Chap18 solutions

Physical Chemistry

  • Homework Help
  • PresidentHackerCaribou10582
  • 11

Info icon This preview shows pages 1–2. Sign up to view the full content.

18 Spectroscopy 3: magnetic resonance Solutions to exercises Discussion questions E18.1(b) Before the application of a pulse the magnetization vector, M , points along the direction of the static external magnetic field B 0 . There are more α spins than β spins. When we apply a rotating magnetic field B 1 at right angles to the static field, the magnetization vector as seen in the rotating frame begins to precess about the B 1 field with angular frequency ω 1 = γ B 1 . The angle through which M rotates is θ = γ B 1 t , where t is the time for which the B 1 pulse is applied. When t = π/ 2 γ B 1 , θ = π/ 2 = 90 , and M has rotated into the xy plane. Now there are equal numbers of α and β spins. A 180 pulse applied for a time π/γ B 1 , rotates M antiparallel to the static field. Now there are more β spins than α spins. A population inversion has occurred. E18.2(b) The basic COSY experiment uses the simplest of all two-dimensional pulse sequences: a single 90 pulse to excite the spins at the end of the preparation period, and a mixing period containing just a second 90 pulse (see Fig. 18.44 of the text). The key to the COSY technique is the effect of the second 90 pulse, which can be illustrated by consideration of the four energy levels of an AX system (as shown in Fig. 18.12). At thermal equilibrium, the population of the α A α X level is the greatest, and that of β A β X level is the smallest; the other two levels have the same energy and an intermediate population. After the first 90 pulse, the spins are no longer at thermal equilibrium. If a second 90 pulse is applied at a time t 1 that is short compared to the spin-lattice relaxation time T 1 the extra input of energy causes further changes in the populations of the four states. The changes in populations will depend on how far the individual magnetizations have precessed during the evolution period. For simplicity, let us consider a COSY experiment in which the second 90 pulse is split into two selective pulses, one applied to X and one to A. Depending on the evolution time t 1 , the 90 pulse that excites X may leave the population differences across each of the two X transitions unchanged, inverted, or somewhere in between. Consider the extreme case in which one population difference is inverted and the other unchanged (Fig. 18.45). The 90 pulse that excites A will now generate an FID in which one of the two A transitions has increased in intensity, and the other has decreased. The overall effect is that precession of the X spins during the evolution period determines the amplitudes of the signals from the A spins obtained during the detection period. As the evolution time t 1 is increased, the intensities of the signals from A spins oscillate at rates determined by the frequencies of the two X transitions.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 2
This is the end of the preview. Sign up to access the rest of the document.
  • '
  • NoProfessor
  • Nuclear magnetic resonance, magnetic resonance, Jt, gI µN

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern