 Hello guys. Good evening. Yeah, so we're away in the last class. So we're done with both model right Questions also we have discussed. Okay. Okay Now in this two three points as you write down notes here right on the first point one note as we go away from the nucleus as we go away from The nucleus the total energy of electron of electron increases The total energy of electron increases Increases means what? the energy in first orbit even Is lesser than the energy in the second orbit e2 e3 e4 and so on it goes As we go away from the nucleus the total energy of the electron increase Correct. So we know the formula of energy That is en is directly proportional to That is square by n square this we have discussed at infinity The energy is what e infinity The energy is directly proportional to one by this by zero and hence at infinity the energy becomes zero for an electron So we can say at infinity the electron is no longer It means since there's no energy it becomes zero it means the electron Is no longer a part of the atom It is free from the atom Okay This has also been observed next point to write down The difference in energy in the consecutive levels e2 minus e1 Is greater than e3 minus e2 This is greater than e4 minus e3 and so on copy this down and this is again i'm coming So this is the two terms relation you must uh, you know Keep in mind it's important Okay, now the next Uh, I think we have discussed some questions also on this. Yes or no Regarding radius velocity energy. Yeah some questions here It's simple answer. There's nothing much to much to explain over here You find out energy in first orbit even e2 e3 e4 e5 you find out When you find out the difference between the two like this e2 minus e1 e3 minus e2 and so on You'll find out this order. Okay Means the difference between the first and second energy level Is maximum the energy difference is maximum over here and it decreases as we go away from the This is what we observe when you find out the energy Got it on Now the next one You write down the heading The calculation of There's a constant We call it as readberg constant write down Did you try the assignment? I have shared readberg constant If you do not Solve assignment. There's no point of attending class simply. I'm telling you all Okay, so whether you can do Half of the assignment you must do it Don't come simply for the class. Okay. This won't help you at all And once the things piled up Okay, you won't get time later on to solve those questions again Yeah, I understood. We have just started right So obviously you will get some questions which you which we haven't done in the class Till now, right? But don't worry with that. Whatever It's possible you do that like this one that you are talking about bamas and all we'll discuss it today And then you can try it again So if if if you get some questions, which we haven't done in the class you can leave that simply And later on when we discuss it, you can do that again. Okay Right. So you must solve the assignment all of you. Okay If I do not ask every day, it doesn't mean that you don't have to do that Okay, it is understood that you are attempting you are attending the class and then you are attempting the assignment That is what the purpose we share assignment every after every class. Okay. It is understood between Me and you Correct. So calculation of a readberg constant. Okay. So what is readberg constant? That is it is a constant term basically suppose if you have to find out the change in energy delta e So delta e would be what it is e2 minus e1 Right e2 minus e1 between second and first orbit any two orbit we can take delta e would be this delta e Is positive or negative delta e is positive or negative? positive why because Why because e2 minus e1 e2 is greater than e1 Right. So e2 minus e1 is positive just now we have discussed Okay. Now you see We have two different. Uh, you know Energy level suppose is the energy level we have right All of you are now very comfortable with it that this is one energy level has certain amount of energy This energy level has certain amount of energy Similarly, we have n number of energy levels has different different amounts of energy So this energy here it is more than the energy present in this orbit over here Okay, so what happens if electron jumps from higher to lower energy level what happens over here If it is jumps like this then there will be some amount of radiation comes out from this Because it is higher energy level It is lower energy level when it comes from high to low then the difference Of this energy. This is delta e This energy difference must come out in this process then only the electron comes from here to here Further it comes down again energy releases further comes down again energy releases, right? So i'm talking about this delta e over here. Is it clear? No doubt. So when this obviously electrons Are coming at a lower energy level Then some amount of energy Goes out from the atom and these energy comes out in the form of radiations Okay, and the radiations must have certain wavelength or frequency Right for lambda or nu is the frequency. So what is the energy associated with nu and lambda e is equals to h nu or h c by lambda Would you agree with me on this can we write this one? Yes, this is the postulates of Bohr's model that when electron comes from higher to lower energy level It radiates energy in the form of radiations And when radiations comes out, there must be some wavelength that is lambda or frequency nu Hence the difference in energy delta e we can write with this formula with the help of Planck's theory. Yes Or is there Or Yes, sir. How do you really come? Anyway, delta e is this now. We know the formula of energy e We have calculated it Last class and the formula of energy for your reference. I'll write down here e is equals to Minus two pi square z square e to the power four mass of electrons divided by n square h square. This is the total energy in any orbit the formula was Okay, delta e we have to find out so we can write down here Delta e is h times nu And that would be equals to e2 is n is equals to two Or even is n is equals to one So for any one orbit or better if I write down this as letter, let's take an General expression here. So I'll write down here. What just make a change over here. Let's write it down as n2 minus n1 is it fine means from n2 to n1 it is coming So this would be equals to here. I can write down with the help of this formula minus two pi square z square e to the power four m e divided by n2 square h square minus minus off the same thing two pi square z square e to the power four m e divided by n1 square h square any doubt in this any doubt in this So h nu becomes again at c by lambda And this would be equals to At c by lambda and this would be equals to if I take the constant terms common That would be two pi square m e e to the power four divided by h square into z square one by n1 square minus one by n2 square if you solve this you'll get this Now if I find out one by lambda from this two pi square m e to the power four huh If I find out one by lambda from this then what we get you see one by lambda is equals to two pi square m e e to the power four z square c h cube into one by n1 square minus one by n2 square Okay This constant here. This is a constant term. You see all of you. This is a constant, right? This constant is the reedberg constant reedberg constant represented by r capital r Okay, copy this down then I'll go to the next page constant is defined like this only it is We are trying to find out the wave number That's why one by lambda we have taken here in the left hand side Because one by lambda is the wave number. Okay So the expression for r the reedberg constant we get here is two pi Square m e e to the power four z square divided by c h cube So for hydrogen atom if I write down for hydrogen atom The reedberg constant r is represented by r h for hydrogen atom and this would be equals to two pi square m e e to the power four one square divided by c h cube because atomic number is one so r h is equals to Two pi square m e e to the power four c h cube This is the reedberg constant for hydrogen Okay, and hence for all other atoms reedberg constant r is equals to r h z square This is the reedberg constant for all other The value is approximately around one zero nine six seven eight centimeter inverse In 99 percent of the cases you don't have to use this value Just write down the answer in terms of r. Okay. We are going to the next thing Let us understand first Spectrum we have already discussed the spectrum, but there are different different types we have for this Not very important. Just you need to understand one thing here. That is Absorption and emission spectrum you have to understand that is right down the heading spectrum write down It is defined as it is defined as The pictorial representation it is defined as the pictorial representation pictorial representation of arrangement of radiation of arrangement of radiation in increasing order of wavelength in increasing order of wavelength Or decreasing order of frequency it is It is defined as the pictorial representation of arrangement of radiation pictorial representation of arrangement of radiation in increasing order of wavelength in increasing order of wavelength increasing order of wavelength or decreasing order of frequency In increasing order of wavelength or decreasing order of frequency the classification of spectrum you see spectrum first of all classified into two categories one is based on based on nature And the other one is based on origin based on origin Further based on origin it is classified into two categories that is emission emission spectrum and absorption spectrum absorption spectrum Okay, based on nature it can be of two types It can be of two types One is continuous other one is discreet discreet then also we have two types that is band spectrum spectrum and line spectrum band and line copy this down Okay, so all these things definitions I'm just telling you don't need to write down this because it's not it's not important See continuous is very simple Suppose you have white light Okay, please And you have a white light correct white light When it passes through a prison it gets split into seven different color, right? So you get a spectrum over here of seven different color This spectrum in which all the color with your Are continuous one after the other it is called continuous spectrum continuous spectrum Okay, so white light It splits into seven colors, okay when passes through a prison And the spectrum that we get is continuous Okay Discreet spectrum is what? discreet spectrum like when there is no When all the wavelengths are not present over there It is of two types the band and line band spectrum write down the band spectrum Nothing. Shit is this one a white light passes through a prison We know white light consists of all seven colors So it splits into seven different colors and that we get here over a screen one after the other So it is an spectrum right continuous spectrum. It is all the colors are present over here on the screen. This is continuous spectrum Okay, now make sure I don't band spectrum it contains it contains colorful bands separated by some dark space colorful bands separated by some dark space Okay, so in this what I said Like this the bands are present. These are what these are colorful bands Okay These are colorful bands present over here of different different colors And in between these bands we have dark space present So these are bands and this space here This space between the two bands Are the dark space we have so this is the band spectrum Okay, some of the wavelengths are missing over here Right means suppose two three wavelengths are present So we'll get a band of light here Then one wavelength is missing a dark You know space then again few wavelengths one wavelength is missing dark space few will like that here Okay line spectrum is opposite of it Line spectrum is something like this. We have an wavelength line Right separated by dark spaces Right, so here what happens right down? This is right down here band spectrum So band spectrum the colors are present in the form of bands Okay, and we have a thin layer of dark space line spectrum Here the colors are present in the form of a line one plain one single line will be there And all these lines are separated by dark bands Okay, opposite of it right down This is the ordered arrangement of lines This is the ordered arrangement of lines of ordered arrangement of lines of a particular wavelength a particular wavelength separated by separated by The dark space separated by a dark space now you see This line is spectrum is obtained from an atom obtained from an Atom and this band spectrum Is obtained from a molecule? That's why this line is spectrum for hydrogen. We call it a hydrogen spectrum Okay, okay next write down absorption spectrum Okay, so absorption spectrum is something like this. I'll just draw a diagram You also copy this down and then I'll explain it. Okay. This one is very logical. You can understand it easily Okay, so absorption is suppose we have a prism or prism and this side we have A screen Okay, and we have a light source here We have a light source and there is A gaseous particle any particle present over here any molecule any solution Okay So any solution present over here? Like this In this a solution is present. Okay So this is what we have this is the this is the Slit and through which the light passes through Let me finish this Diagram, I'll explain what is happening Or simply you can also understand and we have basically a light source. That is it nothing much Okay, and this light from here it passes through this solution And then it goes on To this prism And here what happens here? The white light splits into its component Okay, this is splits into its component like this Comes down like this And we have here This side we have a screen like this and this is screen. I am representing here actually Okay, so this is again this goes over here Then this goes over here it deviates like this deviates like this pumps here, right? This is the slit we have This is suppose any solution any substance I am taking This is the prism And this is the screen we have so what we observe here that we were expecting all the seven Colors over here because it is a white light consist of all seven colors But what we are expecting here what we observe here. We observe that the few Wavelengths are missing all the wavelengths are not present here in this screen Okay, a few wavelengths are missing Few minutes are present over here A few are missing on this screen So this suppose these are the wavelengths present and here we have the dark space It means here the wavelength is we are not getting we are not getting these wavelengths over here after the prism So since here we have white light Okay, so it contains all the seven colors But when it passes through this substance and then the prism and then few wavelengths are missing over here So here we have all wavelengths And here we are not getting all wavelengths. It means some of the wavelength has been absorbed. Yes or no And which one who is responsible here to absorb the wavelength or light? Yes, that's right. So the point is Whatever substance we have used here solution on gas That is that probably absorbs a few wavelength And leaves the other wavelength which we get over here right So obviously the substance we are using here It is responsible for the absorption of those wavelengths This spectrum that we get here Where few wavelengths Are missing which has been absorbed by the substance here This we call it as absorption spectrum, okay Now to confirm this and whether this substance only have absorbed this wavelength what we have done We have taken the same substance And when we heat this it emits the same wavelength which was missing over here This confirms that this Substance absorbs a few wavelength And the spectrum that we get here is called absorption spectrum And when we heat this we get the same wavelength which was missing over here That confirms our theory over here and the wavelength that and the spectrum that we get here When we heat this the spectrum that we get here which includes all those wavelengths Which were missing over here in absorption spectrum Which were missing in the absorption spectrum This is a spectrum that we get We call it as emission spectrum Right, so when we heat this the spectrum that we get is emission spectrum This one is absorption spectrum. This is just for you to know this. They won't ask you any question Yes, correct. It is On heating the gas it radiates the same wavelength which which which it absorbed in that particular case How good one I'm coming to that way So did you understand what is absorption? What is emission spectrum clear? Not very important, but you should know this fact That what happens when the white light passes through a substance Point is to sum up all this What happens when a white light passes through a substance? The substance absorbs few wavelengths not all Right, this is what the discussion we have done. Yes or no Now, why does it happen? Why atoms? one more thing If this substance you are taking hydrogen here Then the spectrum that we get we call it as hydrogen spectrum. That is nothing much Okay, now why these gaseous substance or any substance absorbs only a few wavelength? Why not all? That's a very genuine question. Correct. So the answer for this one is what that And after this experiment only we came to know about this fact that within an atom, there are energy levels present Okay, within an atom there are energy levels present. Okay, this only gives us this idea That an energy level present within an atom. All these are energy level. We have discussed this Okay, now suppose the electrons Electron is present over here in this particular Orbit energy level, right? What we have done Then a white light passes through this Right, this is the white light passes through this Atom gas whatever it is So this is the atom of the substance and white light passes through it Okay, now what happens This light Different different wavelength and with different different wavelength We have different different energies because e is equals to h c by lambda So when lambda you change energy will also change actually when white light passes through There will be interaction of electron and the photon of all those wavelengths Right, so it absorbs only those wavelength Corresponding to that if energy level is present in the atom Suppose corresponding to this energy level The atom electrons absorbs energy then this will jump to the next higher energy level Further it absorbs energy it will jump to the next higher energy level So electron absorbs only the those wavelength Corresponding to that the energy level is present within the atom. Are you getting it now? If suppose there is a wavelength that wavelength gives some amount of energy to this electron The electron will have certain amount of energy when it takes that particular wavelength Corresponding to that energy If the energy level is not present within an atom then the electron won't take That particular wavelength it will radiate that wavelength Completely did you get it? So why these electrons absorbs a particular wavelength because there are different different energy levels present within an atom It absorbs wavelength jumps to the next higher energy level When again absorbs jumps to the next higher energy level If that energy level is not present corresponding to the energy of the electron It won't take that particular wavelength Then you need to find out we need to find out n for that prudence n value if you find out, you know the orbit Yes, tell me in doubt So this is the spectrum we have Most of the light they passes through the atom Few wavelength it absorbs Because corresponding to that wavelength atom has energy level present Okay, now from this suppose it comes down here Then some wavelength it radiates Corresponding to this energy difference again comes down It again radiates some wavelength lambda 2 Again comes down Lambda 3 In this transition it radiates one wavelength In this transition it radiates one wavelength In this transition it radiates one wavelength lambda 1 lambda 2 lambda 3 No atom radiates energy When you when you heat it That's why you see an iron rod you heat it changes color continuously Right and finally it becomes blue Because it radiates Radiations when you heat it In anti-r2 you will study this the Planck theory that This phenomenon it is you know discussed over there When you keep on heating an iron atom it changes color continuously Because it is it is radiating energy No, we are talking about this You know the particle nature of electrons, okay? It's not like we are talking about general Objects or any other matter Okay, we are talking here about subatomic particles So it will have a very different kind of you know behavior towards heat And that is what we absorb. It's very simple example. I'm giving you you must see No, no when you heat an iron rod it changes color because it radiates energy continuously Frequency decreases Frequency decreases wavelength increases That's what the different frequency is coming out. No that that it is other way should this The question you are asking it is actually other way. It has been observed that That when we heat an iron rod This way only the color changes takes place first of all dull red Then red then it becomes white and then it becomes blue Right. So frequency continuous. Yes frequency continuously increasing. You see red to blue frequency increases continuously It means what the It means what the frequency that we are receiving when you heat the iron rod That frequency is increasing and hence we are you know observing this as blue or white or anything else Right. So this is the phenomenon we have We observe this phenomenon and then we explain this Okay, when we heat this frequency increases Maybe for different substances possible not for iron rod So it depends upon the energy levels of different different atoms based on the you know atom their electronic repulsion and everything What is the energy level is there based on that? It radiates energy. It radiates radiation And radiation will have certain wavelength certain frequency based on those wavelength and frequency We observe the light the color of the light. So with this experiment The hydrogen spectrum We get to know about That the atom contains energy level And that that is what the boards was talking about The post mix of boards was what? that atom present in an orbit And it neither absorbs not emits energy in that but if the electrons Absorbs energy it jumps to the higher energy level If it radiates energy it comes down to the lower energy level That's what he said Right, and this is what want to be correct when we have this spectrum Analysis when we did we we came to know this fact that within an atom there are energy levels present No, that's what aunts. You are not getting me You are giving energy But the electron is taking up that energy is not that is what the case is Again, you are taking it other way. I have given you this example of iron rod When iron rod changes its color It means it is radiating That freak how do we observe that color is red? Could you tell me that? How do we observe a particular color? Why we find this thing is red or this thing is blue? Because the same frequency we are we are receiving right aunts If you if you receive the frequency of red that color is appeared to be red If if you receive the frequency of blue that color is appeared to be blue Right now coming back to this question when like I take the example of iron rod when you heat it you you observe that there's a change in color From dull red to red red to white white to blue. This is what we observe so when we absorb When we observe it it means what it means it radiates different different frequency When you keep on heating it and then we have this conclusion So you are you are discussing something else You are discussing a general thing when we heat then we supply energy, but the atoms takes energy It is not like it does not radiate energy at that point of time It's not like you're giving energy and the atoms takes all the energy and sit back Right. I am telling you what I am trying to make you understand with an With an example with an example and that example is given in your book also Your doubt is how it is radiating energy Since we are providing it how this goes down to the lower energy level. I am telling you what we are heating it right and electron Gets the energy, but it it won't absorb it In that process it also radiates radiates radiation Right. So different different frequency goes out and when electron radiates frequency Correct. It will definitely come down To the lower energy level and that is what it is happening Okay, so while I am just concluding it what that within an atom there are energy level present electron absorbs or emits energy Depending upon in which energy level it is present And what amount of energy it is absorbing or radiating Right Now based on this only we can define the number of spectral lines Now we got to know about it that within an atom there are energy level present Okay, all of you write down the heading number of the spectral line Okay, so all these things that we have discussed till now today. This is for your understanding, right? The point or the concept that we are going to discuss now Right on this you will get questions Okay, obviously to understand this concept all these understanding require Okay. Now write down the heading number of spectral lines All of you draw this These are That various energy levels we have Like n is equals to one Then n is equals to two three four five six seven eight and nine Infinite energy levels such energy levels possible Right now electron can jump from higher to lower energy level like electron may come from This to this Right from this to this This is the transition of electrons This is the transition of electrons from this to lower energy level And this kind of transition is possible with here also So these are the transitions of electron From any higher orbit to lower orbit and it's equals to one then n is equals to two three four and so on Okay now when the electron jumps To All of you have to draw this. Okay, all of you From any higher orbit When electron jumps to n is equals to one Okay, obviously from here to here It will radiate one particular wavelength Five to one radiate one particular wavelength Four to this one particular wavelength and this then all these transitions will get Different different radiations, right? So we'll get a series of wavelength here And the series that we get here when n is equals to one final n value is one Is we call it as Lyman series lyman Lyman series When n is equals to two, this is barmer series This one is Pastion when n is equals to three it is pastion One mistake I have made here. I'll just correct it n is equals to three is pastion. This should be four Okay, so Lyman barmer pastion. This is Bracket and this one is fund This one is fun. So this is that various series that we get So the n value the final value of n is one for Lyman. Okay, nf is one This transition from any higher energy state to n is equals to one Barmer series when any higher transition state to n is equals to two Pastion is any higher transition state to n is equals to three and so on. Copy down this Let me know once you are done First one is Lyman second one is barmer third one is pastion p a s c h e n The third one is pastion p a s c h e n The fourth one is bracket br ac ke double t The fifth one is fund p f u and d p f u and d fund After this also, we have Humphrey series and all but not important. Okay Now Would you all of you agree with me on this then we'll get here a series of wavelength. Yes or no What is the n i value of Lyman series and i means the electron Present in the orbit initially that is n i n i value can be anything between from two to infinity. Yes or no for Lyman says i'm talking about Suppose nf i will write it as the final shell or the energy orbit in which the electron jumps third one is pastion p a s c h e n And fifth one is fund series p f u and d fund series okay So suppose it nf is the final orbit so for Lyman series. What is the value of n i possible value of n i n i for Lyman series could be anything from two to infinity. Yes or no Yes guys So we'll get a series of wavelength in this agreed We'll get a series of wavelength And hence we'll have a maximum value of wavelength And a minimum value of wavelength for each of these series So we need to know what is the maximum and minimum value we have here Right in terms of r we'll try to find out. I'll show you how We'll find out the maximum and minimum value of wavelength correct so One second guys. So I was talking about the wavelength, right? Okay So let us understand the general thing first of all here Obviously when the you know electron jump from one particular orbit to the lower energy orbit right, so if electrons jumps from This one To this orbit it comes down to the lower energy level To this orbit then obviously it radiates energy in this process, right? Suppose it is n i the final initial orbit And n f in which the electron jumps the final one. So in this process it emits radiations, right the radiations Of certain wavelength suppose lambda Okay, we can find out this delta e delta e is equals to what we can write We have at c by lambda. We know because lambda that comes out in this transition Right and delta e value. We know it is at c by lambda Is equals to we can write e f minus e i the final minus initial E f minus e i and this is only we have done in red bug Relation what is one by lambda is equals to r z square r h in fact here z square one by n f square Minus one by n i square Oh, it is full top One by n i square minus one by n f square because total energy is negative, right? So we'll write one by n i square minus one by n x just a second We'll get this Depending upon this value n f and n i we can find out maximum and minimum wavelength over here Right, so for hydrogen what we can write For hydrogen One by lambda the radiation that comes out is equals to r One by n f square minus one by n i square Correct this one we have So basically you can consider this As the formula of wavelength also wave number also when there's a transition between the two orbit n i and n f Correct We need to find out lambda max and lambda minimum for various series limel barmer pasture bracket fund using this formula Okay, now we are going to see this the first series we have that is lineman series Now here. I want you to interact That in lineman series, what is the value of n f? Could you tell me the final orbit? What is the value of n f here? One Is it always one? Is it always one? Yes, it is always one because lineman series is defined when the electron comes from to the first orbit Always one right that is one thing Could you tell me the value of n i? What is the possible value of n i the possible value of n i could be anything from To to infinity two three four five infinity Right that is a possible value of n i so we need to find out what is the value of n i So that this wavelength that comes out in the transition that becomes maximum or Minimum okay, so let us try and understand this how to find out the value of n i One by lambda is equals to r one by n f square Minus one by n i square This is the formula we have Okay, now for maximum wavelength You see what we need to do here for lambda max correct Maximum wavelength r is the constant n f is also only one we cannot change that we can change only n i so that lambda would be the maximum Okay for lambda max The value of n i we need to analyze here You see If n i is two that is the minimum value here Then one by this term would be the maximum And one by this term would be the maximum it means this term will be minimum This term will be minimum then one by lambda will be Minimum and one by lambda is minimum then lambda would be maximum So what we can say for lambda max n i should be Minimum so it is inverse relation lambda max n i should be minimum it means n i value is two and for lambda minimum n i value should be maximum and its value is infinity for lambda minimum Did you get this relation? Tell me Yes, what I said Nothing you have to memorize here. Okay when it is there to memorize I myself tell you that this point you have to memorize this But here you don't have to memorize anything Once you know this formula R is a constant n f value is also fixed you can change only n i So we have to change n i so that this would be maximum or minimum Right, so you see if lambda is minimum we are taking that is two If n i is two here not lambda n i is two we are taking since it is minimum So one by n i square would be maximum Hence we are subtracting a maximum value in one by n f square So when we subtract a maximum value this term will be the minimum since we are subtracting the maximum one so this is minimum It means one by lambda is minimum one by lambda is minimum means what lambda is maximum for lambda max n i should be minimum For lambda minimum n i should be maximum. How many of you understood this clr? You can type if you got it Correct. Now nothing you have to do once you know this thing that lambda max n i minimum lambda minimum n i max You just need to substitute and find out lambda in terms of r. So could you tell me what is the value of uh, if I write down one by Lambda max here for example, this is equals to r you let it be as it is One by n f square n f square is one square n i square. We know n i value is two So two square. So one by lambda max Is equals to three r by four So lambda max is equals to four by three r These kinds of questions you will be getting Gourman you are getting this only The question that you were asking similarly for one by lambda minimum this would be what r into One by one is square minus one by infinity square that would be zero only the lambda minimum is equals to one by r Do you see I have already told you that in this series will get a series of wavelength maximum and minimum so wavelength Falls in which range here Less than equals to the maximum value is four by three r And this wavelength It falls in this range one by r When you substitute the value of r here, this is important When you substitute the value of r here, you will get a definite range of wavelength And that wavelength falls in ultraviolet reason This question also they have asked many times That balmer or lineman series falls in which region So it is ultraviolet reason very important must remember it Any doubt in this tell me any doubt Now I want you to respond here the second one is balmer series Tell me the value of nf value of nf2 value of ni Could be anything from three to infinity, right? so three four five and so on so for lambda max What is the value of ni? What is the value of ni three? for lambda minimum What is the value of nf? Sorry ni infinity Okay, so these two value we can substitute in the relation and we can find out the lambda. Could you tell me the series the range here for the lambda? quickly The value of lambda it falls in this range less than equal to 36 by Five r and greater equal to Four by r here and this wavelength If you substitute the value of r this wavelength falls in visible reason This is the only series that we could see Okay, others we cannot see past tense it is nf value is three Ni value could be anything four five six seven and so on and you know of lambda max and lambda minimum and for this lambda max value i'll write down here lambda max for pastion is 144 by seven r and lambda minimum For pastion is nine by r And this wavelength here it falls in infrared reason Okay, so this reason you must remember it is infrared next write down bracket bracket series bracket series also falls in infrared reason infrared reason Okay, so nf is is four here Ni could be anything from five to infinity Okay, lambda max lambda minimum you can find out here fund series nf is five Ni anything from six to infinity Okay, this also falls in infrared reason So first one is uv second one is visible third fourth fifth in product done finished Okay Now the next one we have to understand the last part of this particular discussion is the number of spectral lines What is the number of spectral lines? Let us understand this with an example Suppose an electron jumps from fourth to first orbit What are the various possible ways we have over here? means By how many how many ways electrons from fourth comes down to one? Okay, that is what we need to find out and the number of possible ways is the number of spectral lines that we get So one of the possible ways is what one of the possible way is First electron from four it will come to three Then from three it will come to two And then from two it will come to one This is one possibilities Another one is what from fourth one it directly jumps to two And then it may come from two to one Okay, or another possibility is what it jumps from four to one directly Okay, so like this how many possibilities we have three plus two plus One that is there are six different ways different ways By which electron can make this transition hence the number of spectral lines is six Yes, should you tell me fifth one is also infrared or the first one is ultraviolet Second one is visible last three is intra infrared Four to three and three to one we have discussed it This is the way we have Four to three and three to one that way also you can go No, see one possibility is this We can jump from four to three Three to two two to one Three to one if you consider Right three to one if you consider that includes this and this also here One thing you have to understand here That from the initial orbit it may jump to any lower bit Right from here it may jump to any lower bit But after that you have to make the transition one by one you cannot make it from three to one directly From three it will come down to two and then from two it come down to one But initial jump is anything it can jump directly from four to one four to two and four to three Yes, so lower one we have to follow one by one one step and then the second step and then the third one Right So this is how we can find out the number of spectral lines, but I won't suggest you to go by this way Okay There's a formula for this the best way is to use that formula Write down the number of spectral lines produced in this case only suppose if I am considering Is equals to We get ni minus nf into Ni minus nf plus one Divided by two This is the formula you use you'll get the answer So for this one also you see ni value is four nf value is one Answer is Plus we use this formula and we get the answer then Yes, that is what we are getting to this Now till here it it is a bit, you know difficult to understand things because there are so many experiments And we were using the result of those experiments of classical physics Now from here on what we have done with the the difficult part of this chapter difficult not in the sense of you know Solving questions, but again to understand those things all those basics You know Experiments which has been done in order to understand the property Those things is a bit difficult to understand But in terms of solving questions, it is not that difficult But now from here onwards it is you know easier than the things that we have discussed later Right previously Now the next thing you need to understand here Is the dual nature of Matter, okay, we have already discussed it One more thing we'll see here That is D Broggy hypothesis D Broggy Hypothesis So D Broggy is the name of the scientist He also suggested that That all the molecules all the object contains wave property with it, okay particle as well as wave properties That's why this we also call it as Dual nature of matter matter the hypothesis Explains the dual nature of Matter this explains the dual nature of matter Write down in this Write down in 1924 D Broggy in 1924 D Broggy proposed that D Broggy proposed that That all microscopic material All microscopic material particles In motion All microscopic material particles In motion Dual characters Dual characters That is That is That is the wave properties That is the wave properties as well as The particle properties So what he suggested Louis D Broggy the name of the scientist He suggested that any particle Okay, any particle in motion Consists of wave nature means Puzzles wave nature with it Okay And when the particle has wave characteristics Then there must be some wavelength Of that particular wave Which is associated with the object Right So what is that wavelength? Okay, write down next time According to him According to him The wavelength associated with the particle of mass m According to him The wavelength associated with A particle of mass m Moving with the velocity v Is given by Is given by Lambda is equals to H by p Where p is the momentum And h is again the plane constant Any mass m moving with the velocity v the momentum is what could you tell me? Any mass m moving with the velocity v. What is the momentum mv? H by mv Okay This we can derive with the help of Planck's theory and Einstein equation. Okay, so you see here first of all the formula of lambda we get lambda is equals to H by mv that is what we are going to use to solve the question Okay, but how did he get this? According to Planck's theory what we can write we have e is equals to h nu or hc by lambda Okay, c is the velocity now Einstein mass energy Equation that is e is equals to mc square If we equate the two we'll get mc square is equals to hc by lambda This is wave property. This is Particle nature mc square. So since the molecule contains both so we can equate energy for both. So we get lambda is equals to h by mc c is the light of speed of light right velocity of light For any other molecules any of the object we can write velocity as mv And this is the wavelength associated with any mass of any mass m moving with the velocity b See, I said what first of all, this is the formula of wavelength associated with any object of mass m moving with the velocity b Now we know the relation of Planck e is equals to hc by lambda And we know Einstein mass equation mass energy equation here Is e is equals to mc square. So this is the wave characteristics lambda wavelength associated with it Energy is this and energy of a particle is also mc square e is equals to mc square So these two energy term we can equate Because he suggested what that the any particle consists both wave as well as Particle nature with it. So even you equate it becomes mc square is equals to hc by lambda And when you solve this for lambda is equals to you get h by mc For any object of mass m with velocity v we can write lambda is equals to h by mv Okay Now the basic formula is this only but we can represent this in two different forms and those forms are also important Okay, see the formula that we get here what lambda is equals to h by mv So could you write down this lambda in terms of kinetic energy? What is kinetic energy? This is the first formula If any object of mass m velocity v Right moving with the velocity v then the kinetic energy k is equals to half mv square So what is mv from this? Both you multiply by m and then to you multiply this as mv is equals to 2 mk. So hence wavelength lambda is equals to what? H by root under of 2 mk where k is the kinetic energy. You must remember this Okay, this k is the kinetic energy This is also kinetic energy, correct? One more formula we can also write here That is we know this thing if any charged particle charged particle q moving under A potential difference v Then the kinetic energy of charged particle is q times v the potential difference And this kinetic energy if you substitute here in this equation The lambda for any charged particle we have h by 2 mq times into v Where this v is the This v is the potential difference Potential difference not velocity. Did you understand all the three formula? Any one of these three formula you can use to solve the question depending upon the data given What happened auto? Yeah, I understood that but what happened so especially in the school today Because every day you will have this thing. No, uh The school glasses and all Okay, tell me when you want the break you want the break now Okay, so tell me tell me all of you just give me a suggestion. What time we should have start 6 15 Okay, auto is asking me 25 minutes. I can't give to go. I can go maximum for 20 minutes Okay, so auto is asking for a longer break. So guys, we'll do one thing. I can you know Start at 6 20. Is it fine with all of you? Five minutes more I can consider Okay, fine. Fine. Take a break now. Okay. Take some rest. I can understand The school thing and all okay, so we'll resume the session at 6 20 Fine. Okay. Take a break Hello Yeah, guys, can you hear me? Okay, anyone has joined just now This class Yes No, not Akhil sir. I think one. Yeah, sanjana, right This is the first class sanjana. Okay. So just now you have joined. No, you are not there before the break Okay, fine. So sanjana. We are doing uh atomic structure, right? So you have missed You know a few things So probably it will be you know difficult for you to you know, go align with the glass now But uh, don't worry like uh, you know, you try to Understand it whatever we are doing it now But definitely we'll share the recording and then you can watch the recording whenever you get time And then you can get back to me if in case of any doubt, okay. Yeah So, yeah, so we have discussed, uh, you know, a few things that is deep rocky wavelength We have discussed lambda is equals to h by mb is the formula and these two formula also we have discussed. Okay Now one more thing we'll discuss here and then we'll see the questions Based on it Now you see, uh from this deep rocky wavelength. We can prove one of the postulates of board model Okay, what is that I'll show you What happens that it suggests that electron moves, uh, you know Uh In a path and it consists of wave properties with it but it so Suppose the electron is moving in a path. This is a circular path Of the electron right And since it contains wave properties with it Along electron is moving along this path. Okay in the circular path And since it contains wave properties So there is wave also associated with this with this one with this electron this We also the wave is also moving this way. This is the second The other wave associated with it. Okay. Now in this one complete rotation, this circumference what I am assuming I am assuming there are n wave Creates in one complete, you know rotation, right? So write down this Consider an electron Is moving in in a circular path Nothing. Nothing. We are doing deep rocky only just continuation of that Consider an electron is moving in a circular path off radius r off radius r and In one complete rotation in one complete rotation n number of waves creates Like this meaning what? From this point to this point, you see here if you try to understand I have just you know I had already explained you how we define a wave here So from this point to this point, you see we have one wave, right? This distance is one wavelength from this point to this point Now from this point to this point you have another wave Right, then we have another wave another wave another wave. So basically we have n number of waves creates in this That's what I am assuming So what is the circumference its radius is r. I am assuming. So what is the circumference for this? It is 2 pi r Circumference is 2 pi r and since n waves creates over here So in terms of wavelength if I write down the circumference it is n times into lambda How many of you understood this n wave creates 2 pi r is the circumference Why? It's simple. Let's see what I said n waves creates, right? So from this point to this point one wavelength Then this point to this point another wavelength This point to this point another wavelength and so on we can go There are n number of waves we have here till this point Okay, so since n wave over here we have so length of this path is what n times into lambda And n times into lambda is what the circumference of this path 2 pi r and we know lambda is equals to just now we have seen the formula and H by m into V, right Lambda is equals to H by mv Okay, now when you solve this you'll get if you cross multiply this and solve you'll get m v r Is equals to n H by Could you tell me where we have discussed this? Where have we discussed this particular relation m v r is equals to n h by 2 pi? That is the board postulate Right board postulate that is m v r is equals to n h by 2 pi So board has given this relation But there was no any proof Okay, he observed it He has done some experiment and observed this and based on his calculation The angular momentum should be equals to n h by 2 pi that is what he said But there were no any mathematical derivation of it So after de Broglie hypothesis when we have this information that particle contains dual nature Okay, after that we can be you know, we will be able to derive be I know we derive this particular relation which again confirms Which again confirms the you know the Confirms that that the postulates of board's atomic model was actually Okay, so this was the mathematical derivation of it Understood this Okay, now after this one more thing what happens here that if we try to Find out The position of an electron in this orbit Right Since the electron possess Wave characteristics also It's very difficult to find out the position and The momentum of an electron simultaneously Since it contains Wave property if you try to find out position its momentum will be changed If you try to find out momentum its position is changed So both the term we cannot find out simultaneously Right both the term we cannot find out simultaneously because it contains wave characteristics So write down one point here Since the electron contains Oh, just a second. Let's write down the point. I'll explain since the electron contains wave nature Since the electron contains wave nature Then the exact position and momentum of an electron then the exact position and momentum of electron The exact position and momentum of electron We cannot find out simultaneously So this is one thing now. We'll discuss this just a second. We'll discuss this but this point actually comes when we get the wave nature of no and microscopic particles like electron And this is observed by or given by a scientist called hyzenberg Okay, and the principle of this which gives this fact There's just now I've told you is to call it as hyzenberg Uncertainty principle So write down this and then I'll discuss what is the meaning of this one. Okay, write down hyzenberg's Uncertainty principle statement you write down statement According to hyzenberg uncertainty principle according to hyzenberg's uncertainty principle It is impossible to measure It is impossible to measure It is impossible to measure the exact position and exact momentum The exact position and exact momentum of a moving microscopic particle In brackety write down electrons It is impossible to measure the exact position and exact momentum of a moving microscopic particles like electrons Next line, the Heisenberg uncertainty principle may be expressed as delta x into delta p greater equal to h by 4 pi. So Heisenberg also has done its research and he suggested that, okay fine, exact position and exact momentum we cannot find out, but the uncertainty in position delta x and uncertainty in momentum delta p follows this relation, delta x is the uncertainty in position and delta p is the uncertainty in momentum. So delta p we can further write it as m times delta v because mass is the constant. So delta p we can also write in terms of mass and delta v where this delta v is the uncertainty in velocity, uncertainty in velocity. So if I substitute this here then the expression becomes delta x into delta v greater equal than 2 h by 4 pi m, m is the mass here. So this is the relation of Heisenberg uncertainty principle, we have copied this down first, okay, copied, done, okay. Now let us try and understand this. Now suppose an electron is moving in a path, okay circular path, suppose at some point the electron is present over here at this position, which we cannot find out, okay simultaneously position and momentum of it and this is the nucleus. Now to find out the position what we do, we will just try to, we will use a radiation here and we use the radiation in order to like we strike this radiation over here, okay, suppose this is the radiation we have, so this radiation is the incident photon suppose I am using in order to find out new in I write down, some frequency we are using so that it will go here, it strikes with this electron and when it, when it reflects back, okay when it reflects back then here I will use a microscope so that it can absorb the reflecting photon, reflecting photon and then we can find out the position of it, okay at this position it is present. This is the method we use, okay and generally what happens, we use high frequency for this purpose so that the wavelength is small and we can receive it easily, okay high frequency we use so wavelength is small, so what happens if you try and try to find out the position of it will incident a high frequency light on this, it reflects back, it receive it and we can understand, but in this process what happens the moment you take low wavelength means high frequency and when it strikes at it, okay reflects back, the moment you receive it by that moment you receive it and try to find out the position of it, it changes its position, it goes to the another position because high frequency means what, high energy so wavelength is fine, small, but frequency is very high over here, all these energy of photon it takes and it changes its position, right, so the moment you receive this and find out the position of it, at that time the electron is not present over here, means if you try to find out the position of it, it has changed its position because of the radiation we are imparting, correct because the whole of this energy of photon transferred to the electron and hence it change its position, if you want to determine momentum then radiation if you will use a larger wavelength, larger wavelength means what, larger wavelength means small energy, right, so you can find out, we can find out the momentum but we won't be able to find out the position at that point of time, that's why it's difficult to find out the exact position and momentum both of the electron simultaneously at a point, right, exact relation we cannot find out, value we cannot find out but the uncertainty in position and uncertainty in momentum, it follows this relation and this is Heisenberg uncertainty got it, hello, am I audible, see what I said, if you try to find out the position of it, correct, at this point of time it has c, at this point of time to a certain velocity to certain momentum but the moment you try to find out the position of this with the help of this photon and this microscope, okay, you are imparting energy into this electron, right, so the momentum also you are changing because it takes energy, it goes out and its velocity changes hence its momentum is changing, so in order to find out the position you are changing the momentum and hence that also you are not finding out because you are not able to find out because when it takes energy it moves to the other position by the time you take this, you know, you receive this reflected photon and try to find out the position of it, correct, so that's what I said, we usually take a radiation, a lower wavelength radiation to find out the position but in that way we are providing energy to the electron and hence electron changes its position and momentum, right, hence it is difficult to find out the both thing at the same point, did you get it, position means in the orbit in which orbit the electron is present, what would be the possible distance from the nucleus that is the position, yes, so what happens here now you listen to me all of you, yes, yes, yes, I am coming to that point, now all of you listen to me very carefully, now Heisenberg what he said, he said that the exact position and momentum of an electron, any microscopic particle we cannot find out simultaneously but according to Bohr if you see he has already given the radius, velocity, once you have velocity you will have momentum and you will have the radius but according to Bohr it is possible to find out the, you know, we know the exact position and momentum of an electron, again here is a contradiction, right, so that's why later on the entire concept get, you know, got changed after this when Heisenberg uncertainty principle comes into the picture, right, Bohr's was saying that we have orbit in the orbit the electron is present, radius of the orbit is this, velocity of the electron is this and we can find out the momentum of the electron that is MV, all these things were known but when Heisenberg uncertainty principle comes into the picture then all these concept has become, has got changed now, right, because one of the thing is the contradictory of the other one, right, so after this what happens when Heisenberg uncertainty principle comes into the picture which says that we cannot find out the exact position and momentum of an electron with accuracy simultaneously then a new concept of finding an electron, you know, that is introduced and that concept is based on the probability of finding an electron, okay, around the nucleus and this three-dimensional space where the probability of finding an electron is maximum is called orbital, so after this Heisenberg uncertainty principle we came to this conclusion that there is nothing called orbit within an atom but it is orbital which is present, right, the difference between orbit and orbital is in orbit the position of the electron is known, right, its shape is circular, right, but it is not for orbital, orbital shape may or may not be circular means the path that the electron follows may or may not be circular, correct and in this the exact position is not known, okay, we can have anything in the orbital, so I am not going into this orbital part, now let us discuss some questions based on these two miracles but I'm just trying to relate all these things so that when we start orbital you can connect with it, what I said that Heisenberg uncertainty principle it says that exact position and momentum of an electron we cannot find out, okay, simultaneously and he has given this relation that uncertainty in position and momentum is this and it follows this relation, right, but what happens after this? Whatever you know the work Bohr has done now there is a question there was a question on his attempt that he made to explain the atomic model according to Bohr's we know the exact path of an electron because we know the radius at this distance in the circular path the electron is moving according to him, so we know the exact path of the electron we know the radius of that particular path that is the circular path orbit, okay, we know velocity of electron in that particular orbit and we know the momentum kinetic energy of the electrons also in those orbits, correct, but that has changed now because says that the exact position and momentum we cannot find so after this we started looking for a three-dimensional space where the probability of finding an electron is maximum and this three-dimensional space is known as orbital, did you get it? Yes, okay, now this orbital part we'll discuss it later, okay, we'll see this later, let us discuss some questions based on the concept we have discussed today, correct, so try question number 55, question number 55, okay, aura is getting C, is it C, shittish is getting D, arab is getting B, who is getting A? I think I get all the four options yes, rubab is getting A, so I got all four, A, B, C, D, aria got B, sanjana got D, yes, so those who got B, B is the correct answer I guess here, okay, so look at the question, the difference between the incident energy and threshold energy of an electron to the effect experiment is five electron volt, correct, so what is given? In the question it is given, question number 55, difference between the incident energy so h nu in minus h nu naught it is given and that is five electron volt, correct, the de Broglie wavelength of the electrons, obviously the kinetic energy k max is given for the electron that is five electron volt k is given so lambda is equals to what? h by root under 2 mk, we have discussed this formula, lambda in terms of kinetic energy so that would be 6.6 into 10 to the power minus 34 divided by 2 into the mass of electron we know 9.1 into 10 to the power minus 31 into kinetic energy is 5 but we need to put this in joule, right, so 1.6 into 10 to the power 19 this is what we get, root over of it, okay, now when you solve this it is 40, 20 to the power minus 9, correct, so answer would be 6.6 into 10 to the power minus 9 and these things will be here as it is 2 into 9.1 into 5 into 1.6 so 1.6 into 5 is 8, 8 into 2 is 16, 16 into 9 is 144 something, okay, it's 144 something you're getting the closest option is 145.6, option b is correct, yes, could you tell me question number 57, no it's not, yeah you can do 58 also, you can try, in fact you can try 57 to 60, all four you can try, okay, I'll discuss 57th one first, 57, all of you see I think all of you have got the wrong one, wrong answer here, 57 the correct answer is c here, why c because it is asking for de Broglie wavelength, de Broglie wavelength lambda is equals to we can write h by mv, right, so lambda and mass is inversely proportional here you see, so for heavier object obviously the wavelength we don't observe because it is inversely proportional, right, that's why the particle which has maximum mass has least wavelength, electron obviously we have the minimum mass over here 10 to the power minus 31 proton 10 to the power minus 27 more than that of electron, alpha particle has the maximum mass over here, that's why the wavelength for alpha particle is minimum, alpha particle is minimum, okay, so this is the 57th one 58th one, what is the answer for 58th one, an electron of mass m and charge e is accelerated from rest through a potential difference v, the kinetic energy, we know the kinetic energy is what q into v, when the charge q moving across a potential difference v, the kinetic energy is qv, so it is e into v, so 58th one is v, okay 59th one, if the uncertainty in position of an electron is zero, means delta x, uncertainty in position delta x is zero, then the uncertainty in momentum of the electron is 59th one, if it is zero then delta p is what, infinity, okay delta x, what is the relation we have here, delta x into delta p greater equal to h by 4 pi, so this is zero, this must be infinity, okay, that's why you see uncertainty in position, if you make it zero then this becomes so uncertain, it becomes infinity, correct, that's why the both think position and momentum we cannot find out simultaneously, okay, six zero question number 16, what is the answer, so lambda d Broggy wavelength is h divided by 2 mk root over of it and that would be just to substitute all the value, question number 60, the answer will be option b here you'll get, okay, h is 6.626, 10 to the power minus 34 divided by 2 into 9.1, 10 to the power minus 31, kinetic energy is 4.55, 10 to the power minus 25 root over of it, little bit of calculation you will have in this chapter, okay, answer you will get 7.28, 10 to the power minus 7 meter, always take care of unit in this kind of questions, okay, try this question, finish all four then we'll start discussing, yes, correct, mg is milligram, you can use calculator if you want, yeah it is sino, so keep it in 2 kz, finished, okay, question number 66, the d Broggy wavelength 1 milligram grain of sand blown by 20 meter per second wind is, so lambda we need to find out, lambda is equals to h by mb, everything is given 6.626, 10 to the power minus 34 divided by the mass is 10 to the power 1 milligram, 10 to the power minus 6 and velocity is 20, you solve this you'll get the answer, okay, you can also do one thing for, you know, to solve the question you see the options if you see, in option it is given 3.3, 3.3 everywhere, correct, so for this one it is easily understandable, you can understand this, that you can take approximation here and instead of 6.626, you can take 6.6 to solve this question, this approximation you can make, depending upon the question, right, so it is 3.3 into 10 to the power minus 29 meter, right, so answer is option A, certainty in position and momentum are equal, so delta x equals to delta p, uncertainty in velocity, fine, so we can write m delta v here, so delta v we need to find out, it is delta x by m, so we can write down the uncertainty, Heisenberg uncertainty principle, delta x into delta v is equals to h by 4 pi m, you can substitute v in terms of x, sorry we need to find out velocity, fine, so delta x is m delta v square is equals to h by, what is the option here then? Yeah, yeah, that's fine, can do it easily, answer is option D here, calculate the wavelength of a track, track star running 150 meter dash in 12.1 second if the weight is this, so what do we do here, again we use the same formula, 68th one, oh yeah, this two will come out option B, correct, yeah, it's option B, yeah, yeah, same thing, so 68 is what lambda we need to write down, h by mv, again same formula, you can substitute all the values here and find out lambda, okay, answer for this one is 68th one, what is the answer you are getting, the answer given is option D, is it D, 68th one, 68th one, what is the answer you got, D, okay, D as in Delhi, okay, yeah, the last one question number 69, the uncertainty in locating of circulating electron is equals to its de Broglie wavelength, okay, so in the question it is given delta x equals to lambda equals to h by mv, given in the question, right, the minimum percentage error in its measurement of velocity under this circumstances with approximately, so what is the question, we need to find out percentage error, means delta v by v into 100 is equals to what, this is what the question we have, okay, so delta v by v, could we write down this as, could we write down this as delta p by p into 100, same thing, uncertainty in position is equals to, sorry, uncertainty in velocity is equals to the uncertainty in momentum, we can write this, okay, so we have the relation into delta p is equals to h by mv, what can we do after this, we need to find out delta p by p into 100, so we need to have this expression, right, one correction here, h by 4 pi, right, h by 4 pi, fine, so this delta x we can write h by p, mv is nothing but p, so delta x is h by p into delta p is equals to h by 4 pi, h and h gets cancelled, so delta p by p is equals to 1 by 4 into 22 into 7 and since percentage error we need to find out, so into 100 into 100, now this would be 88, 100 by 88 is 1 point something, so you will get around 8 approximately, right, so around 8 approximately 8 you will get, yeah that's the option we have here, so approximately 8 is the percentage error here we have, clear, no doubt in this, in this you don't have to solve all because there are a lot of calculations in this, so I want you to solve first of all 47 and 48, 47 and 48, it is not j-level, there's a basic level question we have, you can have it in, j means you can say, sometimes they ask in j means, but on these topics you will have this kind of question only, okay because only one thing is there, that is what you need to apply, but for j-advanced level I will share the PDFs with you after the session, question number 47, yeah that's right, which transition in the hydrogen spectrum have the same wavelength as Balmer transition in this of HE plus, okay, so for HE plus we can write 1 by lambda is equals to z square divided by into 1 by from n4 to 2, so nf square minus 1 by ni square, so nf is 2 and z value is what, z value is 2 here because it is helium, so r into 2 square 1 by 2 square minus 1 by 4 square, so when you solve this what is the value you're getting here, in terms of r could you tell me, is it 4, is it 3r by 4, okay 3r by 4, so 1 by lambda is this, now you see for the same wavelength okay, so for HE plus sorry for hydrogen what we can write 1 by lambda is equals to r 1 square right, so this is 3r by 4, so what we are getting on the left hand side, we are getting 3 by 4, 1 by nf square minus 1 by ni square, okay, just you need to check with the option which option gives you this, okay, so I think nf is 1 and 2, 4 and 3, yeah, I think option a is the correct one here, after this you can put these values and check, option a is correct for the 47th one, okay, 48th one, how do we do 48th one, the number of spectral lines can be possible when electrons in the sixth shell in hydrogen atom return to the second shell, so ni is 6, sorry ni is 6 minus 2, 6 minus 2 plus 1 divided by 2, is it 15, oh 10 no, 4 by 2 it is 2 into 5 10, we can take it right, okay, answer is option d for this one, so all these things you need you see here, it's difficult to understand those concepts, if you see each and everything how we are getting norm of the concept and the formula here, little bit difficult to understand, but as far as the question is concerned, they ask very direct question in the exam, I'm again telling you it is not for J advance but for J means you can expect this kind of questions, okay, and other exams, okay, now could you solve this 51 and 52, 51 and 52, wave number is 1 by lambda, I have done this, you check your notes, nu, wave 1 nu bar is 1 by lambda, wave number is the number of wave produced per unit distance, then that's not right Shruti's I guess, check your calculation, no it's not, okay I'll do this right, yeah that is correct Shruti's, b is correct, 51, 51st one is b, b as in Bangalore, the wave number of a spectral line is this, so what is given, 1 by lambda is wave number is given, that is 5 into 10 to the power of 5 meter inverse, you see if you do not know this, suppose if you forgot what is wave number, then unit gives you the information, it is meter inverse right, so it must be 1 by lambda, so unit always plays a very key role in these multiple choice questions, the energy corresponding to this line, easy, e is equals to what, h c by lambda, 1 by lambda is given, all value is substituted, 6.6 into 10 to the power minus 34, 3 into 10 to the power 8 divided by 5 into 10 to the power 5, okay, so 1.3 approximately, so 4 into 10 to the power 31 approximately, so 3.39, so 51, oh yes correct, because we are 1 by lambda right, that's why I was thinking, I was not getting the answer, so 5 into 10 to the power of 5, okay, so this approximation you can take 6.6, always keep that in mind, so 5 into 3 is 15, or this into this is 33. something right, 3.3, 3.3 into 3, 9.3, 8 into 8 plus 5 is 13 by this, so we will be getting see 9. something, so option B we are getting 9.93 into minus 23 kilo joule, for this one the answer is B, 52 what is the answer, if the wavelength of first line of Bama series, what is the first line, what do you mean by this first line? Bama series, could you tell me what is the value of NF, NF value is 2, right, Ni value is what, it could be anything from 3 to infinity, but since it is first line, it means Ni value is 3, just above it, the lowest possible value, right, so when you solve this, we will get 1 by lambda is equals to R of hydrogen, so 1 square, 1 by 4 minus 1 by 9, so lambda is equals to 36 by 4 R, so R is equals to 4 into lambda, lambda is given, it is a nanometer, so let it be, you can keep this in nanometer also and last you can change because the answer is given in nanometer only, so I will write down this as it is 4 lambda by 36, this R will substitute in the other equation which is second line of this series, so 1 by lambda nu is equals to R, 1 square, 1 by NF is 4 and this one is 16, just you need to solve this, substitute the value of R and you will get the wavelength, the answer given is options C that is 486 nanometer, answer given for this one is C, okay, so here you see the R value that I have given you 109678, this value you don't have to memorize at all, you have to write down in terms of R only, like in this question you see the lambda is given, so we will find out R in terms of lambda and then we can substitute it here and we will get the answer, options C is correct, okay, fine, did you get it, fine, okay, so we will start from this next class, okay, so we have covered 70% of the portion, fine, I will share the assignment BTF with you on the group, you can try that, Shalini, can you hear me, are you there, oh sorry, Sanjana, are you there in the group, Sanjana, what's that group, you have recently joined, today only you have joined, okay, so you don't have the other videos, right, so what you do, you just ping me, okay, I am there in the, okay, you can ping me, I will send you the videos, the two, three videos that we have done on this chapter, separately I will send you personally, you can, you know, finish those videos so that you will have an idea that what is going on, okay, in case of any doubt, you can get in touch with me, anytime, okay guys, thank you, bye, thank you.