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Spin Population Excess

When a sample is placed in a magnet a net polarization forms in all its nuclear & electron spins. Sensitivity in NMR and EMR experiments is largely determined by the net polarization of the spins being detected. This net polarization is influenced by two main factors:

  1. g - The spin gyromagnetic ratio.
  2. Bo - The applied magnetic field strength.

Each spin type has its own gyromagnetic ratio and hence a relative sensitivity. By changing the spin type and field strength below one can see the resulting spin resonance frequency and spin population excess.

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Above, Bo represents the strength of the magnet the sample is in, Spin will be the type of spins detected in an experiment, and W is the (Larmor) frequency where the spins will be detected. The value of a is the net number of spins per million (or 100 million) responsible for net polarization. Note how the large the electron spin excess is relative to nuclei excess values. This is because the gyromagnetic ratio of e- is much larger, making ESR a more sensitive technique than NMR.

The large circle represents a cross section of the sample in a magnet, and within the circle are crude representations of the spins. Each will either be "spin up" or "spin down", the relative amounts dictated by the Boltzmann equation.

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