 Hello everyone, I once again welcome you all to MSB lecture series on interpretive spectroscopy. Today, let us look into briefly about mass birth spectroscopy. So let us me begin with some background to mass birth spectroscopy for a wide variety of chemical problems associated with synthesis, characterization and elucidation of structure involve a spectroscopic study intense spectroscopic study to accumulate evidences in support of molecules that are generated in the laboratory. That means basically when we make a molecule to know whether we have made a molecule the same molecule we anticipated or something else got or we got some byproducts and all those things to understand in a proper way we involve spectroscopic studies. In most of the spectroscopic studies what we do is we observe lines or bands as we see in case of IR, UV visible, NMR, ESR and mass spectrometry which involve some sort of excitation or transitions and absorptions or emission of appropriate energy taken from the electromagnetic radiation or involving electromagnetic radiation of different wavelength and different frequency depending upon the energy required for such transitions. For this purpose a quantum source with a broad or nearly flat response or a range of energies a glob or incandescent light earlier was used or by scanning a wide range of energies through a continuously variable window varying magnetic or electric fields in case of NMR, ESR or mass spectrometry. So only in fluorescence fluorescence resonance spectroscopy I am referring to a narrow band of energies emitted by a quantum source exactly matches the trans energy in an absorbed material. So because of the considerable success resonance spectroscopy achieved in optics and atomic physics a number of attempts were made by scientists soon after the discovery of gamma radiation to extend its utility in fluorescence spectroscopy to nuclear transitions. Most of these early experiments either were inconclusive or led to resonance absorptions which were so small and questionable. So the reason for these failures was mainly the line width of the transition as compared to the recoil energy suffered by the source and the absorber as a result of the transition. The width or of a spectral line emitted by a source is related to the mean lifetime or of the excited state from which the transition to the ground state originates by the uncertainty principle tau r equals hash. That means this one will be equal to 6.58 into 10 raise to minus 16 over r r in seconds electron volts. So in optical transitions where r equals to 10 raise to minus 10 seconds or r is approximately equal to 7 into 10 raise to minus 16 electron volts in the case of fluorescence excitation or may be several seconds in which case tau is less than 10 raise to minus 16 electron volts. So when a nucleus undergoes a transition from state e to the excited state to the e ground state by the emission of a photon the conservation of momentum requires that the momentum of the autumn p m is p m remember recoiling in one direction is just equal and opposite to the momentum of the photon p gamma emitted in the opposite direction. The kinetic energy of the recoiling autumn is e r so that for an autumn of mass m and velocity v we can use here e r equals half mv square that is p m square over 2 m. Moreover the momentum of a photon of 0 rest mass is related to the energy by this equation e equals p r c. So that when you just square it p r square equals e square over c square since the 2 momentum must be equal it follows the fact that e r equals e r square over 2 m c square. So this is the background for mass per spectroscopy. So that means now what is mass per spectroscopy is of course the made an attempt to see nuclear spin transitions using gamma radiation. So mass per spectroscopy is a versatile technique used to study nuclear structure with absorption and re emission of gamma rays part of the electromagnetic spectrum it comes at the end. Then technique uses a combination of mass per effect and Doppler effect or Doppler shift to probe the hyper plane transition between the excited and ground state of the nucleus. The spin transition and the electronic transition electronic spin transition now nuclear spin transition mass per spectroscopy. How the spectroscopic method is all you can see mass per spectroscopy request the use of solids or crystals which have a probability to observe the photon in a recoil less manner. Many isotopes exhibit mass per characteristics but the most commonly studied isotope is 57 iron. Introduction about this one is Rudolf L. Mossbar in his name this mass per spectroscopy is known. Obtained a bachelor's in physics from the technical institute of Munich Germany and started doctoral work in 1955. Meanwhile he was working as an assistant lecturer in the Institute for Mathematics and in 1958 he obtained his doctoral degree and also he graduated and during that time he showed experimental evidence for recoil less resonance absorption in the nucleus which became popularly known as Mossbar effect. In 1961 Mossbar was awarded the Nobel Prize in physics and he became the professor of physics at California Institute of Technology. So, this is a a chose the typical Mossbar how gamma energy is emitted here. This is the recoil less emission and this is resonance of the ocean and this is gamma radiation. It is the ground state and this is the excited state of nucleus. So, that means the recoil energy associated with absorption or emission of a photon can be described by the conservation of momentum. So, pr equals p gamma. The recoil energy is inversely related to the mass of the system. For a gas the mass of a single nucleus is small compared to a solid and the solid or crystal absorbs the energy as phonons quantized vibration states of the solid. But there is a probability that no phonons are created and the whole lattice acts as the mass resulting in a coil less emission of gamma ray. The new radiation is at proper energy to excite the next ground state nucleus. The probability of recoil less events increases with decreasing transition energy. So, of course these equations already I showed you in my previous slide. So, now what is the Doppler effect? So, Doppler shift describes the change in frequency due to a moving source and a moving observer. For example, it is given by f equals v plus v r over v plus v s into f o and what is f is the frequency measured at the observer and v is the velocity of the wave in this case and c is the speed of light and v r is the velocity of the observer and v s is the velocity of the source which is positive when heading away from the observer and f o is the initial frequency and then this can also be correlated in this fashion. In case where the source is moving towards the stationary observer the perceived frequency is higher. For the opposite situation where the source travels away from the observer the frequency recorded the observer will be lower compared to the initial wave. The energy of a photon is related to the product of Planck's constant and the frequency of the electromagnetic radiation. So, thus for increasing frequencies the corresponding energy also increases and the same is true in the reverse case where frequency decreases therefore energy decreases. So, this is E r equals h c by lambda equals h nu. So, this is the equation of course generally we use all energy calculations between drought state and the exact state. The energy difference between the hyperfine states are minimal and the energy variation is achieved by moving the source towards and away from the sample towards and away from the sample in an oscillating manner at a velocity of a few millimeters per second. The transmittance is then plotted against the velocity of the source and a peak is seen at the energy corresponding to the resonance energy here. Then in case of the most common isotopes studied using mass per spectroscopy is 57 E f e, but many other isotopes have also have displayed mass per spectrum. Two criteria should be satisfied that the exact state is of very low energy resulting in a small change in energy between ground and excited state. This is because gamma rays at higher energy are not observed in a recoil free manner meaning resonance only occurs for gamma rays of low energy. The resolution of mass per spectroscopy depends upon the lifetime of the excited state, the longer the excited state the better the image. So, then both the conditions are met by 57 E f e that is the reason it is very popular and well studied and that is used extensively in mass per spectroscopy. So, then is it possible to do similar studies with other elements in the periodic table? Yes, there are quite a bit of elements we can study using mass per techniques. See whatever that is marked in the red color here the all one can use mass per spectroscopy to see nuclear transitions to understand about nuclear structure in these red colored elements in this periodic table. Let us discuss about hyperfine interactions in mass per spectroscopy. So, mass per spectroscopy as a probe that gives insight into the structural elements of the nucleus as I mentioned such as isomer shift quadrupole interactions and magnetic splitting mass per spectra are capable of revealing all these effects. What is isomer shift? An isomer shift occurs when non identical atoms play the role of source and absorber thus the radius of the source is different that of the absorber and the same holds that the electron density of each species is very different. The coulombic interactions affect the ground and excited state differently leading to a energy difference that is not the same for two species this is well illustrated in this equation shown here. What is delta is the change in energy necessary to excite the absorber which is seen as a shift from the Doppler speed 0 to v 1. The isomer shift depends directly on the s electrons they are very close to the nucleus and then can be influenced by shielding of P, D and F or electrons. From the measured delta shift there is information about the valence state of the absorbing atom. This shows the energy level diagram per shift shows the change in the source velocity due to different sources used here. The shift may be either positive or it can be negative here it can also come here. So, now let us look into quadrupole interaction. The Hamiltonian for quadrupole interaction using again 57 iron nuclear exact state is given in this equation here you can see here. The nuclear exact states are split into two degenerate doublets in the absence of magnetic interactions. For the asymmetry parameter doublets are labeled with magnetic quantum numbers with the doublets having higher energy. The energy difference between the doublets is given by this equation here delta eq equals eqv over 2 into square root of 1 plus eta square by 3. So, the energy diagram corresponding spectrum is also shown here. This is the energy diagram this is first you can see here isomer shift is there and then quadrupole splitting is there you can see two lines are there and one is here one is here and one is positive one is negative here. So, then magnetic splitting magnetic splitting seen in mass space spectroscopy is due to the nuclear spin moment undergoing dipolar interactions with the magnetic field again. So, this is gn and then beta n b effective m i. So, here gn is a nuclear g factor this is nuclear magneton beta n. In the absence of quadrupole interaction the Hamiltonian splits into equally spaced energy levels on either side either side you can see for example, here if you see typical in the ground state to excited state i equals 3 by 2 again 57 iron we had taken i equals 3 by 2 there and then this is isomer shift and then you can see here this is split into minus half and plus half nucleus here and then here this 3 by 2 is split into 3 by 2 half minus half minus 3 by 2 as a result we see 6 transitions are there and you can see they are equally spaced from here 0 3 and 3 here symmetrically. So, the allowed gamma stimulated transitions of nuclear excitation follows the magnetic dipolar transselection rule delta l equals plus or minus 1 and delta m i equals 0 and plus or minus 1. So, both are possible here i equals magnetic quantum number and the direction of beta defines the nuclear quantization axis and if you assume g r a isotropic where g x equals g y equal g z and b is actually a combination of the applied and internal magnetic fields then this equation will be h equals g beta s b as minus g n beta n b dot i. So, electronic Zeeman term is far larger than the nuclear Zeeman term meaning the electronic term dominates the equation. So, s is approximately calculated in this fashion will be equal to plus or minus half or s x and s y equals 0 s z is plus or minus half. So, we are considering z axis. So, h n equals a s i minus g n beta n b and i. So, now with these calculations it comes and eventually what you get is you get this term here. So, substituting the internal magnetic field with b internal a s over g n beta n and this results in a combined magnetic field term involving both the applied magnetic field and the internal magnetic field. Internal magnetic field generated because of the magnetic behavior of those nucleons. So, which is simplified by using the effective magnetic field b effective the net magnetic field x minus by the nucleus. So, this one is h n equals this h is net magnetic field influenced by this one is g n b n beta effective into i. So, now a different form of molecular excitation is that of changes in the energies of the atomic nuclei. In general, enormous energies are involved and such excitation will not be of interest to the study of organic chemistry unless the atomic energy levels are detectably influenced by the chemical surroundings of the nuclei. Usually this is not so, but there is no one form of nucleus spectroscopy known as mass bar spectroscopy which is capable of giving chemical information. That technique would be used widely if there are more nuclei with the proper nuclear properties. For organic chemistry probably the most important available nucleus is the iron nuclei and many biological systems we have iron 2.2 percent of the natural mixture of iron isotopes. So, iron occurs in many biologically important substances such as hemoglobin, myoglobin, cytochromes and also iron storage substances such as ferritin and so on. And there are a number of other types of stable organo iron or aromatic compounds are also known as simple as ferrocene, cyclobutadiene, iron tricarbonyl or cycloactatetroin, iron tricarbonyl because iron FVCO5 if you take its 80 electron species with the metalene 0 valence state. And then of course in case of ferrocene again its 80 electron species with iron is plus 2 state whereas in case of tetroin it is only 6. So, 2 electrons are coming 2 double bonds are giving eta 2. So, 4 electrons are there and it is also a neutral 0 species. These compounds in all these compounds one can use mass bar spectroscopy as a probe to analyze these molecules. These compounds present unusually difficult problems in how to formulate the bonding between carbon and iron, but important information has been obtained for substances by mass bar spectroscopy. For example, here when we react cycloactetetroin 4 double bonds are there and of course we know that 4 all the 4 double bonds cannot go to the same metal because of the puckering nature of that one. So, only at most at a time eta 6 it can is eta 6 or it can be eta 6 and eta 2 for the other one, but nevertheless it cannot show. So, this information of course one can also get by simply look into other ligands here, but nevertheless to get more insight into the internal structure mass bar spectroscopy is quite helpful in iron compounds. So, the essence of mass bar technique is applied to Fe 57 follows a radioactive sieve nucleus is converted into for example, the essence of mass bar technique as applied to Fe 57 follows a radioactive cobalt 57 nucleus captures an electron and is converted to an excited Fe 57 nucleus, which then emits a gamma ray and becomes an ordinary Fe 57 nucleus. So, this how you can tell how Fe 57 is formed from radioactive cobalt 57. If the excited Fe 57 nucleus is in redic material, so that there is no recoil motion associated with emission of the gamma ray, then this rays extraordinarily monochromatic has a very small delta nu even though of great energy 14.4 kilo electron volt that means 3.3 into 10 raise to 5 kilo calories per mole. When such a gamma ray passes through a sample containing 57 atoms Fe 57 also held rightly the gamma can be absorbed to produce another excited Fe 57 nucleus. So, the chemical environment of the iron atom can change the wavelength at which the absorption occurs. That means, the problem is how to vary the wavelength of the gamma rays to match the nuclear absorption frequency. The way this is done is almost unbelievably simple move the sample back and forth a few millimeters per second in the path of the gamma rays and measure the velocities at which absorption takes place. So, this is a simple method strategy that is used. So, the velocity of light is 3 into 10 raise to 11 millimeters per second. Of course, according to conveniently we use different units here we are using millimeters. Therefore, a Doppler effect of 1 millimeter per second corresponds to a difference of only 1 power in 3 into 10 raise to 11. So, however the selectivity of the recoil less gamma ray emission from excited Fe 57 nucleus and the order of 1 part in 5 into 10 raise to plus 13 equivalent to about 7 centimeter variation in the distance from the earth to the sun. So, just for comparison it is given. The mass per spectrum that has helped to corroborate the structures of cyclo tetra trine iron tricarbonyl which is shown here. The separation of the two absorptions one is here one is here one is positive one is negative side corresponds to a sample Doppler velocity of 1.23 millimeters per second. So, this Doppler effect means that there is the very small energy difference of 1.4 into 10 raise to minus 6 kilo calories per mole in the two transitions shown here. So, this is a typical mass per spectra of cyclo octetra trine tricarbonyl complex and then for example, among the following those can act as mass per nuclear is just if you remember the period table that I showed among them of course, no doubt you know that 57 iron shows and extensively studied. So, what are the other elements that one can use for this purpose is you can see here 199 iodine and 57 iron and 121 antimony also one can use mass per spectroscopy as a tool to understand their nuclear structures. So, let me stop here.