Homework-1: Spin Physics.

  1. Most magnetic resonance imagers operate at 1.5 Tesla, but recently clinical units have been approved that operate at 3.0 Tesla. What is the resonance frequency of the following nuclei in each of the magnetic fields?

    1H
    23Na
    31P

  2. What is the energy of the photon that will be absorbed by a 1H nucleus in a 1.5 Tesla magnetic field? How does this compare in energy to a 2x1019 Hz x-ray photon? What is the ionization potential for a typical organic molecule? Which of the two photons will ionize the molecule?

  3. Based on Boltzmann statistics, which molecule in question number one will have the greater signal? At which field strength will the signal be greater? Based on natural and biological abundance, which nucleus will have the greater signal?

  4. A sample has a T1 of 0.8 seconds. The net magnetization from the smaple set equal to zero and then allowed to recover towards its equilibrium value. After 1.0 seconds, what fraction of the equilibrium magnetization value will be present?

  5. A sample has a T2 of 50 ms. The net magnetization is rotated into the xy-plane and allowed to decay. Who much transverse magnetization will be present 20 ms after being placed in the plane?

  6. A hydrogen sample is at equilibrium in a 1.5 Tesla magnetic field. A constant B1 field of 2.34x10-4 Tesla is applied along the +x'-axis for 25 microseconds. What is the direction of the net magnetization vector after the B1 field is turned off?