At magnetic field 16.45 T, find the ¹⁹F NMR resonance frequency in MHz to 1 decimal place. Given nuclear g = 5.255, $\beta_N=5.05\times10^{-27}$ J/T and $h=6.626\times10^{-34}$ J s.
The adjacent Zeeman-level separation is $\Delta E=g\beta_NB=h\nu$. Thus $\nu=5.255(5.05\times10^{-27})(16.45)/(6.626\times10^{-34})=6.5884\times10^8$ Hz, or 658.8 MHz. A further factor of 2π is unnecessary because h, rather than ℏ, is used.
More Spectroscopy: Atomic spectroscopy; Russell-Saunders coupling; Term symbols and spectral details; origin of selection rules. Rotational, Vibrational, Electronic and Raman spectroscopy of diatomic and simple polyatomic molecules. Line broadening and line widths; simple properties of Gaussian and Lorentzian line shapes. Molecular spectroscopy: Absorbance, Beer- Lambert’s law, Einstein’s coefficient, Jablonski diagram. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of Nuclear Magnetic Resonance: Gyromagnetic ratio; Chemical shift, nuclear coupling. questions
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