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Q 1-2-1 How many allowed orientations do each of the following nuclei have in a magnetic field?

Part 3: Examples and Questions: Embedded Questions. Q 1-2-1 How many allowed orientations do each of the following nuclei have in a magnetic field? 2 H ( I =1), 7 Li ( I =3/2), 17 O ( I =5/2) What are the values that m I can take in each case?.

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Q 1-2-1 How many allowed orientations do each of the following nuclei have in a magnetic field?

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  1. Part 3: Examples and Questions: Embedded Questions • Q 1-2-1 • How many allowed orientations do each of the following • nuclei have in a magnetic field? • 2H (I=1), 7Li (I=3/2), 17O (I=5/2) • What are the values that mI can take in each case? No. of Orientations = 2I+1  2H has 3, 7Li has 4, 17O has 6 mI = -I, -I+1, -I+2,……, I-1, I for 2H mI = -1, 0, 1; for 7Li mI = -3/2, -1/2, +1/2, +3/2 for 17O mI = -5/2, -3/2, -1/2, +1/2, +3/2, +5/2

  2. Part 3: Examples and Questions: Embedded Questions Q 1-2-2 A magnetic nucleus such as 14N, with I = 1, has three allowed orientations in a magnetic field:mI = +1, 0, -1. Calculate the angle q betweenm (the nuclear magnetic moment) and B0(the applied field) for orientations with mI= +1 and mI = 0.

  3. A 1-2-2 mz mz m B0 cos q = h g mI mz m 2p = h g q m  I (I + 1) 2p mI q = m  I (I + 1) For mI = 0, cosq = 0 q = 90° For mI = 1, cosq = 1/  1(1+1) q = 45° cosq = 1/2 Part 3: Examples and Questions: Embedded Questions

  4. Part 3: Examples and Questions: Embedded Questions Q 1-5-1 An NMR spectrometer has a superconducting magnet with a field strength of 9.4 T (Tesla). Calculate the Larmor frequency (in MHz) for each of the following nuclei from the appropriate magnetogyric ratio (g). 1H, g = 26.75  107 rad T-1 s-1 13C, g = 6.73  107 rad T-1 s-1 19F, g = 25.18  107 rad T-1 s-1 At what field strength would protons have a Larmor frequency Of 100.0 MHz?

  5. Part 3: Examples and Questions: Embedded Questions A 1-5-1 g nL B0 = 2p nL(1H) = [(26.75  107)  9.4 ] / 2p Hz = 400.195 MHz nL(13C) = [(6.73  107)  9.4 ] / 2p Hz = 100.685 MHz nL(19F) = [(25.18  107)  9.4 ] / 2p Hz = 376.707 MHz B0 = [ 2p (100.0  106) ] / (26.75  107) = 2.35 T

  6. Part 3: Examples and Questions: Embedded Questions Q 1-6-1 For protons at equilibrium in a magnetic field, calculate the energy gap DEm (in Joules) between the a and b states for field strengths of 2.35 and 9.4 T. (g = 26.75  107 rad T-1 s-1;h = 6.62620  10-34 J s.) Calculate the ratio of a to b protons at room temperature (298 K) for each of these field strengths. Use the Boltzmann distribution (k = 1.38062  10-23 J K-1.)

  7. h g B0 = 2p nb = e-DEm/kT na Part 3: Examples and Questions: Embedded Questions A 1-6-1 DEm At2.35 T, DEm= {(26.75  107)  (6.62620  10-34)  2.35} / 2p = 6.63  10-26 J At9.4 T, DEm= {(26.75  107)  (6.62620  10-34)  9.4} / 2p = 2.65  10-25 J At2.35 T and 298 K,nb/na = e(-6.63  10-26) / [(1.38062  10-23)  298] = 0.999983885 At9.4 T and 298 K,nb/na = e(-2.65  10-25) / [(1.38062  10-23)  298] = 0.999935592

  8. Part 3: Examples and Questions: Embedded Questions Q 1-12-1 – part 1 From the data provided in Figures 1-12-3 and 1-12-4, calculate the values of 1JCH for the CH2 and both CH3 groups in ethyl acetate.

  9. Peaks Dn (Hz) Average 1JCH 2-3 1641.0-1493.2 = 147.8 147.85 3-4 1493.2-1345.3 = 147.9 5-6 691.1-561.6 = 129.5 129.16 6-8 561.6- 433.3 = 128.3 8-10 433.3-303.6 = 129.7 7-9 524.6-396.6 = 128.0 128.00 9-11 396.6-268.6 = 128.0 11-12 268.6-140.6 = 128.0 Part 3: Examples and Questions: Embedded Questions A 1-12-1 3 9 11 2 8 4 7 6 12 10 5

  10. Part 3: Examples and Questions: Embedded Questions Q 1-12-1 continued If you did not know that the compound was ethyl acetate, could you identify it from this spectrum alone? What difference would it make if you knew the molecular formula, C4H8O2? NO – Not enough information about other possible nuclei This would help to narrow down the number of possible compounds. Using a combination of the chemical shift and coupling information, it would be possible to eliminate all except the most likely compounds.

  11. Part 3: Examples and Questions: Embedded Questions Q 1-12-1 continued What would be the effect on the overlap of the two methyl quartets if the spectrum were run on an instrument with a field strength of 7.1 T? Make a sketch to correct scale. [Remember that both d and 1JCH values will remain the same.]

  12. Part 3: Examples and Questions: Embedded Questions A 1-12-1 continued g nL B0 = 2p nL(1H) = [(6.73  107)  7.1 ] / 2p = 76.05 MHz ppm separation of the two CH3 signals for a field strength of 2.35 T = 17.23 + [(22.33 – 17.23)/2] – 10.68 + [(15.77 – 10.68)/2] = 19.78 – 13.225 = 6.555 ppm At 7.1 T, 6.555 ppm = 498.5 Hz = separation of CH3 resonances Overall width of multiplets e.g. 691.1- 303.6 Hz = 387.5 Hz Therefore signals are separated at 7.1 T

  13. Part 3: Examples and Questions: Embedded Questions A 1-12-1 continued 500 Hz 190 Hz

  14. Part 3: Examples and Questions: Embedded Questions Q 2-2-1 So far as possible assign all the peaks in the 13C NMR spectrum of ethyl salicylate to the appropriate carbon atoms in the molecule (Figure 2-2-6). Why does the triplet signal at about dc 77, due to 13CDCl3 in the solvent, remain uninverted in the J-modulated spectrum?

  15. Part 3: Examples and Questions: Embedded Questions G A 2-2-1 B or A A or B C, D, E or F H J 13CDCl3 signal behaves like a quaternary 13C signal – magnetization vector is not affected by 1H pulses and remains in phase A B C D E F G H J

  16. Part 3: Examples and Questions: Embedded Questions Q 2-2-2 How does the sample magnetism due to a 13C-1H system evolve in the following sequence? Use vector diagrams such as those in Figures 2-2-3 and 2-2-4, and show the sample magnetism as separate vectors due to 13C nuclei with a and b protons attached. 1. In a rotating frame chosen to match the Larmor frequency of the slower vector (that due to 13C nuclei attached to a proton after a 90°x pulse in the 13C channel and a further delay of 1/4JCH seconds.

  17. Part 3: Examples and Questions: Embedded Questions Q 2-2-2 continued 2. After a second period of 1/4JCH seconds. 3. After simultaneous 180°y (13C) and 180° (1H) pulses applied at the point reached in 2 above.

  18. Part 3: Examples and Questions: Embedded Questions Carrier Frequency A 2-2-2 b a x´ x´ 13C-H(b) 13C-H(b) y´ y´ 13C-H(a) 13C-H(a) 90°x 90°x 1/4JCH 13C 13C Delay

  19. Part 3: Examples and Questions: Embedded Questions Carrier Frequency A 2-2-2 90°x 180°y b a 1/2J 13C 180° x´ 1H 13C-H(b) x´ 13C-H(b) y´ y´ 13C-H(a) 90°x 13C-H(a) 1/4JCH 1/4JCH 13C

  20. Part 3: Examples and Questions: Embedded Questions Q 2-6-1 Carry out the full assignment of protons in the 1H COSY plot of hexan-2-one shown in Figure 2-6-3. Make sure that the couplings shown as off-diagonal signals are consistent with your assignments.

  21. C D E A B Part 3: Examples and Questions: Embedded Questions A 2-6-1 C E B A D

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