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In NMR experiment we provide an external radio frequency signal which will induce transition of nuclear spins to higher states,and then it returns to ground state precessing around the magnetic field in Larmor frequency,which is the same as that of absorbed radio frequency.One thing i don't understand is the underlying reason for resonance. Why is it that a system absorbs a certain frequency called the natural frequency? Another thing is both protons and neutrons have different magnetic moments so they should have different Larmor frequencies(right?),but we obtain only one resonance frequency in the experiment so which one does it correspond to?Another thing is how do neutrons which are neutral particles have magnetic moment?

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The answer lies in what Nuclear Magnetic Resonance is,

Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a magnetic field absorb and re-emit electromagnetic radiation. This energy is at a specific resonance frequency which depends on the strength of the magnetic field and the magnetic properties of the isotope of the atoms

It is the magnetic moment of the total nucleus, a composite from the intrinsic moments of the constituents and the moments possibly coming from angular momentum eigenstates. One frequency only because each nucleus has one magnetic moment and can be kicked to an excited state by one photon, i.e. to a higher energy level of the quantum mechanical solution of the composite problem.

A non-zero spin is thus always associated with a non-zero magnetic moment (μ) via the relation μ = γS, where γ is the gyromagnetic ratio. It is this magnetic moment that allows the observation of NMR absorption spectra caused by transitions between nuclear spin levels.

To answer your last question, a neutron is a composite particle made up of three charged quarks, (and so is the proton), en.wikipedia.org/wiki/Neutron , which are in a specific wave function. How exactly the magnetic moments of the baryons appear is a study of the internal state functions and QCD is still at the stage of development in calculations.

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