Chapter 5 Multiple Choice Questions

Fundamental constants

Planck's constant h = 6.626 10-34 J s
Boltzmann's constant kB = 1.381 10-23 J K-1
Vacuum permeability ?0 = 4? x 10-7 J s2 C-2 m-1
Gas constant R = 8.314 J K-1 mol-1

Magnetogyric ratios
Magnetogyric ratios of common nuclides can be found in Table 1.3, page 3.

. If Δn(t)/Δneq in eqn 5.1 equals 0.5 at t = 1.40 s, what is the value of T1?

. Suppose that the 13C nuclei in a molecule in a 600 MHz spectrometer can be 100% polarized (p = 1). If T1 = 5.0 s, how long does it take for p to reach a value equal to twice the thermal equilibrium polarization at 298 K?
[The polarization relaxes exponentially: p(t) = [p(0) - peq]exp(-t/T1) + peq.]

. Which of the following statements is not a reason why spin-½ nuclei in small molecules in solution usually relax slowly?

. The rotational correlation time of a spherical object of radius r immersed in a liquid with viscosity η is given by the Stokes equation: τc = 4πηr3/3kBT. A small molecule with relative molecular mass Mr = 100 in water at 298 K has τc = 50 ps. Assuming that Mr is proportional to the molecular volume, estimate τc for a small protein with Mr = 8400.

. The T2 of an NMR line is 15 ms. Ignoring other sources of linebroadening, calculate its linewidth.

. A molecule has a rotational correlation time of 1 ns. At what magnetic field would protons in this molecule have the fastest spin-lattice relaxation? [Use eqns 5.3 and 5.4.]

. In the extreme narrowing limit, what is the 15N{1H} nuclear Overhauser enhancement in the absence of other relaxation mechanisms?

. Calculate the ratio T1/T2 for protons in a 900 MHz spectrometer when (i) τc = 50 ps and (ii) τc = 50 ns. [Use eqns 5.3, 5.4, and 5.11.]

. Which of the following statements most accurately explains why the 1H spectrum of 12CHCl3 is a singlet?

. Which of the following statements most accurately explains why the T1 of a nucleus is sometimes longer than its T2?

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