Question on nuclear magnetic resonance and Larmor frequency

[Anonymouse]

The energy difference between two nuclear spin states in an external magnetic field B is given by

$\Delta E = \gamma \hbar B$

Why does resonant absorption of electromagnetic radiation by nuclear spins take place at the Larmor frequency? Shouldn't it be that the photon energy is equal to the energy difference between the two nuclear spin states? Or in this case, does the radiation freuquency just happen to be equal to the Larmor frequency? What is the value of invoking the Larmor frequency into the explanation of NMR? Wouldn't it just be simpler to say the photon energy must be equal to the energy difference between spin states?

 

[azntoon]

The Larmor frequency is invoked in the explanation of NMR because it is the frequency at which resonant absorption of electromagnetic radiation by nuclear spins takes place. The energy of the photon must be equal to the energy difference between the two nuclear spin states, and this energy difference is determined by the Larmor frequency. Therefore, the photon energy must be equal to the Larmor frequency in order for resonant absorption to take place. In other words, the resonance of the nuclear spin states occurs when the photon has the same energy as the energy difference between the two spin states, which is determined by the Larmor frequency. This means that the radiation frequency must be equal to the Larmor frequency for resonant absorption to occur. It is the Larmor frequency that determines the energy difference between the two spin states, and therefore it is the value that must be used to explain NMR.