1 Prof.M.Perucca CORSO DI APPROFONDIMENTO DI FISICA ATOMICA: (III-INCONTRO) RISONANZA MAGNETICA NUCLEARE
2 SUMMARY (I/II) Angular momentum and the spinning gyroscope stationary state equation Magnetic dipole and Bohr Magnetron Torque and energy of magnetic dipole(s) immersed in a stationary magnetic field Larmor precession Space quantisation From spectral triplets to doublets: the need of the spin quantum number
3 SUMMARY (II/II) The Landè splitting factor Bloch equations and resonance The electron spin resonance (ESR) apparatus The ESR experience with DPPH free radical Down to the nucleus: NMR Applications of NMR & one of the cutting edge research topics The NMR experiment with Glycerine, PTFE, PS
4 ANGULAR MOMENTUM
5 MAGNETIC MOMENTUM m = Ip r 2 =IA
6 GYROSCOPE PRECESSION sin L P
7 The orbital angular momentum for an atomic electron can be visualized in terms of a vector model where the angular momentum vector is seen as precessing (wobbling) about a direction in space. While the angular momentum vector has the magnitude shown, only a maximum of l units can be measured along a given direction, where l is the orbital quantum number. THE ORBITAL QUANTUM ANGULAR MOMENTUM
8 The orbital angular momentum is a "vector", actually it is a special kind of vector because it's projection along a direction in space is quantized to values one unit of angular momentum apart. The diagram shows that the possible values for the "magnetic quantum number" m l for l=2 can take the values m l = -2, -1, 0, 1, 2 or, in general m l = -l, -l+1,..., l-1, l. THE ANGULAR MOMENTUM AND THE MAGNETIC MOMENTUM
9 A magnetic moment is associated with the orbital angular momentum, the precession can be compared to the precession of a classical magnetic moment caused by the torque exerted by a magnetic field. This precession is called Larmor precession and has a characteristic frequency called the Larmor frequency Potential energy and energy separation between parallel and antiparallel LARMOR PRECESSION AND ASSOCIATED ENERGY
10 LARMOR (RESONANCE) FREQUENCY w = g B ; g giromagnetic ratio
11 THE TOTAL ANGULAR MOMENTUM
12 ORBITAL ANGULAR AND MAGNETIC MOMENTA m = Ip r 2 =IA
13 A magnetic moment experiences a torque in a magnetic field B. The energy of the interaction can be expressed as The interaction energy of an atomic electron can then be written MAGNETIC MOMENT AND INTERACTION WITH STATIONARY MAGNETIC FIELD
14 MAGNETIC MOMENTS
15 BOHR MAGNETRON AND LANDÈ SPLITTING FACTOR
16 ENERGY INVOLVED IN STATES TRANSITION evaluated in terms of the relevant quantum numbers takes the form g L = Landè splitting factor m B =Bohor magnetron m j = magnetic quantum number
17 THE TOTAL ANGULAR MOMENTUM J Once combined orbital and spin angular momenta according to the vector model, the resulting total angular momentum can be visuallized as precessing about any externally applied magnetic field.
18 BLOCH EQUATIONS y M n 1 m i
19 RESONANCE PEAKS
20 RESONANCE INTENSITY FUNCTION
21 BOLTZMAN DISTRIBUTION the Boltzmann distribution is a certain distribution function or probability measure for the distribution of the states of a system. It underpins the concept of the canonical ensemble, providing its underlying distribution. In more general mathematical settings, the Boltzmann distribution is also known as the Gibbs measure. The Boltzmann distribution for the fractional number of particles N i / N occupying a set of states i possessing energy E i is:
22 TWO STATES POPULATIONS
23 THE (REGULAR) ZEEMAN EFFECT IN H-ATOM When an external magnetic field is applied, sharp spectral lines like the n=3 2 transition of hydrogen split into multiple closely spaced lines. First observed by Pieter Zeeman, this splitting is attributed to the interaction between the magnetic field and the magnetic dipole moment associated with the orbital angular momentum.
24 THE ATOM INTERACTS WITH ITSELF. Normal" Zeeman effect This type of splitting is observed with hydrogen and the Zinc singlet. But another anomalous Zeeman Effect was detected in the Na doublet
25 SODIUM DOUBLET (SPIN-ORBITS INTERACTION)
26 SELECTION RULES In spectral phenomena such as the Zeeman effect it becomes evident that transitions are not observed between all pairs of energy levels. Some transitions are "forbidden" ( i.e., highly improbable) while others are "allowed" by a set of selection rules. The number of split components observed in the Zeeman effect is consistent with the selection rules: any electron transition which involves the emission of a photon must involve a change of 1 in the angular momentum. The photon is said to have an intrinsic angular momentum or "spin" of one, so that conservation of angular momentum in photon emission requires a change of 1 in the atom's angular momentum. The electron spin quantum number does not change in such transitions, so an additional selection rule is: The total angular momentum may change be either zero or one: (An exception to this last selection rule it that you cannot have a transition from j=0 to j=0; i.e., since the vector angular momentum must change by one unit in a electronic transition, j=0 -> 0 can't happen because there is no total angular momentum to re-orient to get a change of 1).
27 ORBITAL AND SPIN MAGNETIC MOMENTS
28 OSCILLATING CIRCUITS PRODUCTING RF SIGNAL
30 CW NMR One of the earliest and simplest applications of nuclear magnetic resonanceis the continuous wave or CW NMR. In this kind of application, both the magnetic field and the RF excitation signal are continuously on. Either the magnetic field is kept constant and the frequency of the RF excitation is varied, or the magnetic field is varied while keeping the RF input frequency constant. Either approach allows you to sweep through the resonance of the sample under investigation.
31 ESR NMR CONSOLE
33 DPPH (ESR) DPPH is a common abbreviation for an organic chemical compound 2,2-diphenyl-1- picrylhydrazyl. It is a dark-colored crystalline powder composed of stable free-radicalmolecules. DPPH has two major applications, both in laboratory research: one is a monitor of chemical reactions involving radicals and another is a standard of the position and intensity of electron paramagnetic resonance signals
34 POLYSTIRENE (NMR) Polystyrene is a long chain hydrocarbon with every other carbon connected to a phenyl group (the name given to the aromatic ring benzene, when bonded to complex carbon substituents). Polystyrene's chemical formula is (C 8 H 8 ) n ; it contains the chemical elements carbon and hydrogen. In NMR hydrogen spin nuclei are excited
35 GLYCERINE (NMR) Glycerol (or glycerin, glycerine) is a simple polyol compound. It is a colorless, odorless, viscous liquid that is widely used in pharmaceutical formulations. Glycerol has three hydrophilic hydroxyl groups that are responsible for its solubility in water and itshygroscopic nature. The glycerol backbone is central to all lipids known as triglycerides. In NMR hydrogen spin nuclei are excited
36 POLYETHYLENETEREPHTALATE - PET (NMR) Polyethylene terephthalate (sometimes written poly(ethylene terephthalate)), commonly abbreviated PET, PETE, or the obsolete PETP or PET-P, is a thermoplastic polymer resin of the polyester family and is used insynthetic fibers; beverage, food and other liquid containers; thermoforming applications; and engineering resins often in combination with glass fiber. In NMR hydrogen spin nuclei are excited
37 MRI Proton nuclear magnetic resonance (NMR) detects the presence of hydrogens (protons) by subjecting them to a large magnetic field to partially polarize the nuclear spins, then exciting the spins with properly tuned radio frequency (RF) radiation, and then detecting weak radio frequency radiation from them as they "relax" from this magnetic interaction. The frequency of this proton "signal" is proportional to the magnetic field to which they are subjected during this relaxation process.
38 MRI In the medical application known as Magnetic Resonance Imaging (MRI), an image of a cross-section of tissue can be made by producing a well-calibrated magnetic field gradient across the tissue so that a certain value of magnetic field can be associated with a given location in the tissue. Since the proton signal frequency is proportional to that magnetic field, a given proton signal frequency can be assigned to a location in the tissue. This provides the information to map the tissue in terms of the protons present there. Since the proton density varies with the type of tissue, a certain amount of contrast is achieved to image the organs and other tissue variations in the subject tissue.
39 Since the MRI uses proton NMR, it images the concentration of protons. Many of those protons are the protons in water, so MRI is particularly well suited for the imaging of soft tissue, like the brain, eyes, and other soft tissue structures in the head as shown at left. The bone of the skull doesn't have many protons, so it shows up dark. Also the sinus cavities image as a dark region. MAGNETIC RESONANCE IMAGING (NMR-> MRI)
40 LOCATING PROTONS THROUGH GRAD(B)
41 LOCATING H ATOMS AND TISSUES there are two regions of the sample which contain enough hydrogen atoms to produce a strong NMR signal. The top sketch visualizes an NMR process with a constant magnetic field applied to the entire sample. The hydrogen spin-flip frequency is then the same for all parts of the sample. Once excited by the RF signal, the hydrogens will tend to return to their lower state in a process called "relaxation" and will reemit RF radiation at their Larmor frequency. This signal is detected as a function of time, and then is converted to signal strength as a function of frequency by means of a Fourier transformation. Since the protons in each of the active areas of the sample are subjected to the same magnetic field, they will produce the same frequency of radiation and the Fourier transform of the detected signal will have only one peak. This one peak demonstrates the presence of hydrogen atoms, but gives no information to locate them in the sample
42 ROTATING B When a rotating field gradient is used, linear positioning information is collected along a number of different directions. That information can be combined to produce a two-dimensional map of the proton densities. The proton NMR signals are quite sensitive to differences in proton content that are characteristic of different kinds of tissue. Even though the spatial resolution of MRI is not as great as a conventional x-ray film, its contrast resolution is much better for tissue. Rapid scanning and computer reconstruction give wellresolved images of organs.
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