Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, most nuclei prefer the lower energy spin +½ state to the higher energy spin −½ state.

At room temperature, the energy from thermal collisions distributes the spins more equally between the two states, as described by the Boltzmann distribution equation.

N₊ and N₋ represent the number of spins predicted in the spin +½ and spin −½ states, respectively.

The energy difference between the spin states, ΔE, is expressed as hν, where h is the Planck constant and ν is the operating frequency of the NMR instrument. k is the Boltzmann constant, and T is the absolute temperature measured in kelvin.

For example, in a 60 MHz instrument, at 298 kelvin, the lower energy state has an excess population of approximately nine to ten among two million nuclei, which produce the NMR signal.

Using a higher operating frequency increases the energy gap and the excess population.