NMRSpectroscopy(B)

NMRSpectroscopy(B) - NMR Topics Supplemental NMR Topics...

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NMR Topics Supplemental NMR Topics Spin Properties of Nuclei Nuclear spin may be related to the nucleon composition of a nucleus in the following manner: Odd mass nuclei (i.e. those having an odd number of nucleons) have fractional spins. Examples are I = 1/2 ( 1 H, 13 C, 19 F ), I = 3/2 ( 11 B ) & I = 5/2 ( 17 O ). Even mass nuclei composed of odd numbers of protons and neutrons have integral spins. Examples are I = 1 ( 2 H, 14 N ). Even mass nuclei composed of even numbers of protons and neutrons have zero spin ( I = 0 ). Examples are 12 C, and 16 O. Spin 1/2 nuclei have a spherical charge distribution, and their nmr behavior is the easiest to understand. Other spin nuclei have nonspherical charge distributions and may be analyzed as prolate or oblate spinning bodies. All nuclei with non-zero spins have magnetic moments ( μ ), but the nonspherical nuclei also have an electric quadrupole moment ( eQ ). Some characteristic properties of selected nuclei are given in the following table. Isotope Natural % Abundance Spin (I) Magnetic Moment (μ) Magnetogyric Ratio ( γ ) * 1 H 99.9844 1/2 2.7927 26.753 2 H 0.0156 1 0.8574 4,107 11 B 81.17 3/2 2.6880 -- 13 C 1.108 1/2 0.7022 6,728 17 O 0.037 5/2 -1.8930 -3,628 19 F 100.0 1/2 2.6273 25,179 29 Si 4.700 1/2 -0.5555 -5,319 31 P 100.0 1/2 1.1305 10,840 * γ has units of 10 7 rad T -1 sec -1 Return
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A Model for NMR Spectroscopy The model of a spinning nuclear magnet aligned with or against an external magnetic field (for I = 1/2 nuclei) must be refined for effective interpretation of nmr phenomena. Just as a spinning mass will precess in a gravitational field (a gyroscope), the magnetic moment μ associated with a spinning spherical charge will precess in an external magnetic field. In the following illustration, the spinning nucleus has been placed at the origin of a cartesian coordinate system, and the external field is oriented along the z-axis. The frequency of precession is proportional to the strength of the magnetic field, as noted by the equation: ω o = γ B o . The frequency ω o is called the Larmor frequency and has units of radians per second. The proportionality constant γ is known as the gyromagnetic ratio and is proportional to the magnetic moment ( γ = 2pm/hI ). Some characteristic γ 's were listed in a preceding table of nuclear properties . magnetic moment μ A Spinning Gyroscope in a Gravity Field A Spinning Charge in a Magnetic Field If rf energy having a frequency matching the Larmor frequency is introduced at a right angle to the external field (e.g. along the x-axis), the precessing nucleus will absorb energy and the magnetic moment will flip to its I = _ 1/2 state. This excitation is shown in the following diagram. Note that frequencies in radians per second may be converted to Hz (cps) by dividing by 2 π .
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The energy difference between nuclear spin states is small compared with the average kinetic energy of room temperature samples, and the +1/2 and _ 1/2 states are nearly equally populated. Indeed, in a field of 2.34 T the excess population of the lower energy state is only six nuclei per million. Although this is a very small difference
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