where N+ and N- represent the number of spins one would expect to measure in the spin-up and spin-down configurations, ΔE is the difference in energy between the two states, k is the Boltzmann constant (1.381 x 10-23 joules/°K), and T is the absolute temperature in degrees Kelvin. At body temperature in a field of 1.0 Tesla, this equation predicts that the N+ and N- are nearly equal; only a small excess (~3 x 10-6) of spins can be expected to be found in the lower energy (spin-up) state when measured.
Another way to think about the distribution of spin states and thermal interactions is using the "Compasses in a Dryer" analogy (pictured left). Here individual nuclei are envisioned as small compasses placed in a dryer. Just as nuclei "prefer" to point in the direction of the main magnetic field, so the little compasses all try to align along the earth's magnetic field and point to the North Star. The compasses are all constantly being jarred by the tumbling dryer and interact with each other (the equivalent of thermal collisions and spin-spin interactions experienced by nuclei). As such, only a small fraction of the compasses will actually point north.
Both classical thermodynamic analysis using the Boltzmann distribution or quantum mechanics provides equivalent estimates for the value of Mo
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Keeler J. NMR and energy levels. From The Keeler Group, Lectures by James Keeler, 2004 (http://www-keeler.ch.cam.ac.uk/lectures/)
Hanson L. Is quantum mechanics necessary for understanding magnetic resonance? Concepts Mag Reson Part A 2008;32A(5):329-340.
What is the difference between "spin" and "spin state"?
When a group of spins is driven into higher energy levels by the action of an RF field, why don't these spins immediately release the absorbed energy and drop back to their original lower energy states?