 Hello everyone I am Ranjan Das in this course of lectures we are going to learn the principles of electron paramagnetic resonance and some of it applications. Electron paramagnetic resonance I am sure most of you have heard another spectroscopic technique called nuclear magnetic resonance. This is abbreviated as NMR and this electron paramagnetic resonance is abbreviated as NMR. There are lot of similarities in these two techniques. Here in NMR the key requirement is that the certain likely I have magnetic moments and because of that magnetic moments some spectroscopy can be done if they are put in magnetic field. In a very similar manner electrons are also known to have magnetic moments and when they are kept in a magnetic field one can do spectroscopy on that. That sense they are very similar. In this course as we learn more of the electron paramagnetic resonance we will see also the similarities and differences in these two techniques. The electron paramagnetic resonance is also known as electron spin resonance or ESR. Both are used in scientific parlance but do they mean the same or is one terminology better than the other? These things we will see later. Right now let us stick to this EPR. This spectroscopy can be used to study host of systems atoms, molecules, free radicals, radical ions, transcendental complexes in all those species which have magnetic moment associated with electron can be studied by this technique. They have wide applications in understanding electron structure, magnetism, phenomenology, photochemistry and biology. They have wide range of applications. So, before we start learning about the spectroscopy it is will be interesting to go through the history of developments of some of the key ideas that led to this spectroscopy. To that end let us start with this person Peter Ziemann. He was a graduate student what you call research scholars of Camerling Owens in the University of Leiden. Now Ziemann wanted to study if magnetic field had an influence on the atomic spectral lines. Those days it was already known that atomic spectra come in the form of discrete lines. So, he wanted to study if magnetic field could show any effect on them. So, as a matter of fact Michael Faraday did try to investigate this but he could not see any effect. And Ziemann's initial attempts also did not show any effect but he was very keen to pursue his investigations. But his professor Camerling Owens did not want Ziemann to waste his time looking for effect that even Faraday could not see. So, he was discouraging him but Ziemann was adamant. He wanted to use stronger magnets, magnets which are lying in Owens laboratory but Owens would not give him permission. So, then Owens went to attend a conference. So, that is the opportunity that Ziemann took to use his magnets and looked into the spectral lines of sodium atoms. And what he saw was that the spectral lines of sodium atom just become a little broad not a great effect but just a little broad. So, this was the first indication of what was to be famously known as the Ziemann effect. Owens came back after his conference and Ziemann was very excited to tell him about his observation that here is the sodium lines and they are showing some broadness if they are subjected to this magnetic field. He was very excited about it but how did Owens reacted to the Ziemann's excitement? Was he happy that Ziemann found something exciting? Did he congratulate him that he saw some effect which even Faraday could not see far from it? He was in fact very angry with Ziemann for not listening to him for wasting his time probably even using the magnet without his permission. So, he simply threw him out of his laboratory. He fired him. So, that could have brought an end to the scientific career of Ziemann but fortunately Ziemann found another position in the University of Amsterdam and there he conclusively showed the spectral lines of sodium paper actually split into 2. Now, this splitting of spectral lines in the presence of an external field is called the Ziemann effect. Now, this effect was now established and he published it in this journal, famous journal Nature and title of the paper was the effect of magnetization on the nature of light emitted by a substance and in the paper he concluded by saying I return my best thanks to Professor K. Owens for the interest he has shown in my work. I leave it to you to figure out if Ziemann was sending a message to his former supervisor. Anyhow, this work was recognized in the form of a Nobel Prize in 1902 for the research into the influence of magnetism upon radiation phenomena. Kamal Ling Owens was of course a brilliant scientist in his own right but he had to wait 11 years before he too could get a Nobel Prize for his investigation of matter low temperatures and production of liquid helium. This Ziemann effect that narrative field could cause splitting was something very difficult to explain or understand the origin of this. Also, many spectral lines were found to come in pairs when they are seen in high resolution. Here is an example of hydrogen atom spectrum and deuterium. So, each of them show this pair of lines together. The difference in their line position is due to the difference of the nuclear mass. So, that is not of serious consequence. It is that these two doublers here and here where this separation is very small of the order of this 0.015 nanometer that was very difficult to understand. Even sodium atom further matter that the bright yellow light that you see in the street lamp that also has pair of two closely line line this very close to each other. So, it is very difficult to explain this doublers. By then Bohr's model of hydrogen atom came. They are the two revolution ideas where that the atoms have discrete energy levels of this kind. And the absorption or emission of radiation takes place because of transition from this one discrete level to another discrete level that is the first key proposal of Bohr. So, this discrete nature of energy levels could very easily now explain the discrete spectral lines seen in the spectrum. But they are still not sufficient to explain then this doublers the way they appear here. This is the sodium atom spectrum and the one is to shown here for hydrogen and deuterium atom spectrum they very difficult to explain. In fact for sodium atom the transition involves 3 p to 3 s orbital. In Bohr's model these are degenerate. So, the limitation was obvious that everything is not quite understandable. But Given effect could be explained based on this model because Bohr had another key ingredient in this model that is the discrete nature of the angular momentum. Before that it was assumed that algorithm can take any arbitrary values. Bohr said that no it will take only discrete values. Later with the Schrodinger formulation of quantum mechanics this is known to be that the angular momentum value will have this kind of magnitude it is called l magnitude of l square will take this type of values. And the component of any arbitrary direction will have any particular z direction m l h cross. Here the value of this small l has to have this type of values similarly m l will take minus l to plus l changing in units of 1. The important point to notice here these are the all integral values. With this ad hoc requirement that Bohr has imposed one can explain the Ziemann effect in this way that motion of charges produces current and current can produce magnetic field as shown by Faraday. So for example if there is a wire through which current is flowing it will produce a magnetic field around it and that can be easily seen by placing a magnetic compass and depending upon the direction of the current the middle of the compass can either move this way or that way or further matter we have a let us say a loop of this kind where current is flowing then it can produce a magnetic field which will have direction either this way or that way. In fact solenoid is the very common example of producing magnetic field by passing current through a coil. So that sense the orbital motion of the electron can have magnetic moment because of this sort of motion in the atom and that magnetic moment can be influenced by the magnetic field which is the Ziemann effect. So it is possible to explain Ziemann effect in this fashion but the trouble is that not all such spectral splitting that was seen in the presence of magnetic field cannot be explained by associating the orbital angular momentum and the corresponding magnetic moment those things many of those spectral lines which are seen to be split cannot be explained that way. Something was missing so Pauli Ulfeng Pauli said that he could explain many of these doublets here for example or doublets which are seen that many of such doublets not necessarily this particular one or this particular one many such doublets could be explained if it is assumed that electrons are allowed to take this quantum number Z n, n and m l in pairs that is two electron will have same values of this kind not more than that. So this sort of double valuedness double valuedness if it is accepted then many of this doublet spectral lines can be explained of course now we know that this is nothing but the Pauli external principle that is what is in mind. So why it should be so was still not clear and not only that that does not explain all the observations of this doublets. Meanwhile important experiment was carried out by these two people Otto Stern and Woller Gerlach what they did was to pass a beam of silver atom through an inhomogeneous magnetic field in this experiment is done in this way let us say this is a magnetic field the pole pieces are made such a way that the field will be very inhomogeneous the field lines will look like this and they have a source of silver atom which is coming here and they are allowed to fall on a detector some sort of scheme here silver atom is known to have this electronic curve 4d10 5s1. So naturally according to this model it does not have any angular momentum so what is expected that since it has no angular momentum it will also not have any magnetic moment. So in this atoms are allowed to go through this inhomogeneous magnetic field they will not experience any particular force so what is expected they will sort of fall here and probably form some sort of lump here that is what the expectation and let us see what they observed. So here is an animation we sort of tries to describe this experiment here is the source of silver atom their collimator so that we get a sort of narrow beam of silver atoms and this long thing is the inhomogeneous magnetic field and this is the screen which detects the silver atom so let us see what happens so the silver atoms are coming from left and going through this magnetic field and see they are falling apparently randomly on the screen so you see that they seem to be piling up in two places yeah now the is piling up it is very obvious that the beams are falling in two places and two piles are formed there so it is not what was expected here that they fall expected that maybe they will fall only one lump so this is again very extraordinary finding it cannot be explained by the known electronic structure. So they send this finding to Niels Bohr in a postcard enhancing that they found the splitting of this silver beam particularly because the silver atoms did not have any angular momentum. So here is the actual photograph the magnetic field was off all the atoms fell here a single lump where the magnetic field was on they saw splitting. They published their result in this journal search group for physics with the title the experimental proof of directional quantization so this is the famous here yet again this is a very difficult experiment that correction once again it is very difficult to explain this observation because this silver atom with this configuration does not have any suppose to have no magnetic moment no angular momentum no magnetic moment but even then it saw splitting it means it must have got something to do with the magnetic field that is experienced by this and this is causing splitting and it was splitting over two lines. So yet another extraordinary finding without any explanation then these two persons said that they have a way to explain this splitting of silver atoms they are two young graduate students of they had a very extraordinary and rather novel model of silver atom they come up with a very novel proposal they said that this Paul is double occupancy of electrons or the Stern-Gulloch experiment result both could be explained if they make an ad hoc assumption that electrons have another degree of freedom which is their sort of spinning about its own axis so then this spinning in this way clockwise fashion or anti-clockwise fashion it can give a magnetic moment in this direction or that direction these two types of magnetic moment can interact with the magnetic field here and it can split into two and similarly it can also explain the double valuedness of Pauli. Important thing is that the angular momentum that the silver atoms would have will have the integral values but half integral values if I call them let us say s this will have value of half m s equal to plus minus half which is quite different from what has been accepted till then so Erenfest suggested that they discuss this with Pauli now Pauli was a towering figure in science and he was a very severe critic of his own work as well as work of others. So when Ulernberg at Gausmit went and talked to him about their model he simply said this is nonsense he damned their work it is also true that the calculation of Ulernberg Gausmit was differing by factor of 2 from the observation so there are then Erenfest send these two young men to discuss with Hendrik Lorenz Lorenz to dismiss their model of spinning electron what is the normal Lorenz complaint here it is okay if the charge is rotating it can produce magnetic field fine but let us estimate what type of situation one needs to produce a situation which can explain this deflection see if so this is the spinning model of electron which is spinning in this fashion there is an electron negative charge this here nuclear sizes are exceedingly small of the order of 10 to the minus 5 meter what is called one Fermi and electron size is even smaller about 1000 times smaller than this so if the electrons rotation of this kind is actually producing the observed effect the surface of the electron has to move at 10 times the speed of light so clearly this is nonsensical so Ulernberg Gausmit become very dejected and came back to Erenfest saying that they wanted to withdraw their paper from publication but Erenfest replied that their paper was either very important or nonsense and he has already sent the manuscript for publication then he added that you are both young enough and you have no reputation so far to lose so you can permit yourself a folly that is if the suggestion of yours turns out to be important he will become famous but if it does turn out to be nonsense then you do not lose anything the paper was published in this journal natural vice and shaften and later calculation using Erenfest correction also took care of the factor of 2 which initially they had trouble explaining so this suggestion of Ulernberg Gausmit did turn out to be very very important now angular momentum integral kind angular momentum can also be half integral that is s equal to half ms equal to plus minus half is also possible here from integral to non-drugal that is a very drastic difference so therefore electrons do have magnetic moment which arising because of this motion so everything really fell into places but the Lorentz complaint that electrons are spinning this way that complains is valid so what is now accepted that one must not take this spinning motion one must not take the spinning motion very literally though it is very easy to visualize the motion of the electron electrons are not really spinning around the axis the way earth rotates around the axis to produce day and night electrons are not doing that kind of motion one must take it to be an intrinsic property of the electron that has angular momentum of this type of magnitude and it takes two components and also it has no internal motion to really give us a visual picture of what is happening there we just take it to be intrinsic property angular momentum of this kind and the intrinsic magnetic moment so these two are intrinsic property we may not feel very comfortable about just accepting this as intrinsic property but we do get used to such ideas when you keep using them often for example in our daily life we have really accepted many of these things as an intrinsic property without questioning them mass for example what is mass is amount of matter what is the matter that is very difficult then answer will be that what the amount of mass that is present so you see we are not making any progress by explaining the concept of mass similarly what is charge electron has negative charge proton has positive charge what are they what are these charges can you really explain them we really do not have an explanation except that we take them to be property of the particles which shows how they interact that is positive charge and positive charge they repel each other that is the way it is so once we know that they have certain properties and to explain the properties we have to have this concept in the same way intrinsic properties of spin angle momentum and magnetic moment can be accepted to say that the host of things are explained and we get used to using them intrinsic properties like mass and charge anyhow coming back to now spectroscopy that Ziman showed the splitting of energy levels now if the energy levels are split one can look at the transition among the split lines and that is nothing but the electron parametric resonance spectroscopy so this was first observed by Russian scientist Zavojski in 1944 in cupric chloride not many people believed his finding not even Soviet scientist he published his work in 945 in a Russian journal so it took time before it was noticed by the international scientific community nevertheless this was his PhD work PhD thesis work and he got his PhD 945 this is the one EPR spectrum that recorded in chromium chloride so these are the way the history of science science in particular 11 to the properties of electron and how it leads to the existence of magnetic moment which can be which can be influenced by magnetic field and that can give rise to different energy levels and that can give rise to spectroscopy and that is the EPR spectroscopy.