Spin-1/2 nuclei have zero electric quadrupole moment due to spherical charge distribution symmetry
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Reference literature and encyclopedia sources confirm that spin-1/2 nuclei possess spherical charge distributions and lack the non-zero electric quadrupole moments that are restricted to nuclei with spins greater than or equal to 1.
non-zero quadrupole moment, which is only observed in nuclei with a nuclear spin greater than or equal to one (I ≥ 1) and whose local charge distribution
Nuclear quadrupole resonance spectroscopy or NQR is a chemical analysis technique related to nuclear magnetic resonance (NMR). Unlike NMR, NQR transitions of nuclei can be detected in the absence of a magnetic field, and for this reason NQR spectroscopy is referred to as "zero Field NMR". The NQR resonance is mediated by the interaction of the electric field gradient (EFG) with the quadrupole mome
where
γ
{\displaystyle \gamma }
is the gyromagnetic ratio and
B
{\displaystyle B}
is the (normally applied) magnetic field external to the nucleus.
In the case of NQR, nuclei with spin ≥ 1, such as 14N (spin 1), 17O (spin 5/2), 35Cl (spin 3/2) and 63Cu (spin 3/2), also have an electric quadrupole moment Q which has energy levels between which resonance can be observed, even in the absence of a magnetic field. Nuclei with spin 1 or 3/2 give only a single resonance line, but a nucleus with spin 5/2 gives two resonance lines,…
The main limitation for this technique arises from isotopic abundance. NQR requires the presence of a non-zero quadrupole moment, which is only observed in nuclei with a nuclear spin greater than or equal to one (I ≥ 1) and whose local charge distribution deviates from spherical symmetry. NQR requires fairly large sample sizes due to the signals being of very low intensity. This poses experimental obstacles due to a large majority of NQR-active nuclei having low isotopic abundances. Nevertheless, NQR spectroscopy has still proven useful in various contexts – as discussed above.
those having an odd number of nucleons) have fractional spins. - Examples are I = 1/2 ( 1H, 13C, 19F ), I = 3/2 ( 11B ) & I = 5/2 ( 17O ). - Even mass nuclei composed of odd numbers of protons and neutrons have integral spins. Examples are I = 1 ( 2H, 14N ). - Even mass nuclei composed of even numbers of protons and neutrons have zero spin ( I = 0 ). Examples are 12C, and 16O. Spin Properties of Nuclei
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.
with non-spherical charge distributions, i.e. all those with a spin quantum number (I) greater than 1/2, may have a nuclear quadrupole moment. In this
Mössbauer spectroscopy is a spectroscopic technique based on the Mössbauer effect. This effect, discovered by Rudolf Mössbauer (sometimes written "Moessbauer", German: "Mößbauer") in 1958, consists of the nearly recoil-free emission and absorption of nuclear gamma rays in solids. The consequent nuclear spectroscopy method is exquisitely sensitive to small changes in the chemical environment of cer
Quadrupole splitting reflects the interaction between the nuclear energy levels and the surrounding electric field gradient (EFG). Nuclei in states with non-spherical charge distributions, i.e. all those with a spin quantum number (I) greater than 1/2, may have a nuclear quadrupole moment. In this case, an asymmetrical electric field (produced by an asymmetric electronic charge distribution or ligand arrangement) splits the nuclear energy levels.
In the case of an isotope with a I = 3/2 excited state, such as 57Fe or 119Sn, the excited state is split into two substates mI = ±1/2 and mI = ±3/2. The ground-to-excited state transitions appear as two specific peaks in a spectrum, sometimes referred to as a "doublet". Quadrupole splitting is measured as the separation between these two peaks and reflects the character of the electric field at the nucleus.
The quadrupole splitting can be used for determining the oxidation state, spin state, site symmetry, and the arrangement of ligands.
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