1D Nuclear Magnetic Resonance Spectra

Abstract

Some atomic nuclei have a nuclear spin (I), and the presence of a spin makes these nuclei behave like bar magnets. In the presence of an applied magnetic field the nuclear magnets can orient themselves in 2I + 1 ways. Those nuclei with an odd mass number have nuclear spins of 1/2, or 3/2, or 5/2, …, etc. (given in the first table at the end of this chapter). In the applications of NMR spectroscopy in organic chemistry, the five most important nuclei are 1H and 13C, followed by 19F, 29Si and 31P, all of which have spins of 1/2. These nuclei, therefore, can take up one of only two orientations, a low-energy orientation aligned with the applied field and a high-energy orientation opposed to the applied field. The difference in energy between these two orientations is given by Eq. (4.1), the Boltzmann distribution by Eq. (4.2), and the frequency $ν$ in Hz corresponding to the difference in energy by Eq. (4.3):where $γ$ is the magnetogyric ratio (also called the gyromagnetic ratio), which is a measure of the relative strength of the nuclear magnet, and is different for each element and for each isotope of each element, B0 is the strength of the applied magnetic field, N$α$ is the number of nuclei in the low-energy state, and N$β$ the number in the high-energy state. A radio-frequency signal applied to the system changes the Boltzmann distribution when the radio frequency matches the frequency $ν$. It is called the resonance frequency or Larmor frequency for that particular nucleus. The effect is to promote nuclei from the low-energy N$α$ level to the high-energy level N$β$ (Fig. 4.1).