'Esr Experiment\r'

'Electron spiral sonority Tabish September 2003 Aim: To determine the dirt? g-comp atomic occur 53nt utilise Electron Spin Resonance. e Apparatus: sedimentation rate setup which includes Helmholtz curves, R. F. oscillator and the foot race assay, and in access, a cathode ray oscilloscope ( range). Theory Back soil Suppose a molecule having a magnetized result µ is placed in a uniform magnetised ? years of intensity B, accordingly(prenominal) the Hamiltonian send a charge be written as ? H=g e ? J · B, 2mc where g is the Land? g- compute, which is 1 for orbital angulate nervous impulse, and 2 for twirl angulate e e? h neural impulse.The factor 2mc , well-nightimes written as µB , is called Bohr magneton, if the softenicle in question is an electron. If the particle is a nucleon, and so the factor is called the portionic magneton. If the angulate momentum J results from a combination of an orbital angular momentum and a spin, then g would be tendi ng(p) by the Land? form: e g =1+ j(j + 1) + s(s + 1) ? l(l + 1) , 2j(j + 1) where l, s and j represent the magnitude of the orbital, the spin and the total angular momenta, respectively. Remember that j croupe go from l ? s to l + s. Conventionally, the static magnetic ? days is assumed to be betokening along the z? xis, which modi? es the supra equation to e ? ? Jz B. H=g 2mc Let us straighta course consider an atom which has an electronic scope recite with total angular momentum j = 1/2 and an delirious give in with j = 3/2 ( bring down ? gure 2). There is however a item-by-item change which fucking be induced by the assiduity of beam of oftenness ? 12 = (E2 ? E1 )/? . As the muscularity does not depend h on the angular momentum give tongue tos, the ground state is doubly loyal add togethering to eigen orders ±1/2 ? of Jz and the excited state is quadruply degenerate suss bulgeing to eigen nourishs +3/2, 1/2, ? 1/2, ? 3/2 of ? Jz . 1Electronic excited sta te Electronic inflection j=3/2 electron spin tintinnabulation Electronic ground state j=1/2 erythrocyte sedimentation rate Zeeman effect If angiotensin converting enzyme now applies a magnetic ? age B along the z-axis, to each single of the angular momentum states acquires a di? erent efficiency. The ground state energy level consequently splits into cardinal sublevels and the excited state level into quadrupletsome sublevels. This is called Zeeman splitting. at present instead of a single novelty of relative relative frequency ? 12 = (E2 ? E1 )/? , many spiritual rebirths of frequencies tight fitting to ? 12 h be practi electrify. by experimentation this is seen as a splitting a single soaking up or dismissal line into several closely detached lines.This is called Zeeman e? ect. As adept would collect noticed, transition should too be feasible among the sublevels of the same energy level. It is therefore possible and this phenomenon is don as electron spin sonority (erythrocyte sedimentation rate). Electron Spin Resonance Let us attempt to understand the phenomenon of electron paramagnetic resonance in moderately more detail. As ESR invloves transitions only betwixt the sublevels of adept energy level, we allow not bother approximately the Hamiltonian of the atom/molecule which gives us the energy levels. We go out only worry about the part of the Hamiltonian which is the result of the apply magnetic ? ld B, which gives us the sublevels. For simplicity, we pull up stakes consider one electron with angular momentum j, in a magnetic ? eld B. In addition we have an electromagnetic ? eld of frequency ? in the direction orthogonal to B. The time-dependent Hamiltonian undersurface thus be written as ? H=g eB ? ? ? Jz + V0 ei? t + V0† e? i? t , 2mc ? where V0 represents the fundamental interaction of the electromagnetic ? eld with the electron. The electromagnetic ? eld is hypothetic to be very weak compared to the applied static ? eld B, and so one can employment time-dependent perturbation hypothesis to study this problem. The states ? hat we will use are the eigenstates of Jz : ? Jz |m = hm|m , ? where m will take 2j + 1 quantifys, from ? j to +j. The energy of these levels is wedded by g where n eB ? Jz |n = 2mc n |n , = geB? n h 2mc = gBµB n. In time-dependent perturbation theory, we know that the time-dependent interaction can cause transition mingled with various |m states. The transition rate per unit of mea confident(predicate)ment time, from i th level to j’th level is given by: 2? ? Wi>j = | j|V0 |i |2 ? ( j ? i ? h? ), ? h ? assuming that j > i . This reflectivity says that transition from state |i to |j is possible when the frequency of radiation ? ( j ? i )/? . This is the intend for resonance, or in our case, h electron spin resonance. ? ? There is one authoritative point about the form of V0 . It happens to be much(prenominal)(prenominal) that j|V0 |i is n onzero only when j = i ± 1. This means that transition is possible between, say, | ? 3/2 and | ? 1/2 , but not between, say, | ? 3/2 and |1/2 . such restrtictions, imposed by the kind of interaction and the nature of states, are called selection rules. 2 The ESR setup Description of the ESR Spectrometer A block draw of the ESR Spectrometer is given in the ? gure above. Basic electric car circuit The ? st stage of the ESR circuit consists of a critically alter radio frequency oscillator. This type of oscillator is inevitable here, so that the slightest increase in its pack decreases the amplitude of oscillation to an appreciable extent. The sample is kept inside the tank coil of the oscillator, which in turn, is placed in the 50 Hz magnetic ? eld generated by the Helmholtz coils. At resonance, i. e. when the frequency of oscillation becomes refer to frequency synonymous to the energy splitting of the sublevels, the oscillator amplitude registers a dip collectible to the tightness of origin by the sample.This obviously, occurs periodically quaternary times in each complete cycle of the supply potentiality of the magnetic ? eld. The result is an amplitude modulate carrier which is then detected using a diode detector and ampli? ed by a chain of triple low noise, high gain audio-frequency ampli? ers to accommodate the input requirement of any oscilloscope. passing stabilized and almost ripple redundant power supply for the above circuit is haveed using an integrated circuit regulator. degree shifter This can compensate the undermined figure di? erence which may be introduced in the ampli? cation stages of the mass spectrometer and oscilloscope. 0 Hz sweep unit A 50 Hz oc on-line(prenominal) ? ows through Helmholtz coils which provides a low frequency magnetic ? eld to the sample. As the resonance is observed at a hardly a(prenominal) gauss only, no static magnetic ? eld is applied. R. F. Oscillator It is a transistorised radio frequency oscillator suitable for the determination of resonance frequency. oftenness range: 10 MHz to 18 MHz Accuracy: Better than 0. 5 % The Sample The sample used in our ESR setup is diphenyl-picryl-hydrazyl (DPPH). It is a wide used standard in ESR experiments. The structure of this organic molecule, doomn in the ? gure, contains tierce benzene rings.Its important feature is that it contains a single unpaired electron, whose orbital angular momentum is 3 O2N N N NO2 O2N zero. So, the electron has only the spin angular momentum, and the material gives a g? factor which is close to 2. 0038. One thus has to compensate with the simple situation where j = 1/2, and only two sublevels are involved. In conventional spectroscopy, submersion intensity is plan against the frequency of radiation to get the absorption spectrum. In the present case, one should bring a single abosorption geB peak at frequency ? = ( j ? i )/? , which is zip but ? = 2mc . However, in this setup it is h di? ult to vary the frequency of radiation. So, what is through with(p) is that the frequency of radiation is ? xed at some ? 0 , and the normally static, magnetic ? eld is swept between the un takeal and electro prohibit entires of a maximum ? eld value. This is through with(p) by supplying an alternating contemporary to the Helmholts coils which are supposed to generate the magnetic ? eld. During the AC cycle, 2mc whenever the strength of the magnetic ? eld (+ve or -ve) becomes equal to B0 = ? 0ge , there is a resonance condition, and radiation is absorbed. Origin of four peaks In this experiment, the CRO is used in the x-y mode.The luff from the AC source, which supplies underway for the magnetic ? eld, is feed to the X plates of the CRO, and the absorption signal is B fed to the Y plates. The point on the extreme right on the CRO 2 4 3 1 screen represents the maximum positive value of the ? eld, and the point on the extreme left represents the maximum negative value ? B of the ? e ld. The point at the affectionateness represents zero ? eld. Without Time the Y-plates, the point on the CRO screen goes from maximum negative value to zero, and the maximum positive value, and then back again to the mimimum value.As one can see from the ? gure, the ? eld strength becomes B0 four times in one single sweep cycle. 0 0 0 nary(prenominal) if the absorption signal is fed to the Y-plates, whenever the ? eld strength becomes B0 , the Y-axis will show a peak. So, one should see four peaks corresponding to points 1,2,3,4 in the ? gure. But one can see that on the X-axis of the CRO screen, points 2 and 3 are the same, because they correspond to the same value of the ? eld B0 , and points 1 and 4 are the same because they correspond to the ? eld ? B0 . So, the four peaks should overlap such that only two are visible.However, the absorption signal passes through some electronic circuitry before being fed to the Y-plates of the CRO, so it very di? cult to make sure that no so ma change occurs in the process. If there is a small phase di? erence between the AC signal on the X plates and the signal on the Y plates, when points 3 and 4 are traced, the peaks do not overlap with those at 1 and 2. So, in practice one would see four peaks. If one has a way of changing the phase of, say, the Y signal, one can adjust the phase manually so that the four peaks merge into two. acquire the numbersWe have the control over the current that is passing through the Helmholtz coils, and this can also be calculated. But what we actually privation for our calculation is, the magnetic ? eld B applied to the sample. Let us ? rst manoeuver the magnetic ? eld through the Helmholtz coils. This can be done easily 4 using the Biot-Savart law. B = µ0 4 5 3/2 I N , r where: µ0 = 4? ? 10? 1 (cgs units) N = number of turns in each coil. r = the universal gas constant of the Helmholtz coils in cm (which is equal to their insularity when they are properly arranged). I = curre nt passing through the coils.The value of B is obtained in gauss. As the current is measured by an AC ammeter, the value of the current, and thus the ? eld, is the r. m. s. value. The peak value of the ? eld will be given by v v 8 2 I N . Bmax = 2B = µ0 v cxxv r Suppose the peak value of the ? eld (= Bmax ) corresponds to P divisions from the center on the x-axis of the CRO screen. Then if Q be the blank of the observed resonances from the center (in the units of divisions), the ? eld corresponding to the resonance will be given by: B0 = Q But the resonance condition is given by: B0 = h ? 0 ? , gµB Bmax P hich can be used to determine the value of g, once B0 is known. Now, for a ? xed ? 0 , B0 is ? xed, although one can vary the current I and get various come out of the absorption peaks. Let us write the expression for B0 and see what is most accurate way to calculate it: v N µ0 8 2 v B0 = I · Q. rP 125 The ESR spectrometer is such that P does not vary as one varies I. So, the best way to tax the above expression will be to plot a graph between 1/I and Q, and ? nd out the slope, which will give the average value of I · Q. The ? eld at the absorption peaks can be calulated as: v N µ0 8 2 v B0 = ? lope of graph between 1/I and Q. rP 125 action Connections Connections are done as follows: • ESR spectrometer and power supply are connected with connecting cables. • Connect the coaxial cable of the induction coil to the oscillator through the socket attach â€Å"input”. 5 • Connect the Helmoltz coils to the power supply terminal marked â€Å"H” coil. • Connect the â€Å"Out-put” terminal marked X, Y, E on the ESR spectrometer to the X plate, Y plate input and ground of the oscilloscope respectively and switch on the oscilloscope. • Connect the power supply with AC mains.Adjustments Adjust the current in the Helmholtz coils at one hundred fifty mA. The front panel controls of the ESR spectrome ter are adjusted as follows: frequency, detector and phase, all centered. Experimental function The X plate of the CRO is callibrated in terms of magentic ? eld as follows: 1. X ampli? er of the CRO is adjusted to obtain the maximum X de? ection (e. g. P divisions. 2. situation the current ? owing in the Helmholtz coils. The magnetic ? eld can then be calculated from the formula for B given before. Number of turn in the coils N = 500 and the radius r = 7. 7cm.The positions of the two peaks of the ESR signal at resonance is measured. Let this be Q divisions from the center. The best possible resonance peaks are obtained by vary the frequency in the range of 12 to 14 MHz and the Y predisposition of the oscilloscope. The pahse knob is adjusted to coincide one pair of peaks with the other. The current through the coils is then varied, keeping the frequency ? xed, and the corresponding position of the peaks from the center noted. A graph between 1/I and Q is then plan and can be use d in calculating the g-factor, as described earlier.Repeat the above procedure for di? erent values of frequency. Observations and calculation S. No. 1. 2. 3. 4. 5. 6. I(mA) 150 175 200 225 250 275 I(A) 1/I Distance of peaks from center (Q) 10 MHz 13 MHz 15 MHz 17 MHz 2. 4 1. 9 1. 9 1. 9 2. 0 1. 6 1. 6 1. 5 1. 4 1. 4 1. 4 1. 4 1. 2 1. 3 1. 2 1. 2 1. 1 1. 1 1. 1 1. 0 1. 0 1. 0 1. 0 1. 0 0. 150 6. 667 0. 175 5. 714 0. 200 5. 00 0. 225 4. 44 0. 250 4. 00 0. 275 2. 636 slope of the graph (= I · Q) = 0. 282, P = 5, N = 500 r = 7. 7cm, µ0 = 0. 1 ? 4? , µB = 9. 2741 ? 10? 21 , h = 6. 626 ? 10? 27 . v N µ0 8 2 v B0 = I ·Q rP 125 v 500 ? . 1 ? 4? 8 2 v ? 0. 282 = 7. 7 ? 5 125 = 4. 657 6 ?0 = 13 MHz 2 1. 8 1. 6 Q 1. 4 1. 2 1 0. 8 3. 5 4 4. 5 5 1/I 5. 5 6 6. 5 7 g = h? 0 µB B 0 6. 626 ? 10? 27 ? 13 ? 106 = 9. 2741 ? 10? 21 4. 657 = 1. 9944 Precautions 1. The direction of the Helmholtz coils should be desirable adjusted so that the ? eld is perpendicular to earth’s ma gnetic ? eld, which is about 0. 3 Gauss. 2. Setup the experiment at a place free from electric and magnetic ? elds and mechanical disturbances. 3. Y-output from the ESR spectrometer should be through a sincere shielded cable. 7\r\n'