NUCLEAR MAGNETIC RESONANCE

Transcription

1 uclear Magnetic Resonance CAPTER UCLEAR MAGETIC REOACE Properties of nucleus to give MR signal: All the nucleus their isotopes present in periodic table are not MR active. For a nucleus to be MR active it should full fill/possess. on-zero uclear spin: On the basis of spin number, nucleus can be divided into two types on-zero uclear pin Magnetic uclei on-magnetic uclei I 0 I = 0 MR active MR inactive Mass number of non-magnetic nuclei will be completely divisible by 4. e.g. 6 O, C, If not divisible by 4, then MR active To obtain a good quality MR signal from magnetic nuclei It should have good natural abundance and less quadrupole moment. On the basis of these two factors, magnetic nuclei can be classified as Magnetic uclei on-quadrupole magnetic uclei pherical hape I = ½ Quadrupole magnetic uclei on-pherical hape I > ½ Major axis Minor axis Conc. uclei Dil. uclei outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

2 uclear Magnetic Resonance The MR signal of non-quadrupole magnetic nuclei will be sharp In case of qudrupole nuclei due to less relaxation time, the MR signals will be broad and sometimes it will not appear all. If more, less t relaxation time (band width) v constant frequency (signal width) t = more then v = less. For quadrupolar nuclei t = very less. o, transition occurs so fast that signal becomes so broad. If t = more i.e. relxation time is more then sharp signals. I alf-integer Integer Atomic Mass Odd Even Atomic umber Odd or even Odd Example (I) 5, O, (), 7 (), 5 () Zero Even Even C(0), 8 O(0), 6(0) Quadrupole enhances relaxation: The signal width in MR is associate with the relaxation time of nucleus with exclusion principle. Presence of quadrupole moment creates fast relaxation of nucleus (less t ) resulting broad... of MR signals. on-quadrupole magnetic nuclei with high natural abundance is conc. nuclei. P F s 99.8% s 00% 9 Rh s 00% 0 00% The nuclei having spin number more than i.e. I are known as Quadrupolar nuclei. Recording of MR spectrum for quadrupolar nuclei is always challenging. ince, the quadrupolar moment of nucleus causes broadening of MR signal. The broadening of MR signal is due to very less relaxation time t for quadrupolar nuclei outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

3 uclear Magnetic Resonance The quadrupolar nuclei having less quadrupole moment less broadening. Quadrupole effect is only when there is gradient (concentration difference i.e. asymmetric electric field) in electric field. If symmetrical electric field no quadrupolar effect. For example: (i) The effect of quadrupolar broadening becomes negligible. If the nuclei is present in spherical electronic environment. (ii) 5 -MR spectrum of shows broad (Quartet) signal due to axial electronic environment. ut 5 + -MR of 4 shows sharp signal. Tetrahedral on-spherical symmetry broad signal (Axial ymmetry) is in spherical symmetry sharp signal (iii) MR spectrum of : Gives broad signal ut MR of 4 + gives sharp signal. Dilute uclei: C s.% 99 g s 6% 5 0.7% 9 i 5.% Resonance frequency (Mz) ucleus Table - Properties of some nuclei with non-zero spin pin in field of.487 T g value / / / / 5/ / / / / / / / 5/ / outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

4 4 uclear Magnetic Resonance MR Phenomenon: uclear spin ucleus efore magnetic field energy same After magnetic field energy difference. clockwise anti-clockwise In the absence of external magnetic field the nuclear spin energy level remain degenerate. As we apply the external magnetic field the degeneracy of spin energy level get break. The nucleus which are aligned with external magnetic field will remain in lower energy level and the nucleus apposing the ext. magnetic field will be in higher spin energy level. The distribution of nucleus into lower and higher energy level will be according to otlzmann equation. = 0 0 E 0 outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

5 uclear Magnetic Resonance 5 g I E hv g m g m I g g 0 + I g g g g Figure : plitting of nuclear spin energy levels in a magnetic field of strength The separation of energy levels E will be directly proportional to the applied magnetic field. The population difference [number of nucleus in ground state and number of nucleus in excited state] between the energy levels will be directly proportional to the applied magnetic field strength. The MR signal strength will be directly proportional to the population difference. Apart from spin motion, the nucleus starts precessional motion due to external magnetic field, which is also known as gyroscopic motion. The frequency of gyroscopic motion will be known as pressional frequency. PF 0 Where, = Gyroscopic ratio for nucleus P. F. Mz Tesla, Mz / Tesla 0 If 0 = Tesla then = P.F. Gyromagnetic ratio will be precessional frequency of a particular nucleus at Tesla magnetic field Mz / T C Mz / T P 7.6 Mz / T 9 F Mz / T Radio frequency outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

6 6 uclear Magnetic Resonance Magnetic uclei Q.Q T = ½ n reflection time short ( t = short) harp signal Conc. uclei (, 9F, P, 0 Rn) pin = ½ Dil. uclei C =.7 5 = 0.7% 9 i = 5. % Where, Q = Quadrupolar, Q = on-quadrupolar When we external magnetic field to the sample the degeneracy spin energy level for break resulting the population difference according to oltzmann equation. The nucleus starts precessional motion in the external magnetic moment and spin motion remain unaffected. P. F. 0 the precessional frequency will be equal to 0 For generating MR signals we needs to apply radio frequency pulse perpendicular to direction of external magnetic field. When PF will become equal to the applied radio frequency resonance will occur, the nuclear transition from ground state spin energy level to excited state spin energy level will result MR signal. Intensity Pulse interval 0 Time z Dete. R.F. 0 x y (overall magnetic field) create (Less energy population gap) due to low energy (radio frequency) population outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

7 uclear Magnetic Resonance 7 90º + 90º maximum on (+) x-axis 70º maximum on ( ) x-axis 80º 0º 70º In MR the energy gap between spin energy level is lowest compared to other spectroscopy due to least energy gap the (appr. 8 ppm/tesler) Population difference is also very small but it is much sufficient to produce MR signal. Due to least energy gap the spin energy levels are very sensitive for saturation so we always apply the radio-frequency in the form of pulse. During pulse time spin transition will occur resulting the MR signal and during pulse interval relaxation of nuclear spin will happence to recreate the population difference. A good quality MR signal can be obtain as average signal of 5-50 pulses for -MR P.F. = 0 OLVED PROLEM. Calculate the PF of (proton) at 5T magnetic field T = 4.57 Mz oln. PF = 0 PF = Mz = Mz. Calculate the value of required magnetic field to resonate 9 F nucleus with 500 Mz radio frequency oln. PF = 500 Mz (Resonat energy) P. F T The P.F. of a proton on a MR specrophotometer is 00 Mz. Calculate the PF of C-nucleus on the same instrument. oln. P F 0. P. F. 00 Mz = 4.57 P. F T 4.57 = [ for C] T P. F. PFC = Mz outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

8 8 uclear Magnetic Resonance In MR the sensivity of nucleus can be reflected as result of sample requirement and MR recording time. For high sensitive nucleus the sample requirement and MR recording time will be higher The two major factor decide the sensitivity of nucleus (i) -Gyromagnetic (ii).a. (natural abundance) The nucleus having higher gyromag. ratio and higher.a. are more sensitive. If is higher then separation of energy level for Tesla mag. field will be high. 5 mg 5 mg C = 0.705,.% = 4.57, 99.85% resulting higher population difference, high number of possible transition and intense MR signal. igher natural abundance of nuclei will provide high conc. of MR active nuclei in the sample to produce high instance signal. e.g. 4. A. 400 Mz Relative sensitivity C % 0 minutes/spectrum.7 0 max. ratio % 0 minutes/spectrum.0 The most sensitive MR nuclei is proton [] because it has maximum and almost 00% natural abundance. As a standard way we always report the sensitivity of MR active nuclei with respect to proton and which is known as relative sensitivity. oln. omenclature of MR instrument: omenclature of MR instrument is on proton. TM = Tetramethyl ilane Proton = 400 Mz The nomenclature of intrument as per standard system can be given according to precessional frequency of TM protons on that instrument. 400 Mz instrument means TM protons resonate at 400 Mz precessional frequency on this instrument. Problem: The operating frequency of MR instrument is 500 Mz. Calculate the precessional frequency of C, P, 9 F on this instrument. Operating frequency = 500 Mz for proton. PF = 0 PF Tesla C PF Mz C PF for P = = 0 Mz PF for 9 F = = 468 Mz ow, maximum 900 Mz MR instrument is available Therefore, magnetic field is fixed. o, we cannot make instrument upto 800 Mz. Why magnetic field fixed Therefore, maintaince is very high i.e. we have to pay for it. outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

9 uclear Magnetic Resonance Classical Magnet (uperconductivity): Large size magnet After this discovery we can generate high magnetic field. 9 Liq. outer jacket Liq. e (Inner jacket) ample tube 00 Mz uperconductivity is not equal to zero. o, we have to maintain the heat treatment. Problem: It is possible to create 900 Mz operating frequency instrument for proton but it is impossible to generate 900 M z operating frequency for C. Why? oln. 900 Mz instrument PF = 900 Mz Tesla 4.5 For C generate magnetic field =? 900 Mz 84 Tesla magnetic field (ut limit is only 5 Tesla) To resonate a proton at 900 Mz, we need Tesla magnetic field which is the maximum limit of magnetic field present available and to resonate C at 900 Mz, we need 84T magnetic field is practically impossible to create. ensitivity of nucleus for MR : The nucleus C give large signal peak i.e. more sensitive. The sensitivity of nucleus means intensity of signal with respect to applied magnetic field. igh sensitive nucleus gives intense signal with less amount of magnetic field. Proton is maximum sensitive i.e. lucky for scieintist. The factors affecting sensitivity: () Gyromagnetic ratio () atural abundance () Gyromagnetic ratio: The nucleus having higher gyromagnetic ratio (r) E = 4.57 Mz E = 0.7 Mz at Tesla C at Tesla (Almost /4th of ) igh ratio, sensitivity more. ince, energy gap more. Population gap = more, number of transitions = more. More intense signal. ave higher separation between spin energy have resulting the higher population difference. outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

10 0 uclear Magnetic Resonance As per oltzmann equation: ignal intensity population difference i.e. ensitivity Gyromagnetic ratio () atural Abundance: The nuclear having higher natural abundance will be more sensitive. For e.g. natural aboundance = atural Abundance γ Relative ensitivity 99.98% C.% C nucleus is almost 400 times less sensitive than proton nucleus. oln. Proton is the maximum sensitive nucleus. ince, it has maximum gyromag. ratio (r) and almost 00% natural abundance thats why the name of MR instrument will be according to the operating frequency of proton ( ). Problem: A magnetic nuclei resonates with 00 Mz precessional frequency at an MR instrument of operating frequency 500 Mz. Calculate the Gyromagnetic ratio for the nucleus. MR instrument frequency P.F. = 500 Mz, = Mz P.F. = Resonating frequency = 00 Mz 500 Mz Mz = Mz 5.54 Mz.74 Problem: Preessional frequency of Deuterium on MR instrument is 50 Mz. Calculate the preessional frequency for P at same instrument. oln. oln. D P P.F. for Deuterium = 50 Mz 50 Mz D 6.56 Mz Mz P 7.5, 7.64 P.F Mz Problem: Calculate the frequency of nuclear spin energy levels for 4 nucleus in a magnetic field of 5.4 Tesla. = 5.4 Tesla 7.90 rad sec T P.F. = Mz instrument. What happens when sensitivity increased outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

11 uclear Magnetic Resonance ince, on increase instrument sensitivity the amount decreases. For e.g. 00 Mz 600 Mz Less sensitive More sensitive and natural abundance = constant for C. 00 Mz 600 Mz C 45 min 0 5 min pectra50 mg sample 0 5 mg If magnetic field = increases population difference increases sensitivity increases. Therefore, on increasing sensitivity on increases Magnetic field we get spectra is less time. i.e. sample quantity less and required time for spectra decreases 600 Mz instrument is important for dilute nuclei. Its cost is so much high as compare to 00 Mz. The sensitivity of dilute nucleus can be enhanced by increasing the magnetic field. Increases in sensitivity means requirement of less amount of sample and less MR recording time. For e.g. At 00 Mz instrument C = one C MR takes 45 minutes and 600 Mz takes 0 5 minutes. For working on cancentrated nuclei 00 Mz instrument is sufficient but for dilute nuclei = 600 Mz. OLVED PROLEM. The g value for F 9 nucleus is Calculate the resonance frequency when it is placed in a magnetic field of strength.0 T (tesla) and is JT. Also calculate relative population in two spin state at 00K. oln. The resonance condition from (9); hv g, hence, v 7 g JT.0T 4 h Js g h Gyromagnetic ratio s 40 Mz The relative population in M I and M I spin states from (0) 7 n / g / kt JT T e exp n/.80 JK 00K. A MR spectrometer operating at a 60 Mz frequency gives proton spectra at a field of.409t. At what oln. field would the spectrum be observed at 60 Mz. (For, v = Operating frequency = hz and 7 E g JT 4 h h Js Js JT T I and g =.790). outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

12 uclear Magnetic Resonance. Find the frequency at which a proton MR spectrometer should be operating under a magnetic field.8. T (g =.745 and oln. E g for transition for = JT ) M I in proton v 4 h Js 7 E JT.8T z 74.8 Mz 4. ketch the MR spectra of C C Cl Cl C C oln. Relative intensity : C :C A spectroscopic technique that gives us information about the number and types of atoms in a molecules. ydrogen using MR spectroscopy Carbon using C-MR spectroscopy Phosphorus using p-mr spectroscopy ilicion using 9 i-mr spectroscopy 9 F MR, 9 n MR and 95 pt MR. 5. The uncertainty in the MR frequency of a compound in liquid state (relaxation time =s) is 0. z. The oln. 4 uncertainty in the frequency (in z) of same compound in solid state (relaxation time 0 s ) is (a) 4 0 (b) 00 (c) 000 (d) 0 (c) From eisenberg uncertaintity principle, h E. t 4 Or. t constant h h. t. t 4 4 (where t = life time or Relaxation time and uncertainty in frequency 0. zsec constant 4 And outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: , (i)...(ii) z 0 constant...(iii) From equation (ii) and (iii) What magnetic field strength is required for proton magnetic resonance at 0 Mz, Given: Thefactor g for proton is oln. ince, V g

13 uclear Magnetic Resonance We have, s J s V 5.75 T g J T Calculate the precessional frequency of a proton in a field of.5 T. oln. The precessional frequency is given by v g h J T T ence, v 6.80 s J s 8. Calculate the value of gyromagnetic ratio. g oln. ince, h J T We have, J s 7 9. Calculate the angular momentum and magnetic moment values for a proton. Given: g = h oln. We have, L II And g II m For proton, I = /. Thus, we have 4 h h J s 4 L J s And m J T.440 J T 7 6 outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,

14 4 uclear Magnetic Resonance. Given T s PROLEM. The resonance frequency of a proton in magnetic field of.6 T is close to (a) 60 Mz (b) 0 Mz (c) 540 Mz (d) 780 Mz [ET Dec. 0]. The nuclear g-factors of and 4 are 5.6 and 0.40 respectively. If the magnetic field in an MR spectrometer is set such that the proton resonates at 700 Mz, the 4 nucleus would resonate at [ET June 05] (a) 750 Mz (b) 700 Mz (c) 5 Mz (d) 50 Mz. In comparision to the frequency of the EPR transition, the MR transition frequency is [GATE 00] (a) much higher (b) much lower (c) almost same (d) none of these 4. For any MR active nucleus, the magnitude of radiofrequency required for observing nuclear magnetic resonance phenomenon depends on (a) trength of the magnetic field. (b) Choice of the nucleus (c) oth on magnetic field strength and choice of the nucleus. (d) The nuclear enegy levels. 5. The sensitivity of a 600 Mz MR spectrometer is more than that of a 60 Mz spectrometer because (a) Population of spin states is directly proportional to the applied magnetic field. [GATE 00] (b) Population of spin states is inversely proportional to the applied magnetic field (c) According to the oltzmann distribution law, the excess population in the lower spin state increases with increasing applied magnetic field. (d) The spectral scan width is more for a 600 Mz spectrum compared to a 60 Mz spectrum. 6. In MR spectroscopy, the product of the nuclear g factor (g ), the nuclear magneton and the magnetic field strength ( 0 ) gives the [ET June 0] (a) energy of transition from to state (b) chemical shift (c) spin-spin coupling constant (d) magnetogyric ratio outh Delhi : 8-A/, Jia arai, ear-iit auz Khas, ew Delhi-6, Ph : , orth Delhi : -5, Mall Road, G.T.. agar (Opp. Metro Gate o. ), Delhi-09, Ph: ,