HW 1 Multinuclear NMR Name:
Points: C6800 Date:
Max. 100 points Spring 2011 Version A
1. A nucleus has a T1 of 5.0 seconds. If the net magnetization is set equal to zero, how long
will it take for the net magnetization to recover by spin-lattice relaxation to 95% of its
equilibrium value? T1 [s] longitudinal relaxation time = 5.0 s (Hint: Use Bloch equations.)
2. A nucleus has a T2 of 100 ms. How long will it take for any transverse magnetization to
decay by spin-spin relaxation to 37% of its starting value? T2 [s] transverse relaxation time =
100 ms (Hint: Use Bloch equations.)
3. What is the energy of the photon that will be absorbed by a 1
H nucleus in a 11.5 Tesla
magnetic field? Compare this energy to a 2 1019
Hz x-ray photon. What is the ionization
potential for a typical organic molecule and which of the two photons will ionize the
molecule?
4. Show that Emag = − µ ⋅ B0 = − µz ⎟ B⎟
5. Find nuclear spins I of 2
H, 10
B, 51
V, and 183
W. For each nucleus list all possible values of mI
in the order of increasing stability of energy state. Calculate the energy difference between the
levels inside a 300 MHz magnet. Calculate the excess of nuclei on the lowest energy level of
10
B at 300 and 173 K.