Hore: Nuclear Magnetic Resonance 2e Chapter 6 Instructions Answer the following questions and then press 'Submit' to get your score. Question 1 What is the strength (B_{1}) of a ^{13}C 90° pulse of duration 1 μs? a) 3.72 mT b) 5.18 mT c) 17.0 mT d) 23.3 mT Question 2 The equilibrium populations of the ^{1}H energy levels of a molecule are n_{α} = n_{α}^{eq} and n_{β} = n_{β}^{eq}. What are the populations after a 5.0 μs pulse when B_{1} = 4.697 mT? a) n_{α} = n_{β}^{eq} and n_{β} = n_{α}^{eq} b) n_{α} = n_{α}^{eq} and n_{β} = n_{β}^{eq} c) n_{α} = ½(n_{α}^{eq} + n_{β}^{eq}) and n_{β} = ½(n_{α}^{eq} + n_{β}^{eq}) d) n_{α} = n_{α}^{eq} + n_{β}^{eq} and n_{β} = n_{α}^{eq} + n_{β}^{eq} Question 3 During a delay, spins with an offset frequency Ω = 250 rad s^{-1} precess through an angle of 60°. How long is the delay? a) 4.19 ms b) 26.3 ms c) 240 ms d) 1510 ms Question 4 The amplitude of a free induction decay drops to 25% of its initial intensity after 1.0 s. Assuming exponential relaxation and Ω = 0, determine the value of T_{2}. a) 0.721 s b) 0.750 s c) 1.386 s d) 1.661 s e) 4.000 s Question 5 The NMR spectrum obtained by Fourier transforming a free induction decay of the form cos(Ω_{0}t)exp(-t/T_{2}) comprises a single line at offset frequency Ω = Ω_{0} . Determine the appearance of the spectrum obtained by Fourier transforming the free induction decay, cos^{3}(πJt) cos(Ω_{0}t)exp(-t/T_{2}).[cos^{3}x = ¼cos3x + ¾cos x; cos x cos y = ½cos(x + y) + ½cos(x - y).] a) Three equally spaced lines with equal intensity b) Three equally spaced lines with relative intensities 1:2:1 c) Four equally spaced lines with equal intensity d) Four equally spaced lines with relative intensities 1:3:3:1 e) Five equally spaced lines with equal intensity f) Five equally spaced lines with relative intensities 1:4:6:4:1 Question 6 In an NMR experiment on a sample with the equilibrium polarization p_{eq}, it takes 0.30 s to record a single pulse-acquire free induction decay. The signal-to-noise ratio (SNR) of the corresponding spectrum is 0.1. Using signal averaging, how long would it take to obtain a spectrum with SNR = 100 when the polarization immediately before each repeat of the pulse-acquire sequence is (i) p_{eq} and (ii) 100p_{eq}? a) (i) 300,000 s and (ii) 3,000 s b) (i) 300,000 s and (ii) 30 s c) (i) 3,000 s and (ii) 30 s d) (i) 30,000 s and (ii) 300 s Question 7 In an inversion recovery experiment, the signals at τ = 0.0 and at τ = 1.60 s have relative intensities -A and +A/3 respectively. Assuming exponential relaxation, calculate the value of T_{1}. a) 1.108 s b) 1.307 s c) 1.456 s d) 1.693 s Question 8 Fig. 6.13 shows the operation of a 90°_{x} - τ - 180°_{y} - τ spin echo sequence. What is the result of the sequence 90°_{x} - τ - 180°_{x} - τ in which the 180° pulse has phase x instead of y? a) The spins are refocused along the +y axis. b) The spins are refocused along the -y axis. c) The spins are refocused along the +x axis. d) The spins are refocused along the -x axis. e) The spins are not refocused. Question 9 The spectrum of a molecule containing an isolated proton is recorded using the pulse sequence: 90°_{x} - τ - 90°_{-x}. In the first experiment, Ω = 0. In a separate experiment, Ωτ = ½π. Which of the following statements is true? a) The two spectra have equal, non-zero intensity. b) The two spectra have zero intensity. c) The two spectra have equal and opposite intensities. d) The first spectrum, but not the second, has zero intensity. e) The second spectrum, but not the first, has zero intensity. Question 10 What is the enhancement factor obtainable in a ^{1}H-^{103}Rh INEPT experiment?[|ɣ(^{103}Rh)| = 8.468 x 10^{6} T^{-1 }s^{-1}] a) 4.66 b) 7.93 c) 27.1 d) 31.6