Problem Set 1, due Feb 10
1) Consider a magnetic field of 11.7 T. Calculate the chemical shift on a ppm
scale for proton nuclei whose frequency is 1340 Hz higher than for the reference
compound TMS (=0 ppm). Are those nuclei shielded or deshielded by the
surrounding electrons?
2) Based on the Bloch equations, which direction does the vector
d 
M point with
dt
respect to M and B?
3) Why is the chemical shift of alpha H of amino acids much larger than for
aliphatic methine groups?
4) What is the ratio of populations between the up and down energy states of a
1
H spin ½ placed in a magnetic field of 23 T at 300 K? At what temperature will
the ratio be 0.9?
5) The chemical shift of water protons moves by 0.01 ppm per ºC. At a field of 7T,
by how much does the frequency move if the temperature is changed by 10ºC?
6) Consider a one-dimensional magnetic resonance imaging experiment. If the
applied magnetic field gradient is of size 0.1 T/m, what is the resonance
frequency shift between proton spins that are separated by a distance of 1 cm?
How many ppm would that be if this were done at 1.5 T static magnetic field (a
common MRI field strength)?
Consider an MRI image taken of some part of the human body. Considering that
the human body contains various substances with a variety of chemical shifts
different from the one of water, the signals of those may overlap with water
signals some distance away. Considering a chemical shift of 4ppm, what
distance would this correspond to? In other words: the signal shows up in the
wrong location in the ‘image’. By how much is it displaced? (assume 1H spins)
7) Show the coupling pattern for the 13C spectrum of a –CHD2 group. Include
coupling to both 1H and 2D (note: for 2D I=1).
Additional problems (not required, but highly recommended) are:
Hore book:
Exercises 1.1, 1.2, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10
2.1, 2.2, 2.3, 2.4, 2.8
3.3, 3.6, (3.7)