  The starting point of all NMR experiments is a spin polarization which
develops when we place the sample in static magnetic field $B_0$. There are
excess of spins aligned along $B_0$ (spin up with lower energy) than spins
aligned opposite (spin down with higher energy) to the field $B_0$. A natural
question is what is the source of this excess spin polarization because
relaxation mechanisms can flip a up spin to a down spin and vice-versa. The
answer lies in the density of states. When a molecule with spin down flips to
spin up it loses energy. This energy goes into increasing the kinetic energy of
the molecule in the gas/solution phase. At this increased kinetic energy, there
are more rotational-translational states accessible to the molecule than at
lower energy. This increases the probability the molecule will spend in spin up
state (higher kinetic energy state). This is the source of excess polarization.
In this paper, we use an argument based on equipartition of energy to
explicitly count the excess states that become accessible to the molecule when
its spin is flipped from down to up. Using this counting, we derive the
familiar Boltzmann distribution of the ratio of up vs down spins. Although
prima facie, there is nothing new in this paper, we find the mode counting
argument for excess states interesting. Furthermore, the paper stresses the
fact that spin polarization arises from higher density of states at increased
kinetic energy of molecules.
