remove this proportionality sign, E equals two will get a constant h times new. What is h? h is the Planck's constant. h is the Planck's constant. This value you should memorize 6.626 into 10 to the power minus 34 joule second. So this is the energy associated with this frequency. E is the energy we have here. Energy associated with associated with one quantum frequency new. This is what we like to understand this. If I write E is equals to h new, what it means. Okay. We have a radiation of frequency new. I have already written here radiation of frequency new. But when we say E is equals to h new means the energy of this radiation is h new. What do you mean by this? Suppose you have a light source, right? You can have a torch, you can have a flash to your phone, right? The light emits from that light source, correct? So when I say this light is coming out of the light, which is coming out of this particular source is of frequency new and its energy is E is equals to h new. E is equals to h new, right? So what do you mean by this? We have a light coming out of a source and energy is h new. So how do we understand this particular? How do we relate this energy with the light that is coming out of any source? Okay. So here what happens E is equals to h new. What Planck suggests that in any radiation the energy available in the form of packets. So you can understand this that in this light of frequency new, there are a number of particles present in this light. Even if you have white light source also, when you project light on any surface, we say this is a light but in that light there are lacks of particles present into those lights one after the other. Like you see this radiation consists of particles means we have particles present one after the other. Just a second. You see, this is the particles we have and it is discontinuous. You see, it is not continuous here. It is discontinuous. So any light source has this kind of particles present in it. And when we strike lights, we are striking these particles. This particle is called quantum. This is one quantum. One particle is one quantum. So we have so many quantum present in a light. But if you have white light in presence in case of light, the term we use, we don't use quantum, but we use photons. So photons are the particles of light. For any other radiation, the particle is known as quantum, right? So quantum is the more generalized term we have. Photon is specifically we use for light. Okay, this is for any other way. This is one thing. Okay. So first of all, when I say E is equals to h nu, it is the energy associated with one quantum. I mean, suppose this light has frequency nu. So the energy E is equals to h nu is the energy of this particle, one quantum. This particle also has h nu amount of energy. This particle also has h nu amount of energy, h nu amount of energy, h nu amount of energy. So energy is what? Energy is available in the form of packets. Okay. It is in discrete manner. It is not continuous. It is in discrete manner. It is not continuous. Right. It is quantized. We also say the energy is quantized. So if I ask you what is the energy, energy with n particles or n photons, photons of radiation with frequency nu, with frequency nu. Okay. Energy of one photon E is equals to h nu we have. So if you have n number of photon, it is n times h nu. Okay. So always keep this in mind. When we write E is equals to h nu, it is the energy of one particle present in that particular radiation. Okay. You can understand this with a very simple example. Suppose you have a gun, right? When you strike, you know, when you hit on a target from that gun. So what happens? The bullet comes out from the gun one after the other. It is not continuous. No. So if you replace the light source by gun, right, then the photon is replaced by the bullets. Each photon you can understand here. It is, it represents the bullets from the gun. So when you strike lights or light on a surface, you are striking with the light particle action. So in case of light, the particle is photon, otherwise it is quantum. So first of all, one quantum or one photon goes and it strikes with the target, then the second photon is right, third, fourth, fifth, and so on it goes. So basically the energy is available in packets and in discrete manner. So we say that light particles are the waves, the energy available in discrete manner in the form of packets. This is the smallest packet of energy. Right? One more thing here, it is important that partial exchange of this energy is not possible. Either it gives the entire energy or it won't give anything. Did you understand the particle nature, the quantum or the particles present in the light wave? Yes. Did you understand this, clear? Please respond guys. So always remember this. So they may ask you in some questions, they may ask you to find out the number of the number of photons required for this energy. Yeah, the last person I'll repeat that again. This is the smallest particle, right? So when it gives energy when you strike light at any surface, then the partial exchange is not possible. You can compare this, this packet with a packet of biscuits. Suppose you have 10 rupees, no good day packet, you have a partly g suppose you have, right? So when you go to the shop to buy that particular packet, they cannot, no, give you one or two biscuits from that packet. You have to buy the entire packet, one 10 rupees or five rupees packet or any stuff. If it is packed, you have to buy the entire packet. You cannot, you know, tear it up and take one or two pieces from that particular packet, right? The same thing can understand it over here. This is very small packet. If there is an exchange of energy, then either the particle or the object or the target, whatever we have on which the light is striking, either it takes the entire energy associated with this packet, which is h times nu, or it won't take anything, it reflects back all the energy. So partial exchange is not possible in this one. Did you get it? Clear? Okay, so these two points you must remember, the light consists of particles and each of these particles, in case of light, we call it as photons. Okay, so photons are the particles of light for other electromagnetic wave, the term we use as quantum, okay, energy associated of the light energy available in the light wave in discrete manner. It is not continuous, means the energy associated with the particles present in the wave that can be either photon or quantum. Got it? So exchange of energy takes place with this photon when photon strikes at any surface, right? And this photon is one after the other. It is not like all photon strikes at the same time. So very simple example, you can always take the example of gun and bullet. First of all, the first bullet strikes at the target, then the second bullet strikes from the same gun, right? Then third, fourth, fifth, six like that. So one after the other, the bullet strikes with the on the target. Same thing we have here also, one after the other, the photon or quantum strikes at the target. Clear? So this is Planck's quantum game. Now we'll see some questions based on this. Like I said, this session is mainly theory. There are a lot of theory in this chapter we need to understand. But from after this, we can have numerical also, we can do some numerical. So some very basic numericals. Question is I'll write down the question. Okay, write down calculate the calculate the energy of a photon of light of wavelength of wavelength 5.862 into 10 to the power. Okay, you need to find out the energy associated with it with one photon. Next one calculate. If there is a lot of calculation, you can use calculator to calculate. Okay, calculate the calculate the frequency and energy of a photon the photon of wavelength 4000 angstrom. Okay, so you always take care of unit in these kind of questions. Solve both questions. What is the answer first one? So you see here calculate the energy of a photon of light of wavelength. This we know the energy formula is equals to h nu. And further we can write this as h C by lambda. Okay, wavelength is given you can substitute all the values here. 6.626 10 to the power minus 34 joule second. This is h. C is three into 10 to the power eight meter per second. This divided by 5.862 10 to the power minus 16 meter. So when you solve this you see unit also you must take care of like I said, so all these second second meter meter gets canceled. And when you solve this you'll get the answer the energy in joules. Okay, so this value the energy here when you solve this, you will get 3.38 into 10 to the power minus 10. Is this the answer? The answer is 3.38 into 10 joules unit. You also write down into this don't forget to write down the unit. Okay, could you tell me the answer in this question? Calculate the frequency energy of photon of wavelength. This Okay, so fine. We know is equals to h nu at C by lambda further 6.626 joule second. Lambda is 4000 angstrom into 10 to the power minus 10 meter. Yes. So you have to solve this, you'll get the answer as e. Okay, frequency is what nu is equals to C by lambda. This ratio gives you a frequency. Nu is equals to three into 10 to the power eight divided by put into 10 to the power minus seven. So it is 0.75 into 10 to the power 15. So which is 7.5 into 10 to the power 14. Sorry, 10 to the power 16 14. And the unit of this is meter per second and this that is second inverse. What is the value of energy you are getting? Yes, it is 4.96 into 10 to the power minus 19 joule. Yes. So this is the answer for this way. You just need to know the basic you know, formula of all these. Okay, you need to take care of units also here. Don't forget that. Okay, that's very important. Okay, one more question you see how many photons of light of light having having a wavelength 5000 angstrom are are necessary to provide one joule of energy done. Check your calculation, Akshath. Yes, that's right. So the 2.5 into 10 to the power 18 photons 18. Okay, so suppose we have n number of photons here, so we can write E is equals to n times h nu. So n is equals to one joule of energy divided by 6.626 10 to the power minus 34 joule per second. Sorry, joule second and nu is C by lambda. So 3 into 10 to the power eight meter per second. And lambda is the wavelength that is 5000 10 to the power minus 10. When we saw this, you see all the units gets cancelled, you'll get a number here that will be 2.5 into 10 to the power 18. These many photons require to gain one joule of energy. Then understood. Now you see the another model that is Bohr's atomic model. First of all, this is the most important, most appreciated and accepted model we have till date. It's not like it is absolute. There are few constraints we have over here. Right, few conditions we have over here. Right. So like I said, the Bohr's atomic model is the most appreciated, accepted and the important atomic model we are the most important one is this. So first of all, you should know, what is the constraint? Write down it is applicable for applicable for only one, only one electron system or hydrogen like species. Okay, one electron system means hydrogen like species means which has only one electron, right, which has only one electron as only one electron. For example, we can have hydrogen, we can have he plus, we can have a light two plus, etc. Okay, so helium has two electrons. So he plus has only one electron, lithium atomic number is three, three electrons. So I like to plus has only one. So this is a constraint here. Bohr's atomic model is applicable for only one electron system. What is the reason for this that also we can discuss, we'll discuss that later in the last once we finish it. Now to understand this Bohr's atomic model, do you think that you should know already? Okay, not things it's formula basically that you should know. What are those formula? The formula is suppose we have to charge q1 and q2 placed at a distance. Suppose this is q1. And this is q2 placed at a distance are from each other, then two three points we can do three formulas we can define over here. First of all, this is electrostatic formula. So the force between the two charges that would be equals to k times q1, q2 by R squared. This formula you should know where k is the k is the Coulomb's constant, Coulomb's constant. And this value is nine into 10 to the power nine Newton meter square by Coulomb's square. You don't have to memorize this value, not required. Okay, this is force of attraction. If you talk about the potential energy here, between the two charges, it is minus k q1, q2 by R, not R squared, it is R. Okay, minus k q1, q2 by R. Okay, these two formula you should know. Another one, suppose if an electron is moving in a circular path, any object, if it is moving in a circular path, then we can define angular momentum here. Suppose we have a circular path. And any object of mass m is moving in a circular path of radius r, then its angular momentum is, momentum is v r mass into velocity into distance. Okay, all these three things you will study in physics. But here we are just using this formula to understand this phototomic model. Done, copied. So these three formula, you know, and now we are going to see m is the mass of this object, whatever the mass we have here, that mass we have here, mass of an object m moving in a circular path of radius r with velocity v. Okay, now. So these three things you keep in mind. Now, we use this particular three formulas to understand the Bohr atomic model. Okay, so first of all, we'll see the postulates of Bohr atomic model. Right on the first point here, according to Bohr, he says that the negatively charged electron or simply write an electron revolves, electron revolves in a circular path called orbit called orbit around the nucleus, around the nucleus. This is the first postulates of Bohr's model, which is similar to the rather for atomic model. So he took the reference of rather for atomic model also. That's why the rather for atomic model was not completely wrong as like, if you see the concept of nucleus that we get from that model, that was right. Okay, it was not completely wrong. Okay, next one, write down, write down, there are, there are energy level present within an atom within an atom, and it is represented by and it is represented by one, two, three, four, or k l m n and so on. Energy levels are represented by this. Okay, these numbers are like this. Third one, if electron stays in an orbit, it neither emits or absorbs energy. It just stays in the orbit, nothing in it does. Okay, neither is emits nor absorbs energy. The fourth one is if electron absorbs energy, absorbs energy, it jumps into, into higher energy level, higher energy level. If electron comes down to the lower energy level, emits energy in the form of radiations, emits energy in the form of radiation. Copy this down. Done. All of you. Now, the last two point is very important here. Sixth and the seventh one. Six point is the force of attraction, the force of attraction between the nucleus and the electron between the nucleus and the electron balances the centrifugal force on electron. Okay, seventh one out of out of infinite number of orbits around the nucleus, around the nucleus, electron revolves only in those orbits in which in which its angular momentum is integral multiple of H by two pi. So these are the postulates of force model. The last two points are very important because to get the formula and other things, we use these two postulates. Yes, H is the flying constant. No, see, this one will discuss the one mathematical derivation of this later on last point. But when Bohr was given this particular point, it is based on his research and study. There is no facts and proofs behind this. Okay, he has done his research. And then he said that the angular momentum must be integral multiple of this. Right, that's what he did. But one mathematical derivation will have this, we'll discuss that later in de Broglie hypothesis later on. Okay, so now, all these seven points are important for you to understand. The last two points are the most important one because we are going to use these two points only here to derive the formula. Now you see, suppose we have an nth orbit, like we have n number of orbits, you see, he said what? See, like this, we have infinite number of orbits present. Okay, and orbits has each of these orbits has different energies. Okay, so here we have some amount of energy in this orbit. In the second one, first of all, it is represented by one, two, three, four, five and so on, or KLM and we represent this. Okay, all these first, second, third, fourth orbits has a definite amount of energy. If the electron present in this orbit, this will have a definite amount of energy this electron has. In this orbit, it has a definite amount here, a definite amount and a definite amount. Okay, so when electron receives energy from any source, like suppose, if you try to, you know, provide energy to these electrons from an external source, for example, okay, if you provide energy through radiation, then electron receives this energy and jump to the higher energy level. Further, it receives energy if you provide another higher energy level, then again jumps to the higher energy level. So when it receives energy, it may jump to the higher energy level. Similarly, if it comes back, if it comes down, it has to release some amount of energy in the form of radiation. Further, it comes down, it has to release another radiation, energy in the form of radiation. Again, comes down, release energy in the form of radiation. Right, this is what Bohr's suggests, infinite number of orbit. Obviously, you see with this particular wavelength, the energy associated is what? Delta E is equals to XC by lambda. XC by lambda. So if it is lambda one, this lambda one, Delta E is the energy difference between these two orbit, these two orbit, third and fourth one. This is Delta A. This amount of energy comes out when the electrons comes down into the lower energy level. This is what Bohr's suggests. First thing is that, okay, not like this, the n number of orbits we have, I am assuming nth orbit here. This is the nth orbit I am assuming. Right, and suppose the electron is present over here. Right, and this is the velocity of this electron. The electron here, the mass of this electron I am assuming Me, the velocity I am assuming Vn, because it is the nth orbit. And Rn is the radius of nth orbit. This charge here, we have electron E. This charge here, we have Z times E. Z is the number of atomic number of the atom, whatever atom we are taking. And this atom must have one electron, like we have hydrogen, HE plus and Li two plus. Okay, okay. So this is the charge we have in the nucleus, Z E, and E is the charge. Now, if you compare this, if I write down this line as here, right, this is the nucleus charge is Z E, this charge is E, and this distance is Rn. Can we write down the electrostatic force between these two charge, which is here actually? Yes or no? Please respond, guys, quickly. We can write down the electrostatic attraction. Yes, the formula you know already I have given you the formula. So I want you to focus on the formula. We'll use that formula only over here. So what is the electrostatic force here? You see the electrostatic force F is equals to K times Z E into E divided by Rn square. Okay, and this force actually this electrostatic attraction force here, this balance the centrifugal force of attraction, which is acting in the outward direction. This force equals to what we can write the centrifugal force centrifugal force. I hope you all know MV square by R. So Vn is square by Rn. Is it clear? Did you understand this? The first equation is this. Did you understand this centrifugal force is MV square by R. You know this. Correct. So this is the first equation we have. Correct. Further, we can write this as Z E square K times divided by Rn is equals to MeVn square. Right, I'll write down this as the first equation. Okay, now the last, yes, the last point you see it says the electron revolves only in those orbit in which its angular momentum is integral multiple of H by 2 pi. So what is angular momentum? Could you tell me MVR, Me, Vn, Rn integral multiple of H by 2 pi. So N H by 2 pi. This is equation two. No doubt in this. Correct. So now you see these two equation you see. K is a constant. We know the value of K. We know the value of K. K is nine into 10 to the power nine Newton meter square coulomb square. This is the value of K. The mass of electron also we know that is 9.1 10 to the power minus 31 kg. We know this value also. We know the value of pi that is 3.14. Right, we know the value of electron the charge on the electron 1.6 into 10 to the power minus 19 coulomb. We know the value of other things. Right, so we have all these that is atomic number. So now these two equation if you see, listen to me very carefully here. These two equation you see, you know all the values except Vn and Rn. Make sense? Agreed? You know all the value except Vn and Rn. Yes or no? Correct. So we have two variables. And how many equation we have? Two. So two variables, two equation, we can solve this for Vn and Rn. Okay, so you don't have to solve this. Okay, when you solve this, you'll get the final expression as this. The radius in nth orbit, Rn is equals to 0.529 n square by z angstrom. Okay, this is the radius we have. Now when formula is this very, very important formula. Okay, similarly, when you find out for velocity in nth orbit, that could be 2.18 into 10 to the power of six times z by n. This is meter per second. This is the velocity we can find out the formula. What is z here? Z is the atomic number. Z is the atomic number. Okay, for hydrogen it is one, but for lithium, LI2 plus it is three. For HE plus it is two. N is the number of orbit, one, two, three, first, second, third, fourth, fifth orbit. So I am assuming Rn and Vn is the radius of nth orbit. And Vn is the velocity of electron in nth orbit. Am I clear? Right? No doubt. This is very important. That's why I'm asking you again and again. Okay, so you need to first of all see this, this formula, obviously you have to memorize. And you should also consider here because mostly they'll ask you to find out the radius ratio. Means they may ask you the radius in second orbit, the radius ratio of second orbit and fifth orbit like that. Okay, so radius ratio if they ask you to find out. So we can see the radius in nth orbit or in any orbit, it is directly proportional to n square by z, because 0.529 is a constant only. Okay, similarly, we can see here, the velocity Vn is directly proportional to z by n. So if you have to find out the radius ratio or the ratio of velocity in two different orbit, just you need to know this relation, because when you take ratio, the constant term, this term and this term will get cancel only. Okay. Now, again, you see this equation here. If I find out the radius in first orbit R1, this will be 0.529, just a second, wait, we are trying to find out the radius of first orbit, radius of first orbit of hydrogen atom. We also call it as first board orbit. Okay, so for hydrogen atom, I'll write down Rh is equals to 0.5291 square because first orbit and values one. Yes, velocity of electron in orbit. Yeah. So first orbit and values one and Z for hydrogen atom is one. So we'll get here Rh is equals to 0.529 and strong. Okay, this is first board orbit. Also we call it as okay. And hence we can also write Rn is equals to Rh n square by Z. This is the formula we have. Okay. Now, we're talking about an electron in anathorbit. Right. So if you talk about the total energy of this electron present in anathorbit, Ge is equals to the kinetic energy of electron plus the potential energy of electron. Okay, so total energy E is equals to the kinetic energy is half MeVn square because we know the velocity here is Vn. I've already told you and mass is Me and the potential energy you see between the two charge Z E and E you see here Z E and E the formula I have given you the potential energy is K times Z E into E by Rn. Is it clear? Did you understand this? The first up in the beginning of boards model I have given you this formula the potential energy between the two charge placed at a distance. Correct. Now, so this becomes what this becomes half MeVn square minus K Z E square by Rn. And we have already discussed that the fifth point the fifth board atomic model the fifth postulates we have that is the electrostatic force of attraction. I am again writing it down here. K Z E into E by Rn square. This equals to the balance the centrifugal force of attraction that is MeVn square by Rn. So when you solve this you will get MeVn square is equals to K Z E square by Rn. So this is the equation one that I have written already. Now, if I multiply this half over here and half over here, this becomes what? This becomes the kinetic energy. Okay. And when you compare this term, the kinetic energy and the potential energy here, the kinetic energy is what is minus of half of potential energy. If you compare this one and this one is this term and this term, it's minus half of potential energy. Yes or no? Correct. So this if you solve this one, the total energy that we get here, the total energy that we get here is if you substitute half of this is K Z E square by two times Rn minus K Z E square by Rn. So E value is negative K Z E square by two Rn. Total energy is this. Now, when you substitute the value of Rn, you will get the expression of E here. So total energy is this, which is negative we are getting here. And when you compare this, this is also very important. If you compare total energy with kinetic energy, total energy is what? It is negative of kinetic energy and negative of kinetic energy is half of potential energy. So this is the relation of energy, kinetic energy and potential energy. Did you get it? Any doubt? Please respond quickly. We'll finish this. There's two more things left. Now you see this Rn you have already calculated. This Rn you have already calculated. You can substitute Rn here and you can find out the formula for energy. Okay, so this E formula I'll write down here the total energy of an electron present in nth orbit is negative of 21.8 into 10 to the power minus 19 Z square by Z square by N square joule per atom. This we can also write this as minus 13.6 Z square by N square that is electron volt per atom 1312 Z square by N square. It is kilo joule per mole. Okay, so these are the formula of energy in nth orbit. So if you look at all this formula, the energy in nth orbit is directly proportional to Z square by N square. This is the relation we have. So again, guys, I am repeating here, you don't have to memorize the, you know, the derivation of it. Derivation is not at all required. What is required here? I have explained this so that you can understand how do we get the formula? Right, but to solve all the questions, you should know the relation of this Rn formula, Vn formula. You should know the relation of kinetic energy, potential energy, total relation you require, plus you also need this formula of energy that is it. Okay, how it is coming? What is the derivation? That is not important. Okay, but for understanding, you should know what is the formula we have? How do we get the formula? So I hope you understand this. Okay, the class was too hectic. I can understand a lot of theory plus, you know, concept and derivation we have done. We have done actually a lot today. So yeah, I'll request all of you, right, that you must revise each and everything before the next class. Okay, we'll start from this only. This formula will see some questions based on this, how they frame the questions, and few more concepts to discuss here. Okay. So you must revise all this. Fine. Okay. So thank you guys. I hope you understand this topic. We've done it in the quiet. Good night. Take care.