 Good evening students. How are we doing? Good evening. All good? Yes We'll continue from where we stopped last class. Oh, just a second. Just a second, guys So I think we have finished last class. We have finished Boards model, right? We have seen few questions also on this correct DPP solution stairs since I didn't share it on the group you check. No The DPP there is given. No, just below that only there is a solution of PDF It's there only. Could you check now? Tell me stairs No, no, no in that solution for all that DPP the solution was given You can check you scroll down. You'll get it. Okay, even for the coming classes Yeah, even for the coming classes that the DPP I'll share the solution is that in that folder only in that PDF only So solution I have shared once okay, it is for all that DPP that we are going to share in the coming classes Okay Yeah So guys last class last class we have discussed both atomic model very important, you know Automic model we have and from this you will definitely going to get the questions Okay, that's good if you resist the book today. Okay, fine So, what have we discussed a quick recap of it so that we can you know Understand just know to continue from the boss model. Yeah, yeah, I think at Balmer series and all we'll do it today Okay, we'll do it today. Then you can again attempt those questions. Okay. Yes, we'll discuss it today. Just a second Yes, yes, yes, we'll discuss it today Spectrum Correct. So what have we discussed? We have discussed that board atomic model board suggest That you know, there are energy levels present within an atom Okay, there are energy level presents within an atom and Electron resides in this energy level this energy level We call it as orbit, right? There are infinite number of orbit that we have discussed last class Okay, infinite number of orbits present like this Okay, so a nucleus Right, and these are the orbits one two three four KLM and infinite number of orbits correct and We have also discussed these energy levels has certain amount of energy and that energy if I write down in any orbit suppose nth orbit the Energy is given by the formula we have seen in that formula is negative of Two pi square z square e to the power four Me Divided by n square h square. This is a formula of energy You see this energy e is directly proportional to Z squared by n square and this is what we have discussed last class now two three, you know, um Conclusion of this board atomic model the first one important also write down if you look at the energy as You go away from the nucleus right, so as we go away from the nucleus The energy means total energy total energy increases Total energy increases, right? You see this for an atom This z value will be the same But as you go away from the nucleus n is increasing and total energy is negative Overall the energy is increasing over here because n is increasing Correct. So energy increases. So what we can say even the energy in the first orbit is Lesson than the energy in the second orbit then third fourth and so on correct point or the orbit where the energy of the electron becomes zero at That point of time the electron is said to be Said not to be the part of that Okay, so write down the next point here at infinity infinity the total energy of an electron energy of an electron E equals to zero and And the electron electron is No longer no longer the part of an No longer the part of an Yes, yes, you can say that when you take the electron out of an atom the atom is called to the ionized Yeah, this is one point. Now the second point is If you look at the difference in the energy E2-E1 this energy is found to be this difference is found to be more than E3-E2 Then E4-E3 and so on the consecutive difference in energy Decreases as we go away from the no the total energy is negative Himanshu So when it increases it becomes less and less negative Hence more value will be more. This is the two points. You must know take care Now you see since we know there are energy levels present so if you find out the change in the energy delta E, okay So write down the calculation of of Difference in energy or energy difference But these parts was mathematical. Okay, it is all about mathematics here. There's nothing no like carry or I know any No logic or information that you should have extra to understand just mathematics, okay So we need to find out the difference in energy and we know the energy in one particular orbit So delta E will subtract and we'll find out. Okay, so suppose the transition of electron Right suppose the transition of electron takes place. I'll write down here. I am assuming the transition of electron from Ni2 just a second electron from Ni2 NF Ni stands for initial orbit and if is for final, right? So we have NF is greater than and I we are assuming means higher energy level the electron is jumping Right, so the electron is jumping into higher energy level. So the difference in energy here. You see so delta E Delta E is Like energy in the final orbit EF minus EI correct EF minus EI Final orbit the energy in the final orbit that is corresponding to NF Corresponding to Ni and we know the formula of E just now. I have written over there. Okay, you see this one more thing I'll just show you here This formula I have written right this formula we are going to use where N is the difference here all these things are same And what happens suppose if the energy if the electron Goes from lower to higher energy level just for an example. Suppose the electron jumps from here to here Second right from the first orbit to any higher orbit like this if it jumps So, we know there's an energy difference. So it takes energy from outside and jump to the higher energy level electrons were here and Was here and it is now in this orbit the next higher energy All right So this difference in energy this difference in energy is delta E. That is what we are calculating Difference in the energy of these two orbit orbit, sorry This difference is delta E and that is equals to EF minus EI Okay, now suppose in the next step what happens this electron Comes back again to the lower energy level this energy it jumps from high to low Then obviously this amount of energy it has to release then only it has to it will come to this energy level right so in this process what happens it radiates some radiation it emits some radiation of Some particular wavelength obviously when radiation comes out will have a particular wavelength of this radiation and Corresponding to this wavelength will have the energy in that energy is at C by lambda Corresponding to this wavelength right and this energy difference. We know this energy difference is delta E So delta E is equals to at C by lambda when the electron jumps to high to low energy level Radiations comes out energy comes out in the form of radiation and corresponding to that wavelength will have the energy that energies delta E at C by lambda So this is the energy emits or absorbs both way you can see the same amount of energy It has to absorb and then it will jump to this level the same amount of energy It has to release and comes down to the original energy state Correct. That also we can use another not an issue. We can use that Okay, I'm just trying to get one expression over here. That's why I'm using this formula You can use that also. That's not an issue valid. Okay Delta E is what you see I'll show you What is delta EF minus EI? EF is more than EI Right if you take the negative side Delta E is what minus negative of something minus one is plus negative of something magnitude-wide if you see Magnitude-wise if you see the energy decreases Overall energy increases because it is negative. No, it's not Look at the expression last class. We have derived for total for change in energy Delta E will be positive No energy increases. That's what I have given you the first point so a bit over here You'll get minus EF minus minus EI So if EF is greater than shouldn't it be negative delta E should be negative Magnitude is less see you're not getting it one and two fine So magnitude if you see mod of E1 Mod of E1 is greater than mod of E2 magnitude is this but since the total energy is negative It is negative. So if you see the negative see the energy here, which includes the sign Then it will be even is less than E2 Because it is negative So suppose if I take this example see this one E is equals to what formula we can write minus 13.6 Z square by n square electron volt per atom correct Now when n increases then this entire value decreases or increases We'll do the question also wait increase if n increases Then the entire value the magnitude decreases But since we have a negative sign so total energy increases correct. Yeah That's what I've said that even E2 E3 increases simple That is what last class also we have discussed that here the electron in this orbit the electron is bonded actually with the nucleus Okay, and it is actually the energy suppose you have to the electron is present at infinite distance Suppose here where the energy is zero it is free at infinite distance now this electron Suppose it is present in the orbit. So you have to place this electron here So you need to supply energy to this electron so that it will come into this order So this energy is getting stored into the electron like this It is the work done that we do on this electric run to be to know to place this electron in this orbit That's why it is negative again You see here we have negative energy and if you want to take this electron out what you have to do You have to provide energy from outside some positive energy you have to give so when this positive negative cancels out each other Completely this is the position of infinite this position we have where the electron is free and this is the Energy required yes, that's what that is that is what the result we got from both atomic model That is the significance of negative energy why electron has negative energy in any orbit We are providing energy. It means what they're adding energy into it So plus minus are cancelling out each other if they cancels out completely electrons free they'll come out from the surface Right, so the total energy which is negative. It is the mathematical thing like it It is a mathematical thing Yes ionizational energy we can understand with this but that is Defined for gases not for solid. That is the difference here Ionizational energy is defined for gas No, we'll have this formula. We'll see what is Delta E will get it's not like EF and EI will substitute with sign Total energy we'll see what we get Can I move on? Ionizational energy will discuss in the next chapter. Let it be. Okay, you cannot understand everything over here We'll discuss it's simple one definition. We have okay It is a amount of energy required to remove an electron from an isolated gaseous atom That is it the energy that you provide to an isolated gaseous atom to remove an electron that is ionizational energy Right, but definition won't help you. There are other things that you need to understand. Okay, we'll discuss that in next chapter periodic properties Did you get it? Can I move on? Just a second can say that that is the no that is the threshold state we have means that is the Transition state from that particular point the electron is free to move from the other thing At infinite distance also it is free to move Free from the attraction of nucleus that is a better way to say At infinite distance the electrons are free from the attraction of the nucleus Okay Can you proceed now? Right, so we are trying to find out Delta E the energy difference EF minus EI EF minus EI the formula we have I'll just write down the formula that I have written in the previous page Same thing just and you substitute with NF and ni so we get here negative of 2 pi square Me e to the power 4 z square By NF square minus minus 2 pi square Me e to the power 4 z square and I square Move to practice. You see the magnitude this magnitude is more than this Minus minus becomes positive for Delta E. You always get positive here right So the expression we get here is I'll take this 2 pi square square me e to the power 4 e to the power 4 H square I have missed know how I have missed x square here x square and x square Divided by x square If I take this as common into z square open bracket 1 by NF square Minus 1 by ni square. Oh, is it ni minus NF square? So 1 by ni square minus 1 by NF square this one from here to this Including this that is for this one This is a constant if you see for an atom For an atom this expression is a constant, right? and This constant we call it as read book constant our Yd Be Rg the read book constant represented by our so Delta E is equals to our times one by Ni square minus 1 by NF square. Oh, just a second. Just a second. I missed one thing here This is again Delta E. We did not take into the consideration Just a second. Nothing is wrong, but one change will do Okay, this side. I forgot to write here. This is the okay, so we get this Z square ni square by NF square what I missed here is this Delta E I have already explained it is at C by lambda Okay, so now I'll write to the next page At C by lambda is equals to or one by lambda if I write down one by lambda is equals to at C will multiply this side Okay, so one by lambda is equals to what we can write two pi square Me e to the power 4 z square divided by C h q C h q into 1 by ni square minus 1 by NF square Okay, now this constant is readable constant this one This is readable one by lambda. We should write you Read book constant Okay, so this is represented by our read book constant is our so one by lambda is equals to our One by ni square Minus one by NF square. What is our are is two pi is square me e to the power 4 z square divided by C times h q Okay, so for hydrogen you see what we can write if you consider the hydrogen atom for hydrogen Z is equals to one if you substitute this one here this read book constant becomes our h for hydrogen that would be two pi is square and E to the power 4 z square divided by C h q Yes, it is for an atom R is this so read book constant r is equals to we can write finally are For hydrogen into h square. Okay, one by lambda if you remember, this is the wave number new bar Right, so final expression if I write down here the wave number new bar is equals to one by lambda Is equals to our h z square into one by ni square Minus one by NF No, it's not Shell number is there and terms written over there So for the hydrogen atom read book constant is our edge for any other atom. It is our edge times that is square. Yes All these are true for single electron system Because all these are coming from Bohr's model Bohr's model is applicable for one electron system Okay, the value of read book constant is not required. Okay, but if you want I can Write down the value the r value is This is the value of read book constant. Yes. So that's why the point of value is not required The value is not required. They won't ask you to write down the value Okay, because it is different for different atoms. There's no any point of talking about the read book constant the value of that Yes, it is our edge between right try this question. Where does it show you the question just try to stick with the formula. Okay Yes, yes, yes, you can write it the answer and see when you see the question There will be options. No, I can tell you one thing in 99% of the cases you don't require the value of our You can write your answer in terms of R only okay, you will have the option you can understand Okay, so look at this question Try this one. Could you write on the write the answer in terms of angstrom? Always try to write it in terms of angstrom in in the form of a into 10 to the power B Always 10 to the one Julie 10 to the power seven are then 6.6 into 10 to the power minus 7 10 to the power 3 is the answer given 6.6 into 10 to the power 3 the answer is given. Could you check your calculation? Done. Got the answer. Okay. See the energy of an electron in the second and third bore orbit of hydrogen atom is given Okay, so what is given first of all the first step is to write down the data e2 e2 is minus 5.4 to 10 to the power minus 12 e3 is minus 2.41 into 10 to the power minus 12 You can see which one is more ideally e3 should be more than e2 and that is what the value we have Okay, we need to find out the wavelength emitted in this radiation means what? Wavelength comes out only when the electrons Comes back to the lower energy level from high to low, right? So obviously the transition is what? The transition is e3 to e2 So delta e is equals to what we can write e3 minus e2 Which you can solve easily e3 is this and e2 is this so five point four two minus two point four one the value is one zero Then three so won't it be e2 minus e3 be final man's initial rate that we take when electron Jumps from lower to higher energy level. It is what it is talking about the wavelength that comes out It means it is the high to low transition Yes, okay When that's what I have discussed this no when wavelength comes out Then the transition is what the transition should be this The transition should be high to low then only the wavelength comes out if you're considering this then you have to You know give the energy you have to provide the energy to the electrons. So since in the question is talking about the wavelength of the Electron that comes the wavelength of the radiation. So it means high to low transition We have so e3 e2 initial Yeah No doubt Yes, okay 10 to the power minus 12 are How do we convert our into jewel one jewel is equals to 10 to the power seven are So this if you multiply by 10 to the power minus seven it becomes june That's why you see this. I know the conversion the unit conversion is very important here in this This is the Delta E Now we can find out what we need to find out lambda Delta E is equals to xc by lambda we can write So lambda is equals to three point zero one Ten to the power minus 19 divided by h value with six point six two six Into ten to the power minus 34 into C is three into ten to the power Sorry, this is one by lambda. No left hand side. We have one by lamb. Yes Now you can solve this you'll get the value of lambda so lambda is equals to suppose six point six two six I am assuming this as six point six 34 and eight so it is ten to the power minus 26 three already we have 3.01. I am assuming it as three into ten to the power minus 19 So depending upon the no data you can take this approximation Okay, obviously you see three and three will get cancelled and this becomes six point six into ten to the power minus seven meter Yes, and one angstrom is equals to ten to the power minus seven ten meter The ten to the power minus seven meter is thousand angstrom, right? so this Six point six into ten to the part three minus three ten to the part three angstrom Any confusion in this you can do like this ten to the part three Angstrom is ten to the power minus seven meter So it is six point six into this so we'll multiply by six point six both sides so this is the answer nothing much just you need to know the formula and Unit conversion you have to know then you can solve these kind of questions Clear no doubt Now you see again, I'll take the reference of that energy level that diagram suppose the electron jumps from this to this energy level So how many different transition possible here one of the transition is it comes from this to this first? From this to this and then from this to this and then from this to this One two three transition possible and in each in every transition it will radiate some radiation Right, so these number of radiations are the different spectral lines Okay, number of spectral lines Like this correct, so one from this we can say there are one possibility is this from this to this this to this and this to this Another possibility is what from here it will jump directly to this and this another two spectral lines Another one it jump rested from here to here one inspector All these possibilities are called the number of spectral lines in a given transition Okay, so obviously when we have two to three two to one or four to one you can do this and count Yeah, but how many is fix such spectral lines possible, but when we have higher number of you know Transitions like from ten to two if it is coming Then there are so many transition possible and it is very difficult to calculate one by one manually Right, so in that case it's the best way is what? Is to use a formula and that formula is I'll write down here Yeah, there are many possibilities possible like this So if they ask you the number of spectral lines the possible transitions number of spectral lines The formula is it is NF. It is ni minus NF Ni minus NF you can understand it this way. This is a number of spectral lines So negatives it cannot be negative and Number of spectral lines you get when electron comes from high to low energy level, so it must be positive So hi means ni the initial orbit right ni minus NF then ni minus NF plus one divided by This is the formula Now based on this I'll just give you some questions so that you can understand what this spectral line means Okay So Calculate the yes, it is just a formula given experimental based on the study. They have given this form Calculate the number of spectral lines first one when electron jumps from jumps from 9th excited state third excited state when the electron jumps from 6th excited state state to third orbit No, it's not Yes Hoja, that's right Ground state is one First orbit is one that is not an excited state. So in the first one the value of ni 9th excited state means 10th orbit NF third excited it means Fourth orbit just to use the formula and I for sixth excited state is seven NF third orbit is three only because it's third orbit So seven minus three Easy, right? So all these kind of question understanding of concept is important But once you know the formula, I would suggest you can use the formula directly to get down Next write down a Spectrum a spectrum write down it can be defined as it can be defined as pictorial representation pictorial representation of arrangement of radiation arrangement of radiation in increasing decreasing order increasing or decreasing order of wavelength or Frequency you are not going to get any questions on this spectrum Okay, numerical questions. You are not going to get but To understand energy levels present within an atom. We are just discussing it nothing much Okay, so Spectrum is classified into two categories first of all the classification of a spectrum if you see it is of two types the one is Spectrum that is based on nature based on nature and other one is based on life Based on life. Okay, based on nature. We have two types of It has two types of spectrum that is continuous continuous and discrete discrete also we have two types that is band band and line spectrum band and line spectrum based on Based on origin. I have written here light by mistake. It is based on origin So based on origin It is of two types that is emission emission and absorption emission and absorption see continuous spectrum is When a white light passes through the prison, I'll show you the diagram. You all know when white light passes through Passes through a prison. We get seven different colors. Okay that From those colors only the light are made of the light consists of seven different colors. So it dissociates or you know Gives seven different color when you get a screen on the other side of the prison to that spectrum Okay, that spectrum is the continuous spectrum. We have that we call it as Continuous spectrum. I'll show you the diagram of this continuous spectrum None of the wavelength is missing in this one See this one the simple one White light passes through a prison and this spectrum is continuous Just a second continuous spectrum Discrete means what? Look at this one here Okay, so if you see this This is continuous white light passes through the prison will get continuous spectrum Where we are getting 6.5 and all the previous question you're talking about this one you said this too No, we won't get fractional value, you know You are getting 6.5 not getting you you asked me if we get 6.5 then Or any fraction yeah, we won't get it You see this tool will you'll get canceled you'll get a fraction value. You won't get a fraction value here Fractional value you won't get because we have supposed see logically you can understand See what happens The possibility is what this will be an odd number If it is even then this will cancel out to end this number if it is an odd number Then this terms become even because it's plus one over here Yes, right, so you won't get fractional value here Which is also logically okay now you look at this is spectrum like I said you are not going to get any I know numerical questions on to this is just basic understanding you must have for this Okay, so this is continuous spectrum all wavelengths are present here on the photographic continuous Absorption means what between this to prison and this white light you place up any any substance Any gaseous substance any molecules you place over here like in this case you see then what we observe on this photographic plate There are some wavelengths which are missing here. You can see this Some wavelengths are missing. Okay. If you want me to magnify it. I'll just show you in the next page You see this now you can see this You put a substance in between the white light and the prison We see some of the wavelengths are missing here to this spectrum that we are getting it is absorption spectrum Okay, now this one is important here to understand why only few wavelengths are missing and How these wavelengths are missing over where did it go because from here we have all seven wavelengths, right? All colors we have over here because it's white light. Correct now this substance and this prison what happens here and How this wavelength are missing what we can conclude from this thing we can conclude that Some of the wavelengths is absorbed by the substance. Yes or no Agreed some of the wavelengths are Absorbed by the substance which is present over here and when this happens what happens? We know this fact That within an atom Electrons are present energy levels are there so when from the one level if I you know draw the energy level like this Which is easier for me to draw a straight line suppose the other energy levels we have so if electrons present over here of this substance and When it absorbs energy, right? It will jump to the higher energy level again another higher energy level This is what happens So electron absorbs only those wavelength corresponding to that energy level present in the molecule if There's one wavelength suppose this wavelength Corresponding to this we have certain amount of energy if electron receives that energy and Corresponding to that energy if the energy level is not present within the atom then electron won't absorb that particular wavelength at all it will Release those wavelengths. It won't take that particular wavelength So these wavelengths you can say corresponding to this this and this wavelength the energy level are present We're present in the atom and hence electron takes those wavelengths those energy and goes to the higher energy level So this is spectrum is absorption is spectrum now when this experiment was done Okay, they have come to this country. Maybe this is happening that electron takes those energy and goes to the higher energy level To confirm this what they have done after this they have taken the same substance and They heat them up when they heat it the similar wavelength Same exactly same wavelength emits from this particular substance, which means what in this experiment These wavelengths were absorbed by the Atom or substance present to this is absorption wavelength when you heat this all these missing wavelength We receive over here. So this we call it as Emission spectrum What it Now why we are doing this because from this experiment only we came to know about this fact That within an atom there are energy level present nothing much you see The same substance to confirm this that the missing wavelength is absorbed by the substance to confirm this We just heat it up when we heat this then the same of Frequency same wavelength it emits that we receive in this photographic plate again on the screen Which confirms that the missing wavelength is absorbed by the substance This becomes absorption and this emitted radiation that we get here it called emission We have definite energy levels then only a Definite wavelength has been absorbed. No, why not this wavelength absorb Because corresponding to this wavelength the energy levels was not present Why this one absorbed because corresponding to this wavelength the energy level present Electron receives this energy and jumps to that particular energy This confirms the presence of energy level within an atom Yeah, got it Line is spectrum means a line and bend is not important at all Bend spectrum means we'll have a bend of wavelength and these bands are separated by some dark space means a few Wavelength is missing over here. No more than one wavelength at a time. It cannot absorb first of all, I'll tell you see And a nishant you see try to understand one It's not like we are giving multiple wavelengths to the atom at a time. We can provide only one Wavelength. No, suppose white light you are striking it, right? So now we have seven different wavelengths in this white light, right? So it's not like it will absorb More than one wavelength at a time First it will go it will absorb one particular wavelength goes to the higher energy level if again There is a possibility of absorbed of absorbing the wavelength then it will absorb the another wavelength again higher energy level So one by one it goes at the time multiple wavelength. It cannot absorb and To which orbit it goes and to which orbit it goes it depends upon It depends upon the energy level of all this so bend means we have a bend of light And it is separated by a thick line that line Line is exactly opposite of it. We have a line of wavelength Separated by a thick dark space. That is the line No, we heat them just to make it sure that the Absorbed wavelength the missing wavelength is absorbed by the substance Just to have a surety of it. See when you heated many things possible It is also possible that the electron go to the higher energy level But at some temperature for some element, they emit radiation also, which were missing over there So one of the experiment confirms this section when we have a bend band of light Band of wavelength. It is banned when we have a single line in line. It is line inspector. That's fine That's not an issue. Our purpose is what to understand within an atom There are energy levels to the query that you are asking in that case also It is it is already understood. No that within an atom there are energy levels present So we are concerned with energy level. It's not like what what energy it is absorbing and what energy level it is going It is energy level present That is it discrete is, you know, it based on the nature. Okay depends upon That is not in our hand it is not we are not doing anything From a particular source, of course some light is coming out where there's some wavelengths are missing So it can have about two types one single wavelength That is line in spectrum and we have more than one wavelength one by one present separately by a thing like No, no, no, it's not based on nature. It is right. So we are not doing anything Got it. So point is this thing is not, you know, it is not that important that we will discuss so much on it But why I have discussed this because this experiment none of you have asked me So, how do you know within an atom the energy levels were present? That is the postulates of course, right? But he hadn't talked about energy levels. He had just given its carry So the that that energy level is present within an atom. We got from this experiment Absorption and emission. So this part is a bit important to understand that how do we get to know that within an atom the energy levels present? Nothing much required over there. They are not going to ask you any questions on this numerical questions specifically Or maybe sometimes they can ask you theoretical, but that is also not important When we supply energy depending upon the, you know energy you are giving in electrons absorbs energy When it absorbs it moves to higher energy level So more than one electron is fine. We are talking about here. It happens with all the atoms now. It is not related with boards Different different electrons in different different orbits will have different different energy So depending upon those energies plus the energies you are giving in If corresponding higher energy level present it will take that energy. Otherwise it won't take Yeah, it is one of the possibility That when it comes down right some electrons goes to the higher energy level some comes down when it comes down It emits see what happens one example. It is given and CRT also you see I am brought you heat correct What happens? It color changes from dull red to bright red bright red to blue and then white it becomes So how this color changes takes place Color changes means what change in frequency? So when we heat it there will be change in frequency and hence different wavelengths comes out from this Theoretically if you try to understand like is that we are giving energy you won't get it maybe but once very simple example We have iron rod you heat it continuously changes its color. How do we absorb? How do we know understand the different color over there because of frequency that is coming out from the iron rod That frequency we receive and then we know Then we realize what color it is blue red or no white whatever it is correct So this example confirms that on heating different different frequency of light comes out from a metal surface That is what happens here also when you heat it different frequency comes out Corresponding to that different wavelengths and those wavelengths if you compare here the same wavelength were missing over here It means these wavelengths which are missing is absorbed by this substance and hence energy levels I think you understood it now Yeah, have you discussed about time period? orbital frequency Time period or orbital frequency Okay, it was there in boards model only this one formula. I forgot to discuss there. I'll just give you now See, there's a term sometime. They'll ask you like radius and velocity relation. We have with RNC Similarly, we have relation of time period of revolution. It's not a no that difficult Time period of revolution write it down. So time period for nth orbit. We write it as 2 pi Rn the radius of that orbit divided by the velocity Vn Rn Vn you substitute you will get the relation as n cube By z square into 1.5 into 10 to the power minus 16 Second this constant term is not required. You should know this relation That the relation of time period is directly proportional to n cube By z square Sometimes they ask you to compare the time period into different orbits also. You should know this Similarly one more time. We have that is orbital frequency not orbit. It is electron velocity of electron It's not orbit time period of revolution is for revolution of electron Orbital frequency is what it is the velocity divided by circumference Circumference, so velocity is Vn Circumference is 2 pi Rn. You see it is exactly opposite of it So this if you solve you will get this the formula as z square by n cube into 6.66 10 to the power 15 Okay, and orbital frequency it is directly proportional to Bittal frequency It is directly proportional to z square by n cube. This is you see it is number of revolution per second second inverse This two formula you also remember that we know the relation of wave number that is 1 by lambda is equals to Rh z square 1 by ni square minus 1 by nx square This is the relation now In different different transition, we can easily understand or find out the wavelength required. Let me draw this You know diagram Write down the heading in this interpretation of hydrogen spectrum interpretation of Hydrogen Spectrum hydrogen is spectrum. Okay interpretation of hydrogen is spectrum. So, uh Suppose we have different different energy levels present here. All of you draw this These are the different different energy levels. Okay, n is equals to one it is and is equals to two and is equals to three and Is equals to four five six Now when electron comes from high to low energy level like this one It will It radiates energy right like from here to here if you comes radiates energy Radiates energy and this also radiates energy. Okay. Similarly, it is possible when it comes down to The second energy level which is like this Okay, this is a transition me Okay, now you see in all these transition there are Energies comes out in the form of radiation. Yes or no guys Tell me in all these transitions energies comes out Yes, so from five to one you'll get one particular wavelength Four to one you'll get one particular wavelength three to one two to one you'll get different different wavelengths Okay So basically when the transition takes place from any higher energy orbit to the first orbit You will have one series of wavelength. Yes or no guys respond fast, right Are there are see another dog. There are infinite number of orbits Correct. I cannot show your infinite number of transition. I'm just giving you one sample of it Correct. If you want me to draw, I'll draw it. Okay. Don't I'll do it like this. Don't get angry and rock Okay No, not an issue. I was just joking. So this is the point there are infinite number of orbits No, so we can draw we can draw infinite number of lines. There are many lines like this Okay, fine It's a point. I'm trying to make is what in all these transition Where one of the you know orbit is fixed the final orbit is fixed No for one particular transition, the final orbit is energy equals to one for one particular transition The final orbit is energy equals to two then three and then four five and all like like this We have traditions Correct So in all these transition when final orbit is one two three four five You will get a series of wavelength. You'll get a range of it, right? So obviously we'll have Lambda max also in that range and lambda minimum also agreed Maximum wavelength and minimum wavelength for one particular transition Correct now you see this When electron jumps to the first orbit from any higher energy orbit If it comes from the first to the first orbit the series of wavelength that you get here This we call it as that it falls in Lyman series Lyman series, it is the name of the scientist and And then on his name only it's given the series Similarly when electron comes to the second orbit again, we'll get a series of wavelength bomber series then passion series Then bracket series then fund series But then also we have Humphrey also we have up to this but that is not All these will get different different series of So could you tell me for Lyman series? What is the NF value? For bomber. What is NF value? Is it fixed? Is it fixed? Is it fixed? Yes, it is fixed for Lyman NF is always one fixed bomber NF is always two Fixed similarly we have pastram bracket and fun But what is Ni? Ni could be anything for Lyman series if you see and I could be anything from 2 to infinity Yes or no and for bomber and I could be anything from 3 to infinity For passion could be anything from 4 to infinity. So ni value for all these series are not fixed NF value is fixed Correct. So what we are going to do next and I and NF value we have you see this and I and NF value we have This is constant only Yes, yes, yes, correct. That's what Ni and NF we have this is constant only So we can find out the range of wavelength for each series. Yes or no So let us discuss first Lyman series now you tell me The NF value is one here Ni value could be anything from two three four five till infinity One by lambda is Equals to I'll write down R for any other atom One by Ni is square minus one by NF Based on the value of Ni because NF is the fixed And I you can change any value you can take so based on the value of Ni Could you tell me the possible value of lambda X in terms of R R? You don't have to substitute and Lambda minimum in terms of odd. Could you find out this to lambda can't be negative stress Why you're getting negative sign done this one Okay Now you see whatever I'm going to discuss now for Lyman series like how to identify the value of you know NF and Ni sorry Ni in order to get the maximum and minimum wavelength This thing is valid for all the series bomber posture bracket fun on the series. Okay, you see NF is things We just need to think about think for Ni only why I've written it By mistake I have written this Ni here. It should be NF. No, that's what probably you are getting negative. Yeah Okay Ni value could be anything from two to infinity now you see You we have suppose we have to get the maximum wavelength. Correct. We'll start from this side if lambda is maximum Right, if lambda is maximum, they can we say one by lambda is minimum in that case. Yes For maximum wavelength one by lambda is minimum. Yes One by lambda is minimum means this entire expression should be minimum To make this minimum we have to subtract the maximum value here means one by and I should be maximum One I and I will be maximum when and I will be minimum has the possible value of ni is what? So what we can say here see for one by If you take lambda max here, it means lambda So if I take maximum wavelength, it means one by lambda is Minimum and for if this is minimum this entire thing is minimum. This entire thing is minimum. It means one by Ni Ni should be maximum Then only it will be minimum and this would be maximum when ni is minimum is minimum so what we can conclude for Maximum wavelength this you can apply for all other different series for Lambda max ni should be Minimum and reverse of this is also true for lambda minimum And I should be Maximum just you need to Keep this in mind Maximum wavelength need to find out so ni value is minimum that is two so we can calculate this by This formula and that is one by Lambda max is equals to R one by one square minus one by two square So when you solve this you'll get lambda max is equals to Is equals to four R by three and similarly lambda minimum if you calculate it would be eldest Right down here. It is R by one by R will be in the denominator So four by three R Yeah, okay four by three R and this would be one by R So one by lambda max is four by three R for lineman series and one by R is the lambda minimum So lambda falls in this range for lineman series four by three R and one by R So when you substitute the value of R because R is a constant only so we'll get the range of wavelength over here You don't have to substitute it and this range is found to be in this a second This is found to be in Ultraviolet reason. This is what you need to memorize Ultraviolet reason so The lineman series falls in ultraviolet reason Similarly, you can find out for Barma series Could you tell me what is the lambda max and lambda minimum for Barma series? Barma series and F is two That is fixed and and I could be anything from three, four, five till infinity What is the lambda max here and? lambda minimum Again maximum wavelength you need to find out and I value should be minimum minimum wavelength Ni value should be maximum lambda max for Barma is 36 by 5 R and Minimum value is four by R. So this lambda falls in this range and this is found to be in visible reason This is only in visible reason Okay, so really for other three you can easily find out. I'm not going to do it again and again I just write it down here the reason that you get Lyman, you'll get ultraviolet UV reason Barma, you'll get visible reason Pasture bracket and fun. You'll get infrared infrared infrared and Infrared all these things right now if they ask any question You can use that formula of one by lambda and you can find out the No possible value Okay, so now we are done with it for any other series passion bracket fund, you know, and I NFL you can find out Lambda max lambda minimum pieces. Okay now the next we are going to understand here is The dual nature of light dual nature of matter This we also call it as D. Broggy D Broggy hypothesis Okay, right down in 1924 obviously the date here is not required here in 1924 the scientist name is D. Broggy D Broggy Proposed that proposed that the Proposed that all microscopic material Proposed that all microscopic all microscopic material particle Microscopic material particle in motion such as electron electron protons atoms Ions All microscopic material particle in motion such as electron proton atom ions and Molecules has Has dual corrective dual character means wave plus Particle nature Molecules has dual character that is wave nature plus particle nature. So what he suggests Right down according to him According to D. Broggy Yes, correct. This is correct. Right down according to D. Broggy According to D. Broggy According to D. Broggy the wavelength associated with the particle according to D. Broggy the wavelength associated with the particle of mass M Moving with the velocity V is given by Again, I'm repeating the wavelength associated with the particle of mass M Moving with the velocity V is given by lambda is equals to H by P P is the momentum which is given as H by M P is what P is the momentum Okay, so now this wavelength is associated with any object of mass M moving with the velocity V Okay, according to Einstein's energy equation, we know any mass M If moving with a speed of light that is C the energy associated with an object is M C square Okay, M C square. This is for light for any other object. We can write down this Velocity C as the velocity V. So this is the wavelength given by D. Broggy. How do we get this? This I am trying to make you understand this one Right, this one is fine. You let it be. Now. How do we get this? We are trying to understand E is equals to M C square we have from Einstein's mass energy equation mass energy equation and we also know for a photon The energy is E is equals to H nu which further we can write it as at C by So now E is equals to what? M C square is equals to at C by lambda if you quit the two will get M C square is equals to at C by lambda and When you solve this for lambda you'll get lambda is equals to H by M See this is for the light particle, but for any object of mass M We can write lambda is equals to H by M times the velocity This is D. Broggy hypothesis, which is given by No, you know, which is given by the help of Einstein's mass energy equation plus So this is the dual nature of Just a little bit only this much not more than that There is it over here quantum mechanics. There are many things in this We are just taking a bit of reference of that that is so Wave length lambda of any object of mass M Moving with a velocity V is lambda is equals to H by MV. We can write Okay So from this you can easily, you know, see that wave length is Directly proposed inversely proportional to the mass M and for heavier object hence For heavier object the wave length is insignificant is insignificant and we ignore this But for microscopic particles like electron proton neutron electron mass, you know, it is in the order of 10 to the power minus 31 So mass is very small. So there the wavelength is significant. We cannot ignore that for electrons. We have to consider Wave as well as the particle nature Right wave as well as the particle nature Nothing velocity can be anything of mass. We cannot change for an object velocity. We can increase or decrease But main thing is mass and it is it is so heavy that this lambda is Insignificant Yeah, it was given for any object of like for the light particles But the same thing we can we are using over here. No, we cannot say that we can say See even for us also the masses 70 75 60 kg is for human being Right the wavelengths. We don't we don't consider the wave particle for us, right? We don't consider that because 60 70 kg is too much for this wavelength. So it is almost negligible zero Heretically we can say but practically we don't have correct now This is the formula we have We can also write down the various, you know form of this particular form like in terms of kinetic energy suppose if K is the kinetic energy we have is the Kinetic energy so K is equals to we can write half MV squared So could you tell me what is the value of MV from this? What is the value of MV from this? No, from this one. There's no lambda in this expression Okay, and we need to find out. So what we can do in this We can multiply with M both sides. It is to MK Is equals to M square B is square. So if you find out MV from this, it will be root under off To MK and this we can substitute here. So the formula of lambda in terms of wavelength is To MK root over of in terms of kinetic energy is this K is the kinetic energy here must take care of another formula Okay. Now one last one in this you see if a charge q is moving with Sorry, it's moving under moving under a potential difference V Then it's kinetic energy is Q into V V is the potential difference this K we can substitute here So further than formula of lambda is H by To M Q V So how did you get the kinetic energy? This you will study in electrostatic Kinetic energy of charge you will study in electrostatic. You can take this as a formula now In 12th grade, you will study electrostatic in physics. There you can understand this But for now you can consider this as a formula kinetic energy of charge q and the potential difference V is 2 Sir Yes, so what if the particle accelerates nothing then although the kinetic energy will be Q times into V It is acceleration then their velocity will be something else. We are not dealing with the velocity here It's just Q charge under a potential difference V Q V is the kinetic energy This is a kid these are the formula you can use Okay, that's yes, not so these are the three formulas We have depending upon the data given you in the question. You can use this formula in order to find out the wavelength lambda Okay, now with this You can actually understand one of the postulates of board atomic model Like you see board what he suggests that the electron revolves in a circular path called orbit Right and de Broglie de Broglie suggest that any moving particle Has electric has no wave nature associated with it Any moving particle has wave nature. So these are the supposed wave associated with an electron moving in a circular path of Radius are like this Suppose this is the wave we have Okay, and what we are assuming in this circular path the electron is moving and these are the wave associated with this electron Okay, we are assuming n number of assume in one complete rotation there are n number of waves So what is wave you see here? This is from this point to this one's could you tell me the distance this point? What is this distance? This is one complete wave. So this distance is lambda Similarly from this point to this point what it is The another wavelength lambda like this we have n number of wave associated here in one complete rotation, correct? so So could we write down the circumference of this orbit is equals to n times lambda Is it clear? Because n waves create lambda lambda lambda lambda lambda and times n lambda is a circumference Okay Circumference, we also notice 2 pi r. Where r is the radius of this orbit and lambda From D Broggy hypothesis we can write lambda is equals to h by mv So when you rearrange this you'll get mv r is equals to n h by What is this relation? What is this relation? Could you tell me? This is one of the postulates of both? If you remember Yeah, the postulates of all right. So board has given this relation according to his experiment There's no mathematical proof for this But after D Broggy hypothesis we got the proof of this particular relation and then we understood that how accurate The postulates of board was Okay, right there one or two Yes, because we have n number of waves here We are assuming n number of waves in that orbit now So wavelength into n is the circumference Yes, I didn't tell me did you get it now there are few limitations of board model also this one a D Broggy hypothesis First of all it is applied only to moving objects not for a stationary objects where the velocity is 0 Right, this is one thing another thing for macroscopic objects like day-to-day life the objects that we use Okay For those particles also those of this all that is not happening applicant Why the same reason the mass is very high and hence the lambda is insignificant These two are the these two are the You know drawbacks of D Broggy hypothesis Now one very important thing you listen to me carefully when yeah Now after this D Broggy hypothesis, we came to know that the electron has both wave and particle nature Right electron has both wave nature and particle nature it consists of dual nature wave and particle nature dual nature wave and particle Okay, so Because of this what happens the exact position of electron is very difficult to identify Okay, the exact position is very difficult to identify and this comes here the problems with the board model Okay, so just here you see what happens. Suppose the electron is revolving in this, you know orbit Correct. Suppose the electron is revolving in this orbit Okay, obviously it is a circular orbit I have given like this but it is so We have electron is revolving in this orbit, correct Now, suppose you need to find out the position of the electron which is revolving in this orbit So for this purpose what we do we use A very low frequency or sorry high frequency of like high energy like that might be Strikes onto this electron Okay, high frequency light we use Which strikes onto this electron Right and when it reflects back Right, there is a receiver this side we keep And that is nothing but a microscope Which we use to you know detect the reflecting light and then we can find out the Position of the electron suppose is the microscope we have This is what we do, right? So since we are using this light suppose h nu the frequency you are using You provide energy to the electron this energy if it emits so we'll get it and we'll find out the position of Right, but what happens here? You are providing energy Reflects back you get this and you understand. Okay, the position of the electron is this that you can do But at the same time what happens the moment it receives energy Right some part of it receives energy. This will change its position So quickly right the new path of the you know the electron moves in this direction because it gains energy It moves in this direction means the position of the electron has been changed by the time you receive this You know signal receive this ready Reflected ray this side by that time the electron has already changed its position Right means the moment you receive here the electron is not present here It has gone to so many so many some other point Some other place, right? So what happens here after this? We came to this conclusion that the exact position and Momentum means the velocity of electron the exact position and momentum of an electron is Is difficult to Is difficult to Measure simultaneously If you try to measure A position its velocity will be changed momentum will be changed if you try to measure momentum its position will be changed So the exact position and momentum Of an electron is difficult to measure simultaneously Right and this particular thing is given by a scientist called hyzenberg Right and this rule. We call it as hyzenberg Uncertainty principle hyzenberg uncertainty principle write down the Principle Yeah, I'll repeat just tell first you write down. I'll repeat the line right on according to hyzenberg uncertainty principle According to hyzenberg uncertainty principle. 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 particles like electron of a moving of a moving Microscopic particles like electron So what he says is that exact position and momentum is difficult to find out simultaneously Okay, so he has given its relation which we call it as mathematical expression of hyzenberg Based on his study. He said delta x into delta p Is greater equal to h by 4 pi where I'll explain this first you finish this write it down delta x is uncertainty in position in position and delta p is Uncertainty in momentum Right this we can write as delta p is the momentum m into v mass of an object is constant only m delta v we can write the uncertainty In momentum where delta v is what delta v is the uncertainty in velocity So if you substitute this delta p here We'll get the another form in terms of velocity delta x into delta v Is greater equal to h by 4 pi and right this is the relation we get Copy down this first then we'll see some more things into this Wait, wait, wait, we'll do it now In this the point you write down the explanation you write down here I'll explain this write down for determining the position of for determining the position of for determining the position of Microscopic particles microscopic particles Just we'll finish this and then we'll get well then we'll have a break Just this is the last thing this explanation will finish and we'll take a break Okay position of microscopic particles radiations of high energy or high frequency radiation of high energy or high frequency has to be used has to be used When these radiation Falls on the object whose position is to be found when these radiation Falls on the object Whose position to be found on the object Whose position to be found the whole momentum or energy Gets transferred to the particle Whole momentum or energy gets transferred to the particle which causes inaccuracy in velocity Right, so that is what I have explained over here velocity inaccuracy in velocity means momentum also right m delta v is the momentum when you reuse this high frequency radiations in order to find out the position of this electron Right then electron was Moving in this orbit right this was the expected path This was the expected path for the electron right moving in this path He provides energy And the reflected radiation is this you receive this and you can find out the position of an electron But what happens since you provide energy to this electron? So it will change its path Right, so it was not there on that same position the moment you take this or receive this radiation from this Okay, so the energy transfer takes place that changes the velocity of the electron here from here to here The electron has some velocity now you use radiation to find out the position But in this way you have changed the energy of the electron right it takes the energy and it Its path will change right it comes out of the orbit. This is the new path of the electron you can see New path of the electron this was the expected path expected path Okay, so this is what this is what hyzenberg said That you cannot find out the exact position and exact momentum of the electron simultaneously Right means if you find out position momentum you cannot find out if you find out momentum then the position will be changed So both you cannot find out at the same time simultaneously and he has given its own relation of Uncertainty in position and momentum should follow this relation. This is the hyzenberg uncertainty principle. Yes It absorbs energy changes its path and hence its velocity also changes Okay No, it is not important to find out They just said we are trying to understand the various properties and characteristics of it. Okay So he just said okay at the same time we cannot find out of this But the problem with this what happens you see earlier boards was saying what that we know the exact position of electron We know if the energy is this it means the electron is in this orbit And in this orbit the velocity is this Right and its potential energy is this kinetic energy is this Right position is this at this distance it is present So once we know the electron is present in one particular orbit according to gore we can find out the No, the velocity of the electron in that orbit Plus position also we know it is in this orbit At this distance from the radius So this when this comes out then there is a problem with the boards theory No, we are not we see we are not going to determine the position of electron not required We are just trying to understand that one of the postulates boards was given was inaccurate According to him. We know the exact position and velocity of an electron right in an orbit Exact position means what whether it is present first orbit second orbit or 10th orbit We know the position where in which orbit it is present and that particular orbit What is the velocity of an electron but according to heisenberg it is not possible Right it is not possible to determine the two particular points simultaneously Okay, simultaneously No, it's not it's still you know It's still if you go for higher study or some research if you want to do into this It's still the many things many research are going on it is not you know done yet And even we are understanding this in a simpler language It is not exactly the way we are doing it because if you go into the actual concept actual thing You won't be able to get it now That's why this chapter is very difficult to study at this level When we are starting our course in this 11th grade, but yes, it is not required at all Okay, so just let it be point. I'm trying to make is what from this principle We come to know about this fact that exact position and exact momentum Exact velocity of an electron of a microscopic particle where the Wave nature is significant right or the particle which has dual nature wave plus particle nature Right for those kind of elements objects. It is very difficult to find out It is difficult to find out that exact position and exact momentum simultaneously If you find one other one, you won't get if you find delta p delta x you won't get accurately There will be some uncertainty into that So he has given its relation of us an uncertainty, which is this into this delta x by four five This is in terms of momentum and this is in terms of velocity Right the relation is Okay, so this is it we'll take a break now Right, so we will resume the session at six 45 anytime between 40 to 45 will start Okay, 43 643 Take a break now. Hello guys. Can you hear me? Okay, so we have discussed Heisenberg uncertainty principle. Okay, so uh So we have discussed that the exact position and uh momentum or velocity of an electron is difficult to find out simultaneously Okay, so since exact position and momentum We cannot find out some, uh, you know simultaneously So after this when this principle came into the existence we we started looking for The small reason or volume Where the position where the probability of finding an electron is maximum Okay, so before this it was an orbit where the electron was present Now it is the small reason or volume where the probability So the certainty there that the electron is present in the orbit Now it converts into a probability. Okay that The probability of finding an electron within a small reason That we started looking for that's suppose in this orbit, maybe the electron is not present. Okay Maybe here it is not present the exact position We do not find out but we can say there's a small reason In which the probability of finding an electron is not exactly the path of position But a small volume we can say where the probability of finding an electron is maximum Right, so certainty is here. It now it converts into the probability. Okay Earlier it was certain that electron is present in an orbit So this small reason or volume Where the probability of finding an electron is maximum is now called as is known as orbit Right, this is a small reason or volume Where the probability of finding an electron is maximum is known as Orbit so from here the concept of orbit has been changed And it becomes orbital this orbital may be circular Maybe like, you know spherical or non-spherical Spherical or non-spherical if you look at the orbit the orbit initially it was Mentioned that it is always a circular path It is always a circular path But it may be you know circular or spherical or may not be spherical can be anything So what is what are orbits sorry orbitals Different types of orbital that we have we'll discuss that later not now means First we'll see some questions based on this whatever topics we have discussed today And then after finishing those numericals we'll see Orbitals right different types of orbitals that we have Correct now You see this question Yes, this two question is all have we done this? Okay fine Then you do this one question number 55 And question of 55 One electron volt is equals to 1.6 into 10 to the power minus 19 joule I have already given you all these things If you do not remember you cannot you won't be able to solve the question No, not all uh You need to do question number 55 Question number 57 Question number 58 59 And 60 Only 56 you don't have to do So question number 55 you see The difference between the incident energy and threshold energy is given So we know h new in Is equals to h new not Plus k max Okay, so this k max we can find out It is h new in minus h new not and that value is given five electron volt That is five into 1.6 into 10 to the power minus 19 Joule right We need to find out the deep Broggy wavelength of the electron So we know half mv square is given or sorry kinetic energy is given Right, so we know deep Broggy wavelength in terms of kinetic energy is what h by 2 mk root under of it Substitute all the values you'll get the answer Electron is 9.1 into 10 to the power minus 31 kinetic energy is 5 into 1.6 into 10 to the power minus 19 joule Just you need to solve this you'll get the answer So answer for this the 55th one is approximately this B that is 6.6 into 10 to the power minus 9 divided by root over of 145.6 meter 57th one what is the answer alpha particle has maximum mass Right 57th one you see The mass of alpha particle is maximum It is uh For you know first we have minimum is for electron Then we have for proton and then we have for alpha particle Okay, so maximum mass and hence the minimum wavelength wavelength of alpha is minimum Then we have wavelength of proton then we have wavelength of electron Answer for this one is option c here. This one is b Because you know lambda and mass Are inversely proportional deep Broggy wavelength right electron of mass m question number 58 Electron of mass m and charge e is accelerated from the rest through a potential difference b the kinetic energy We know kinetic energy for electron is what if accelerated along a potential difference b Then it is e times into b Answer is option b 58th one 59 what is the answer 59 The uncertainty in position of an electron is zero the uncertainty in momentum right that would be infinity Right option d is correct 61 The electron is moving in a kinetic energy of this what will be the deep Broggy wavelength of this electron So we know the formula lambda is equals to h by 2 mk root under operate you will substitute all the values you'll get the answer Uncertainty in position delta x is zero Correct delta x is zero. So it will be something by zero is infinity, you know That's why it is it becomes infinite Okay, hence we cannot find out its simultaneously Any number divided by zero is Infinity that is what's given in the option Zero by zero is undefined What is the answer question number sixty six zero? Yes, yes, correct one by zero is infinity zero by zero is undefined 60 is b correct Yeah, it's b Okay 66 to 69 Finish all the question and then you can answer Then I got only two two responses till now Okay The deep Broggy wavelength question number 66 you see The deep Broggy wavelength of one milligram of a cyan blown. Okay. So lambda is equals to h by mv 6.6 into 10 to the power minus 34 divided by Mass is one milligram to 10 to the power minus six kg into 20 meter per second Okay, so it would be 10 to the power minus 5 29 3.3 option a right 3.3 into 10 to the power minus 29 meter option a is correct 67 uncertainty in position and momentum are equal. So what is given delta x equals to delta p Velocity we need to find out correct that is equals to m delta v So we know delta x Into delta v is equals to h by 4 pi m delta v we need to find out so delta v divided by m into delta x delta v Is equals to h by 4 pi m m m gets cancelled because delta x is m delta v. So delta v is equals to H by pi root over of it into 1 by 2 answer is Option d None of this is wrong. Uh, correct. Okay a b c all are wrong So 68 one Calculate the wavelength of a track Start running this meter dash in second weight is this Okay, so lambda is equals to 6.6 into 10 to the power minus 34 divided by mass is given 50 Into The velocity is 150 meter divided by 12.1 meter per second So when you solve this the answer would be 1.06 approximately 1.06 into 10 to the power minus 36 meter Okay, this is the answer we get for this also none of this is correct option d 69 the uncertainty in location of a circulating electron is equal to its de Broglie wavelength. Okay So delta x is uncertainty in location or position is equals to lambda It is given The minimum percent is error of velocity under this circumstances. Okay Percentage error in velocity. So we need to find out delta v by v into 100 This is what we need to find out Okay, so what we can write delta x into delta v Is equals to h by 4 pi m Okay, delta x equals to lambda is equals to h by mv H by mv we can substitute here. So h by m Delta v by v h by 4 pi m This gets cancelled And hence the percent is added Into 100 is equals to equals to 1 by 4 into 22 Into 7 into 100 88 100 by 88 is one point something. So you will get Approximately 8 percent 69 what is the answer See 100 by 88 is more than one a bit more than one right seven into a number which is more than one The closest option is b that is approximately eight Yeah, so closest option is a you don't have to solve it. Okay, this one also not all the questions we need to do Question number 47 you do it first. Huh that we also you can do are you there not an issue? Correct You're getting a 67. What is the answer for 67? Oh, fine. It's all question number 47 Uh, sir Just a second question number 48 Question number 50 then 51 52 53 51 and 53 Yes, tell me Which one No, no, no You try you'll get it. You don't have to find out the minimum or maximum to this Just a second guys. Let me just go back What did you do? Sir, I wrote a delta x as m delta v and P as m delta v as well Just a second You'll get only one answer. Let me check this answer question in momentum Delta x equals to m delta v is given So finally Delta x is m delta v Uncertainty in position and momentum are given Uncertainty in position and momentum are equal so delta x equals to m delta v Then it should be m delta v here. No, I think then it ends up now I have substituted wrong delta x is m delta v. So we'll get here m into delta v square H by 4 pi m correct Yeah, so if you find out delta v here, it will be 1 by 2 m root under of h by Pi You get it b not d here Yeah position is delta x momentum is m delta v. Yeah, that's correct B only you will get This is a calculation mistake Try this Okay Let's do this So the first one 47 which transition In hydrogen spectrum have the same wavelength as bommel transition is this so we know 1 by lambda Is equals to r h z square For helium it is 2 square 1 by nf square or 1 by ni square nf square minus 1 by ni square So this would be r h into 4 1 by nf square is 4 2 square ni square is 4 square correct, this would be r h 1 by 1 square we can write minus 1 by 2 square we can write you see if it is hydrogen then this would be 1 square here we can write So it is for hydrogen nf value is 1 we are getting here if you compare this and and i value is 2 we are getting So option a no doubt This kind of question. It is very difficult to solve this for nf and ni So better you write down the expression and compare with if you write down the expression for hydrogen spectrum you will get this only 1 by lambda r h into 1 by ni nf square minus 1 by ni square that's what the expression we have here It's the answer 48 the number of spectral lines that can be possible when electrons in sixth cell In hydrogen atom return to second cell So ni is 6 And nf is 2 So answer would be 6 minus 2 Minus 6 minus 2 plus 1 divided by 2 So 2 into 5 that would be 10 no doubt question number 50 The ratio between longest wavelength of hydrogen atom In lineman series. What is the longest wavelength? Could you tell me lambda max? I have already done this in the class Lambda max 4 by 3 are i guess right? Yes, 4 by 3. You don't have to memorize it and Shortest wavelength in bomber series lambda minimum. What is that? Lambda minimum in bomber series 1 by r This ratio if you find out it would be 4 by 3 the answer is correct the ratio is 4 by 3. Is it 4 by r? Just let me check So lambda max for lineman is Is 4 by 3 r and lambda minimum is 4 by r. It's not 4 It's not 1 by r. It's 4 by r. So if you take the ratio here, it would be 4 by 3 r is to 4 by r That would be 1 is to 3 That's right. It is given for he plus Okay, it is given for he plus. So you need to take here z square correct Okay, not an issue. So you need to take here z square here. So for hydrogen, sorry Okay, hydrogen. It is 1 square here and here it will be 2 square. That is what the change we have Just a second It will be in the denominator Because lambda we are taking 1 by square and 1 by 2 square So answer is 4 by 3. We are getting correct One is for hydrogen And one is for helium. So z square will come in the denominator Correct No doubt. Yes 51 The wave number of a spectral line this is given energy. So what is given 1 by lambda is given We need to find out e 5 into 10 to the power 5 So e is equals to what at c by lambda At c into 5 into 10 to the power 5 H value is 6.6 10 to the power minus 34 c is 3 into 10 to the power 8 5 into 10 to the power 5 Okay, so 5 into 3 is 15 15 into 6 is a 9 9 point something you'll get 90 approximate value is 9.93 10 to the power minus 20 See one thing these kind of expression you don't solve it. Okay, because you see look at the option One option is quite far from this to write and when you see this suppose it is 6 5 into 3 is 15 1515 15 into 6 is 90 But it is more than six. So answer would be More than nine point more than nine over here. So nine points something you get the closest option is this B is the correct one 53 A photon of wavelength 300 nanometer. Yeah, one more thing guys. I I would like you to memorize the value of hc in electron volt Okay, the value of hc in electron. I'm sorry At c in electron volt is 12 42 12 42 electron volts in electron volt. You can put this value directly h into c Okay, you must remember this Question number 53 a photon of wavelength 300 nanometer absorbed by gas and then immediate two photons One photon is red wavelength is the wave number of the second photon. What is the answer 53? A photon of wavelength 300 nanometer is absorbed by a gas See this one The energy that is absorbed that is incident energy E incident is equals to what? Corresponding to this wavelength the energy is being absorbed And then immediate two photons Correct. So the energy of the two photon we can assume e1 and e2 So this is the equation we have because total energy in is equals to total energy out Oh, we have done this Right, so I'll just do this quickly. So it is at c by lambda Is equals to at c by lambda one Plus at c by lambda two Further we can write one by lambda Is equals to one by lambda one Plus one by lambda two Lambda and lambda one is given you can find out lambda two from this expression the answer would be You will get the option Option a are you getting option a? Yes Correct option a is correct for this one one important property. You can you know, you can keep that in mind here One by lambda is what one by lambda is wave number You see this wave number is additive in nature additive in nature Right. It's very important suppose we have Like suppose we have an atom which absorbs a wavelength of lambda We have electrons present here and this one suppose it is bombarded with A wavelength right or frequency lambda on this atom if the Photons or electrons comes out from this which obviously have certain wavelength Then we cannot write that lambda incident Is equals to the two wavelength that comes out from this it is not correct Because lambda is not additive We cannot add the lambda like this But wave number is additive we can write one by lambda in Is equals to one by lambda one Plus one by lambda two Okay, wave number is additive. This is correct Frequency is also additive. We can also write new in Is equals to new one Plus new two. This is also additive. Correct So this two property you must remember. Okay wave number and frequency is additive in nature Wavelength is non additive. You will get one questions on this. Okay. It's it is asked in j also, right This property you must remember theoretical questions. You may also get from this Wavelength is non additive, but wave number and frequency is additive in nature Correct understood Right So, okay, sir. Okay, guys. So we'll wind up over here. Right next class. We'll start with schrodinger wave equation Schrodinger wave you don't have to do it in detail. Okay, because it is beyond our syllabus We'll just try to understand the orbital concept from this and then few rules We have different orbitals quantum numbers nodal plane. That is it for this chapter Okay, so most probably next class will finish this chapter. I'll share the assignment with you dpp's Okay, and the solution dpp I have shared The same dpp contains the solution of all the dpp's I'm going to share for this particular topic Okay, so please refer that solution pdf for any query Okay, guys understood Yeah, thank you. Thank you so much. Take care. Bye. Bye