 Okay, so if not, we will go ahead and start our next topic. So today we will start studying about Mossberg spectroscopy. But before starting Mossberg spectroscopy, we will go a little bit on the spectroscopy in general. We try to learn a little bit about spectroscopy in general that what is spectroscopy because we actually use this term so commonly. So let's take a look into a little bit more details. So when we do spectroscopy, we actually measure at least two parameters. One of the parameters is the intensity and one of the parameters is energy. And generally we see a signal like this and this particular signal actually give you information about two important parts. First is that what is the maximum point that you are getting this signal, which particular point it corresponds to the y-axis and which particular point it corresponds to the x-axis. And this two system where it is dissecting the x and y-axis, this actually give you two important information. First the intensity. The intensity give you an idea about how much of a system is a present. So it is, can be written as quantitative. So you can have a quantitative measurement of that system. For an example, you are looking into an optical spectroscopy, you are looking into a particular optical absorbance, say in two pi-star absorbance of MIT. If you know that you have a one molar concentration versus a 10 molar concentration, if you record what will be the difference, the 10 molar concentration will have 10 times more absorbance compared to the one molar concentration. And that will define with respect to the intensity. The bands will probably look the same, but the intensity will differ. So the intensity give you the idea how much of that particular system is present there. So it is quantitative. On the other hand, where do you cross the x-axis, the energy axis? That is giving you an idea what is that particular transition is, which is connected to what is your sample. So that is known as the qualitative measurement, you can say. For an example, if you take a amide bond based protein versus a polyethylene glycol polymer, and if you record the optical spectroscopy with the same concentration, the first thing you will see the bands are not in the same position with respect to the energy axis. So that is from there you can say that this is actually pi to pi star transition happen at 195, 222 nanometer or 300 nanometer. So all these particular terms you say with respect to the wavelength, we are actually saying with respect to the energy. And from there we can qualitatively say exactly what is present on it. Now when we say about intensity and energy, there are different ways to represent it. So you can do a simple optical spectroscopy. In optical spectroscopy, what is the generally or typically used y-axis, absorbance and the generally used x-axis is the wavelength. So in the absorbance, it is actually giving an idea about the intensity. So it is in lieu of intensity we write absorbance, but it is actually defining the same thing as intensity. Whereas on the other side, the wavelength, it is actually giving an idea about the energy. How? Because we know energy can be written as hc by lambda. So this is the lambda, this is the energy they are connected. So this wavelength over here that we have drawn, it is not anything, but it is a representative of the energy. Obviously they run in the opposite side. So higher the wavelength you go, you are actually lowering the energy. On the other hand side, if you go lower in the wavelength, it is going to the higher energy. And over there, if you see some absorbance bands, so you can say like what is the absorbance over there, from there you can quantify how much the sample is there. And from this particular bands, you can say about the wavelength or energy and what is that particular sample. So that is what happens in optical spectroscopy. On the other hand, the other way you can do that for an example, if TIR or IR spectroscopy. In that case, instead of an absorbance, we take something called transmittance, percentage of transmittance. Like how much of the electromagnetic radiation you have given to the sample, how much it is passing through. So it runs from close to 0 to 100. So if it is 100 percent transmitting, that means nothing is absorbing. So 100 percent transmittance is equivalent to zero absorbance. And if you are having a huge absorbance, that will be giving you a low transmittance value. So a transmittance value over here is written, but it is now actually giving you an idea how much is the intensity of a particular band. Higher is the transmittance, higher is the intensity. On the other hand, when we look into a FTIR, you can see the X axis is something called a wave number. That's omega centimeter inverse. So if this is also again actually a definition with this, it is connected to the energy, hc omega cross. So this is nothing but opposite to the wavelength. So now higher is the wave number, higher is the energy, lower is the energy. So that is how this IR spectroscopy is given. Now if you take a look into any other spectroscopy, that you have come forward in your life, you will always find there are two axes. One is the intensity, one is the energy. Intensity gives you an idea like how much of a sample is this, qualitative. Quantitative and energy is given by the X axis. It gives you like the qualitative data, what exactly, what are the different kind of samples you have in your system. So that is how the different spectroscopy has been done. Now one thing is also very important in all the spectroscopy, exactly what I am changing. So it is quite straightforward that I am giving an energy from the respect to the electromagnetic radiation that is changing something in the molecule and that is why I am getting a signal. And that signal I represent with respect to intensity versus energy, that is fine. Now the question is from where this particular change is happening. So spectroscopy, one of the most important part is change in energy states. Because unless you change the energy state, you won't see any signal. So what are the different energy states are happening? So I am going to give you a few examples, what are the different energy states are changing and then we will pass it to the mass spectroscopy. First one, I am going to talk you about the NMR spectroscopy, nuclear magnetic resonance. So nuclear magnetic resonance, what are the things I am changing? So over here the state I am mostly interested in is nuclear magnetic state. So first is a nuclear state, but this term magnetic is also there. So what that means that I have a state, so this line I am drawing by that I am showing you with respect to the energy value at one particular point where the molecule is and over there I am writing say it is i, i is representing its nuclear magnetic state and say this i value is half. Now this i value is half over here unless you put a magnetic field there is no other electronic state, sorry the nuclear magnetic state or nuclear state is interacting with that at this point. It is only one state, i equal to half. But once you put a magnetic field over here then you see a change in the energy of the state and this state can now present in two different states and say one is in i equal to plus half, one is i equal to minus half. So what is this plus half and minus half? I am coming into a little bit later but what happens over there in presence of the magnetic field these two states actually comes on from this original i equal to half state and this happens only in the presence of the magnetic field. So we generally write this m and put the i as the subscript. So it gives us in presence of the magnetic field only these states can be deeper. And over there you can give an electromagnetic radiation and then this i equal to plus half state can be transformed into i equal to minus half state and you see a resonance, you see a signal. Now the question is that what is that electromagnetic radiation I should use that will depend what is the energy gap over here and that depends on the applied magnetic field. In NMR, in NMR typically this electromagnetic radiation we are using it happens to be in the radio frequency and radio frequency is one of the most weakest electromagnetic radiation you can come up. So it is a very weak electromagnetic radiation that means this energy gap over here is actually not that split up it is very close to each other. Now the question is what this plus half and minus half mean to come. So generally what we studied that plus half and minus half means the nuclear spin state can orient in two different ways one along with the axis one against the axis if it is along with the axis it is plus half if it is against the axis it is minus half. But the question comes what is this plus half and minus half like why where these numbers are coming from. So if you understand if you want to understand that you have to look into exactly what happens to this nuclear spin state when a magnetic field comes over there. So in the beginning what happens you have a nuclear spin present over here which can be present in any particular direction it can be in any particular direction it can be present in three-dimensional it can be present in any particular direction because there is no one to influence it. Now once you put the magnetic field you are perturbing the system. So the previously the nuclear spin state the i is equal to half state it is actually stable in any particular direction with respect to the surrounding of it that means whatever the Hamiltonian is. But once you put this magnetic field now you are perturbing the overall Hamiltonian you are including or introducing something new with respect to that now you change the full scenario now you have a different Hamiltonian and a different Hamiltonian and with respect to that you can find this particular spin state which was previously can orient in different ways now it can orient in the following way. The first way is it goes towards the top side with respect to the magnetic field and not only that it present but it also start rotating around it making this kind of cone shape so you can imagine so it is actually rotating around and this kind of motion is known as a precession motion. So this particular nuclear spin start precessing around why it is happening because it is a spin state i equal to half which is a non-zero value that means it has a non-zero value and that is why it actually originally have some magnetic field present in there in this nuclear spin state and this magnetic field in the influence of the external magnetic field started interacting with it there actually you can imagine there you are putting two different magnets one strong one this external one and one is a weak one the nuclear spin one and the weak one is actually controlled by the presence of the magnet strong one and it start precessing around the system okay now when it start precessing what is the angular momentum because it is actually having a motion so obviously it is going to have some angular momentum the angular momentum is fine as following i into i plus one h by 2 that is the angular momentum of this system and it has been also found that it is not only it can stay upside it can also have a motion with a downward direction and this also can precess creating a another very similar looking cone but upside down and over here what is the angular momentum the same root over i into i plus one into h by 2 that is the angular momentum of the system now where is this plus of and minus of coming now over there when is cones are prepared or cones are actually formatted or generated we try to find out with respect to the magnetic field it is always going to be the different amount of motion is actually generated however the overall precessional motion that is going to be same but at which particular direction it is moving that is also going to be same up and down but how much it is actually moving that can be differ with respect to the magnetic field because that is going to differ what is the energy difference between these two states so to describe it much more easier way because i don't want to use this kind of a huge expression in my energy root over i into i plus one into h cross by 2 that is very tough to use so with respect to that what we want to use is that this is making a motion on the top side or downside that is fine but how much it is actually creating a projection on the original external magnetic field so it is creating actually a projection on this external magnetic field and we try to figure it out what is the value of this projection and what has been found this value is nothing but half into h by 2 pi this is also half into h by 2 pi so from there this term half actually comes now you can question like where why it is particular this term half that is a quantum mechanical phenomena that is coming because of this nucleus pin of half if it is 3 by 2 you can get different orientation starting from 3 half half all together and now if it is along with the axis we say to differentiate these two halves we say this is the plus of system and this one against the magnetic field direction we say it is the minus of system so that is how this plus of and minus of terms comes because it is along with the axis we say it can be found easily because it is along with the axis the magnetic field are not against each other the external and the small magnetic field you have in this molecule so that is why this is the ground state and this one actually moving against the tide or the external magnetic field so that is why it is the excited state minus so that is how this term plus of and minus of actually originate so with respect to that the same system happens even with all the different orbital quantum number that we have defined like plus 3 plus 2 plus 1 all those things we define all those things actually come for the similar way okay now in that NMR if we go a little bit further NMR the energy gap between the nuclear state of say half how much it is going to differ i equal to minus half and i equal to plus half and i like am i to ensure that it is in place of the magnetic field so how much will be the energy gap that delta e what are the things will be dependent on first thing is obviously the external magnetic field and the second thing comes is that nuclear itself so this nuclei has a magnetic moment right the magnetic moment obviously it is connected with this quantum number half but it doesn't show up the actual magnetic moment that can be different and this magnetic moment can differ for different nuclei although they may have same spins nuclear spin state so for an example i'm taking a few nuclei right you have probably already encountered in your life so these four nuclei proton 13c 19f 31 all of them the thing common is they're all the most commonly found isotopes nuclear spin state is half so all of them is going to split in plus half and minus half now if i put a similar amount of external magnetic field does it mean that all of them will split up with the same energy gap if it is then the NMR will not work because all of them are going to pieces at the similar region they're going to give you the same bands thankfully they are not that is because their magnetic moment the nuclear magnetic moment which is a property of the nuclei itself that means it is a property of this particular each of the isotope itself that is actually different and if i put that in the term of e h by 4 by mc that is the unit which can be taken as the nuclear pore magneton unit forget about that actual term but the values you can see 7927 for proton for 13c it is 0.7022 for 19f it is 2.6273 for 31p it is 1.1305 so the rest of this is same that is i equal to half but this magnetic moment is different and depending on this magnetic moment this energy gap will be different and they are going to follow the same ratio they have and that is why if i use the same magnetic field of one particular magnetic field say i am using 1.5 tesla or something like that one particular common magnetic field what is going to differ is that energy gap that will be differ for each of them and this delta energy gap we can differ or define with respect to a electromagnetic radiation and as we have discussed earlier this is nothing but a radio frequency so for each of them i can write a radio frequency at which they will be doing this change they will attend the resonating condition and that happens if i take it as a 500 megahertz that means 500 into 10 to the power 6 hours or per second unit for proton that will not work for 13c because they have different magnetic moment so where what it will work the same ratio of this so find out what is the ratio of this with respect to that the same ratio will work for 13c and that is 126 megahertz similarly for 19f it is 470 megahertz 19f and proton pretty close but not exactly same and 31p it is 202 megahertz so that is how the nmr actually works you actually give a a electromagnetic radiation in the form of radio frequency so whenever we talk we have a 500 megahertz nmr machine we are talking about the radio frequency that we require to achieve the resonating condition over here and when you say 500 megahertz we actually talking about the proton nmr so what proton in this particular fields generally it is 1.6 to 2 tesla energy gap and that particular external magnetic field if you apply you need 500 megahertz of radio frequency to make sure the resonating condition is met if you want to do the 13c in the same experiment same instrument what you need to do you have to change the radio frequency you have to change it to 126 so that it can occur and similar and so forth that is how it actually want what in the nmr so again it is very important why i'm talking about this nmr so much it will be clear in a few minutes but first and more important thing over here what i'm changing is the nuclear spin state i already have a nuclear state it has a non-zero value only if you have a non-zero value you can split it up if you have a i equal to zero value you cannot split up so you are not going to see any nmr for an example 2 of c you don't see an nmr however if you have a non-zero value and generally i equal to half is a simple one because you have only two different spin state possible plus up and minus up if it is a one state i equal to one you can have two three states plus one zero minus one so you can precess in three different directions and you can have three different projection on the external magnetic field what we are talking about so this is what is actually happening over here so we are only seeing the difference in presence of magnetic field now what happens if we do the same experiment with electronic spin you can also do that same system with electronic spin you can have a spin state of half of one unfair electron in the presence of a magnetic field you can split it up it can go to s equal to now minus half is the ground state and plus half is the excited state why it is different with respect to nucleus because they have the different charges opposite charges so due to that their signature changes plus to minus the rest of the things remain same and this is the energy gap you have it is also again depends on what is the magnetic field you are using and also two important parameters which define the condition of the electron in the molecule which is term as a g term and a beta term beta is nothing but e equal to 4 by mc for electron i'm not going to the details of it but over here the magnetic field is important and the g value defines how the electron is behaving in the molecule okay if it the electron is free not interacting with anything else the g value is around 2.0023 it should have been 2 but it's a little bit higher because of the relativistic efforts anyway so over here again the electron spin if you put it around the external magnetic field can orient in two different ways and precess and create two different orientations one is with the system minus half one is against the system plus half and again if you take the projection of it you'll find it is half into h by 2. Whereas what is the overall angular momentum root over s into s plus 1 h by 2 that is same for both of them but their projection is half into h by 2 okay and once we say plus up because of this directionality on its minus up because it is against the magnetic field so that is also happened for electron spin and we call them the ESR electron spin resonance or EPR electron parametric resonance and over there this energy gap a little bit different because the magnetic field generated by the electron is not exactly same as the nucleus so this g value this beta value is different over there the electron has a much more smaller mass so this value is much more higher and with respect to that this energy gap is falls in a totally different region now if you want to excite it hit with a electromagnetic radiation this electromagnetic radiation falls now in the range of microwave previously the NMR was in radio frequency but EPR falls in the