A solution and solid state study of niobium complexes University of ...

Chapter 3
Electrons, neutrons and protons are considered to posses spinning properties and
when these spins are paired against each other, the overall spin of the atom can be
determined. The rules for determining the overall spin (I) of a nucleus are as follows:
i. If the number of protons and neutrons are both even, the nucleus has no spin.
ii. If the number of protons plus the number of neutrons is odd, the nucleus has
a half-integer spin (1/2, 3/2, 5/2).
iii. If the number of protons and the number of neutrons are both odd, the
nucleus has an integer spin (1, 2, 3).
According to quantum mechanics, a nucleus of spin I will have 2I + 1 possible
orientations. 2 Hence, a nucleus ( 1 H) with spin 1/2 will have 2 possible orientations.
When no external magnetic field is applied, the spin orientations are of equal energy.
In the presence of a magnetic field, the energy levels are split. Each level has a
magnetic quantum number (m) as indicated in Figure 3.1.
Energy
Figure 3.1: Energy levels for a nucleus with spin quantum number 1/2.
The spin state +1/2 has the lowest energy as it is aligned with the applied magnetic
field, whereas the –1/2 spin state has higher energy because it is opposed to the
applied field. The two spin states are separated by an energy difference, ∆E, which
is dependent on the strength of the magnetic field as well as the size of the nuclear
magnetic moment. The difference in energy between the levels can be determined
from:
∆E =
2 P.J. Hore, Nuclear Magnetic Resonance, Oxford University Press, New York, 52, 1995.
(3.1)
43