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Why are excess nuclei required to produce an NMR signal?

In NMR, an excess population of nuclei is required to produce a signal. If saturation is achieved (same number of nuclei in the α and β states) no net signal can be produced. A signal is produced when a radio frequency causes one state (could be either α or β) to invert. During the process of inverting, the net oscillating electric field of the nuclei is tipped to the xy plane until they undergo relaxation back to the inverted state. Even if a particular set of nuclei are saturated, they will still undergo resonance, thus producing an oscillating electric field in the xy plane. This should be detectable; however, it is not. I am guessing that this is because the oscillating electric fields cancel each other out (since they are occurring for both the α and β states). This would result in canceling out the net electric field; however, I am not sure of my guess.

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