Magnetic Resonance
The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field B: ν = γB. It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 25 °C is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p. The gyromagnetic ratio is related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant.
The ratio of the shielded proton magnetic moment μ′p to the electron magnetic moment μe can be measured separately and to high precision, as the imprecisely-known value of the applied magnetic field cancels itself out in taking the ratio. The value of μe in Bohr magnetons is also known: it is half the electron g-factor ge. Hence
A further complication is that the measurement of γ′p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes, so a conversion factor is required. The symbol Γ′p-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant.
Substitution gives the expression for the Planck constant in terms of Γ′p-90(hi):
Read more about this topic: Planck Constant, Determination
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