What is the formla for the energy difference between the allowed nuclear spin states for #""^1 H# nuclei?

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Answer 1 · 2016-01-05T02:31:38

The formula is #ΔE = hν = γh(B_0-B_e)#.

In the presence of an applied external magnetic field, #""_1"H"# nuclei exist in two nuclear spin states of different energy.

A large magnet creates a homogeneous external magnetic field, #B_0#.

The energy difference #ΔE# between the spin states is proportional to the strength of #B_0#.

NMR spectroscopy records transitions between these spin states induced by a radio frequency electromagnetic field called the #B_1# field.

In practice, the electrons surrounding the nucleus produce a small magnetic field #B_e# that opposes the #B_0# field.

The field experienced by the proton is then #(B_0-B_e)#.

Finally, there is a proportionality constant #γ# (the gyromagnetic ratio) that is characteristic of a proton.

The final equation is

#ΔE = hν = γh(B_0-B_e)#, where

#ν# is the frequency of the #B_1# field.

The graph below shows how the energy difference between the two spin states varies with the applied field.

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