 Welcome to the basic science course in chemistry. I am Anindya Datta, Department of Chemistry IIT Bombay and I and my colleagues are delighted to be a part of this initiative which we sincerely hope will prove to be highly beneficial for first year and undergraduate students across the country. So, in this course we are going to take you some rudiments of chemistry that you have studied to some extent in 11, 12 perhaps, but now we will try to answer questions that might have come to your mind while studying this in school and this is something that is going to prepare the field for further studies no matter which branch of engineering or science you are in at the moment. We will start our discussion with atomic structure, but before that let me give a credit where it is due in my part most of the things that we are going to talk about come from this course that we teach to our first year undergraduate BTEC and BS students it is called CH107 physical chemistry, but it is by and large about quantum chemistry. Now this course has developed over many many years with a lot of contribution from many different people the ones that you see now on your screen. So, a lot of effort has gone in to build the contents and that is what has given the course the shape it now is in. So, let me begin with a word of thanks to all these colleagues of mine and also to the students the teaching assistants who have participated in this course and the students who we have taught many of the things that we are going to discuss today have actually arisen out of our attempts to answer questions asked by our students and then we felt that this should be taught. So, that is how we learn together it is not as if it is one way traffic. With that very very brief forward let us now say that what your textbooks are going to be you already have a textbook given to you but in addition to that I would like to recommend physical chemistry by Irelia Wein. Macquarie and Simon is in my opinion the best book in this genre if you want to study physical chemistry a little more detail and we will not have to refer to Pillar and Macquarie too much in this course this is these are only as reference books for those who want to learn little more beyond this course essentially hope that we will be able to rouse the curiosity among some of you so that you will want to know more about quantum chemistry for them Pillar and Macquarie's quantum chemistry books are recommended. Another book that I find two books that I find to be very useful are quantum chemistry by Prasad and quantum chemistry by A.K. Chandra. In fact, the first book I studied on quantum chemistry was the one by A.K. Chandra when I was a student. So, the question that we tried to answer in this part of the course is something that mankind has asked forever and the question is what is everything made up of in our ancient Indian culture it was felt it was thought it was believed that everything is made up of five elements of Panchabhoot that most of us would know about little philosophical way of answering this question but actually makes sense if you think of it in a qualitative manner Panchabhoot is perhaps the best explanation that would have come at that time. In ancient Chinese civilization everything was believed to be made up of two opposing forces Yin and Yang good and bad up and down so on and so forth even that does make sense even today as we come to the modern understanding of structure of an atom you will see that there are two completely opposite things that are played there at play there of course with advent of time by that by now all of us know that it is not five elements or two elements but in chemistry we have many elements 108, 118 what is the current number I leave that to you to find out and in high school I think we have all studied this periodic table which is a nice systematic arrangement of all these elements that allow us to sort of rationalize their properties to a very great extent but then a question does not stop there element fine let us take any one element let us take iron or let us take hydrogen or whatever suppose I take a piece of iron and suppose we keep breaking it down make smaller and smaller and smaller pieces the question is do I stop somewhere or can I keep on making smaller and smaller pieces again in ancient Indian civilization an answer to this was provided by a scholar whose name is believed to be Kanad and Kanad actually had said that everything is made up of things like small fundamental particles and that was a resonated much later in Dalton's atomic theory that all of us would have studied in class 8 or something that everything is made up of atoms so hence we go to the concept of atoms and molecules but a question does not stop there so question that was there is Dalton thought atoms are indivisible are they really indivisible as we know that towards the end of 19th century by many experiments like this a cathodic experiment the existence of subatomic particles was established so they were called electrons and then of course if something that is negatively charged is present in an atom it has to be balanced in and young remember it has to be balanced by something that is positively charged so protons and eventually neutrons were discovered as well so the next question was how were all these subatomic particles arranged in the atom again many attempts were made to answer this question one of them had that had some had some prominence versus Thompson's plum pudding model where it was believed that the positive charge is delocalized over the atom and the negative charge is embedded in this cloud spherical cloud of positive charges well this did not hold water because I mean why would that happen why do we not get annihilation but even this gives us an idea of delocalized charge we are saying spherical cloud of positive charge right so this charge cloud is something that we go back to eventually we will come to that but all this mostly was a philosophical discussion except for this periodic table subatomic particles dulcetanamic theory those these things the first very very important experiment in my opinion that came towards unraveling the structure within an atom was performed by a student of rather Ford actually his name was Marston the experiment that was formed that was performed was at that time alpha particles had been discovered already and it was known that they are very highly energetic particles so rather Ford asked Marston to do the simple experiment take an alpha particle emitter keep a gold foil in front of it and then see how many alpha particles go through state and try to see whether there is any deviation in the path of the alpha particles how would you know if our particles go straight or they bend a photographic film was placed in the circular manner and this kind of a chamber is what was actually used for the experiment so the alpha particle emitter would be here gold foil would be here and in this empty place the photographic film would be placed in fact this kind of chambers are used for modern experiments even now so it was expected that everything would go through state because alpha particles are so very highly energetic and gold foil is so thin and the observation was that it is true that most of them went through straight but some of them did get deviated and 1 in 20000 would turn back so these arrows that you see here they sort of denote in a cartoon notation what kind of paths are taken by the alpha particles 1 in 20000 actually turned back a result that is very very easy to neglect or push over saying there is a freak result the greatness of rather Ford and the courage of Marston was that they took this result seriously and hence this rather Ford model was proposed what is the model the model is that all the positive charge and most of the mass of the atom is at one point point that is called nucleus and the rest of the atom is practically a void that is why alpha particles go through straight but then what about the electrons they have to be in this void space but if they are stationary then they will be attracted by the nucleus and they would just fall upon the nucleus and get annihilated to explain this rather Ford invoked a planetary model it is known that planets go around the their stars right earth goes around the sun learning from that example rather Ford proposed that these electrons actually go around the nucleus in circular orbits and when they do so the centrifugal force would exactly balance the electrostatic attraction and that is what rather for expected would keep the electron from falling into the nucleus and resulting in annihilation of the atom makes sense right nice model the problem was that from classical electrodynamics it is expected that a charge particle in motion would keep on emitting energy so two problems with that if you look at the emission spectrum emission spectrum means look at the light that comes out and see what is the intensity of light coming out of a particular color so if this is the situation that you have an electron that is moving a charge particle in motion it would give out energy continuously then you expect what is called a continuous spectrum you have all colors no demarcation clear demarcation between two bands unfortunately as we are going to say a little later it is known that for elements the emission spectrum actually has discrete nature we get what is called line spectra besides the problem is if the electron actually emits energy continually then it is going to lose energy right so initially you start from a situation where some centrifugal force is there it is balancing then when it loses energy then it would move slower centrifugal force would be lesser so it would be drawn in a little closer so this way it would actually go around and around in a spiral and fall onto the nucleus and if you do that calculation you will see that the time required for an electron to fall into the nucleus is something like picosecond 10 to the power minus 12 second so that does not give you a stable atom so that is why Rutherford model could not really make too much of headway but it was an excellent start please understand that the experimental result is actually correct it is true that there is a nucleus it is true that the electron is in the mostly void space of the atom but what is not true is that electron is going around in circles to address the situation it required the guts of Niels Bohr but you know no invention no discovery no new observation comes without prior knowledge by and large so even Bohr had help and the help came in a series of fascinating observations made in physics towards the end of 19th century and beginning of 20th century one of them we have already discussed right we said that we have line spectra of atoms we already said that another one was black body radiation we have studied black body radiation in physics in class 11 and 12 I guess so you might be familiar with this kind of a diagram where you plot the energy distribution against wavelength this is called a spectrum it was known that if you increase the temperature the spectrum becomes sharper and more intense and the maximum moves towards smaller wavelength that is higher energy why does that happen to explain it there is something called Rayleigh-Jeans model they tried to explain it by using classical oscillators within the cavity of the black body and they failed they encountered what is called ultraviolet catastrophe so Rayleigh-Jeans considered large number of oscillators oscillating at whatever frequency each can have its own frequency and their distribution is expected to give the distribution that you observe in the spectrum unfortunately Rayleigh-Jeans model can nicely map the spectrum at longer wavelength but it gives a monotonic increase this turnaround is not there in Rayleigh-Jeans model so to answer this question Planck proposed another model and he found that the only way you can actually provide a theoretical description of the spectrum of a black body is to consider that energy is quantized rho here is energy density so you see something called like e to the power hc by lambda kt there hence we get e equal to nh nu that means energy is quantized these oscillators can only take up some certain fixed values of energies integral multiples of h nu where h is a constant called Planck's constant very small number I will leave it to you to find out what the value is and n is 0, 1, 2, 3 this kind of a number okay cannot be negative 0 and positive numbers whole numbers so quantization is something that had already come in an attempt to explain this experimental observation that was one beginning another beginning was this line spectra so what you see here is x axis is wavelength and you get a line well the color is something that is added later actually these are black and white photographs but what you do essentially is that you place a prism or a grating in path of light that comes out of the atom and you disperse it remember dispersion Newton's experiment you take sunlight and put it through a prism it breaks down into what we call seven colors so here the emission emitted light from an atom is made to go through a prism and it breaks down into component colors what you expect from Rutherford model is something that is shown in the top a continuous spectrum what you actually get is discrete lines for sodium these are the lines for hydrogen these are the lines in fact there are more we will talk about that later for calcium magnesium neon so discrete lines which means that only certain packets of energy are coming out of these atoms another signature of bondization so to explain these lines what one can do is one can write an empirical equation like this for each of these spectral lines here wherever they occur the wavelength 1 by lambda or wave number is given by r infinity r infinity is called Riedberg constant multiplied by 1 by n 1 square minus 1 by n 2 square where n 1 and n 2 are 2 integers 1 2 3 4 so on and so forth completely empirical the question is why where does this come from and Riedberg constant you see is we have written it up to 1 2 3 4 5 decimal places so we can actually determine it to 5 decimal places that is the point it is doubted to be the most accurately determined physical constant right and this is the these are the lines for bummer series you see bummer series easier because it is in the visible range but I think you might know that there are actually more Lyman bummer passion bracket fund in different areas different regions of electromagnetic spectrum but all of them can be actually explained by this kind of formula the question is why so to explain why and knowing that Rutherford model does not really go too far Bohr said that I do not know why but I can see very clearly that energies of an electron in an an atom have to be quantized and what you figure was that the angular momentum has to be quantized MVR equal to NH by 2 pi now why angular momentum has to be quantized that can be explained later when we talk about de Broglie hypothesis there is something called de Broglie wavelength associated with the electron so in order to have constructive interference in the wavelength this is the condition that has to be satisfied the interesting thing is from here Bohr could work out an expression for energy which turns out to be minus ME e to the power 4 by 8 epsilon 0 square h square into 1 by n square do you have to remember this no please remember 1 by n square that is all that is required you there is no need to remember the constant what is important is that the energy expression has something in n square in the denominator so now what Bohr said is that as long as this condition is satisfied that MVR equal to NH by 2 pi we have what he called stationary states stationary not as in electron is not moving stationary in energy energy of electron does not change where when they are in the stationary state that is what he meant and then what he said is that there are certain allowed stationary states each is associated with a quantum number n which is 1 2 3 so on and so forth so what would be the energies of this states maybe I will just draw even though it is drawn here you might get confused because the orbits are shown if I just draw the energies let us say this is the energy of the lowest level n equal to 1 whatever its value is energy for n equal to 2 what will that be remember there is a minus sign so it will actually go up and the proportionality will be 1 by n square 4 4 times and then we have n equal to 3 so these are the different energy levels that are there and it is constant multiplied by 1 constant multiplied by 1 by 4 constant multiplied by 1 by 9 and so on and so forth so these are the stationary states now suppose an electron is there in n equal to 3 that is an excited state it has to come down to the ground state or something how does it come when it jumps Bohr said when it jumps from one stationary state to other the energy difference delta E is emitted and this delta E is equal to h nu so that is what is said by Bohr delta E is equal to h nu so now when you equate this delta E to h nu you see you get 1 by n 1 square minus 1 by n 2 square what we have written is n i square minus 1 by n i square minus 1 by n f square i for initial f for final and that if you remember is exactly the same form as read bug equation and from here the read bug constant that is calculated is in agreement with the experimentally determined read bug constant to that seventh place of or sixth place of decimal and the other thing that was calculated using this was ionization potential of hydrogen atom which turns out to be 13.6 electron volt so Bohr theory gives us very good values of energy but then when people took a closer look at it it turned out that Bohr theory was incomplete so with better spectrometers it was found that the spectral lines that were thought to be one are actually many this what is called fine structure to explain this Sommerfeld did an extension of Bohr model taking hints from Einstein's work now plenty of non-mathematical popular literature is available on Bohr model and Sommerfeld model I encourage you to read those so what Sommerfeld said was that corresponding to each value of n it is not necessary that the orbits are always circular you can have elliptical orbits and depending on the ellipticity of the orbits the energies will change a little bit it will not be just depending on n this secondary quantum number k is what Sommerfeld used that is also going to have some effect on the energy. Then the Zeeman effect experiment was done magnetic field was applied and it was found that now the spectral lines increase in number you are splitting of spectral lines that was explained by saying that you have situation like this for any given value of n and k combination it is not necessary that there is only one circular well there is only one elliptical orbit you can have more than one and the number is 12 plus 1 where l is the modified secondary quantum number. So, the range goes from plus l to minus l so here we see 1 2 3 3 orbits so plus 1 0 minus 1 so for this the l value is actually 1 and magnetic quantum number m values are 1 0 minus 1 and if we have this orbits that are oriented in different direction discrete different directions angular momentum vector is perpendicular to the plane of the orbit right. So, that angular momentum vector can also take up discrete orientations in space this is called space quantization I am going a little fast because I think you have studied all this in class 11 12 and how many values of m can be there that was also determined that you can have 12 plus 1 values. So, what does m determine m determines the z component of angular momentum remember we are going to come back to this. So, this model gave rise to a lot of excitement you can see this kind of picture in many places including the logo of our department of atomic energy. However, end of the day this model had to be scrapped why because first of all it is evident that Bohr theory by itself is incomplete you make a new observation you have to extend it that is the problem. Secondly the major tool that Bohr used was calculus integration which is the tool of classical mechanics. So, on one hand you are saying that classical mechanics does not work but you use its tool as long as it works the moment it does not work you say that classical mechanics does not work. So, there is a little bit of dichotomy here but the most important objection against Bohr theory spin is something that I did not talk about we will talk about that later. The biggest problem of Bohr theory came from Eisenberg's work Eisenberg showed that for atomic particles subatomic particles this kind of uncertainty holds uncertainty in position multiplied by uncertainty in momentum has to be greater than or equal to h by 4 pi. So, you cannot determine the position and momentum accurately like what Bohr model tries to do. So, Bohr model is too deterministic in nature and remember uncertainty principle is not about not being able to do the right experiment it is about a natural threshold something that you cannot cross no matter how good an instrument you build. If you study high level courses in quantum physics or quantum chemistry you will learn more about uncertainty principle. But for now let us just say that uncertainty principle was the final nail in the coffin of Bohr model. So, even though it gives us a very good agreement with many experimental results one has to discard Bohr theory and move on to something else look for something else. In fact, this uncertainty principle gave rise to a lot of interest beyond the world of science. So, you get you so this kind of cartoons and all came up but the biggest problem is that uncertainty principle says that you cannot really continue with this nice logic that we have of the classical world you cannot take it too deep into the quantum into atomic world. So, Bohr model has to be discarded you have to look for something else and this something else was provided by Schrodinger in his famous equation this is what we will discuss in the next module.