I Nuclear spin quantum number

EcqW electrochemical cell potential I nuclear spin quantum number... 

I = nuclear spin quantum number Q = quadrupole moment t] = asymmetry parameter = correlation time for molecular rotation coq = Larmor frequency. 

I = nuclear spin quantum number J= coupling constant R = receptivity Tj = relaxation time y = gyro-magnetic ratio d = chemical shift. 

The isotope has a nuclear spin quantum number I and so is potentially useful in nmr experiments (receptivity to nmr detection 17 X 10 that of the proton). The resonance was first observed in 1951 but the low natural abundance i>i S(0.75%) and the quadrupolar broadening of many of the signals has so far restricted the amount of chemically significant work appearing on this rcsonance, However, more results are expected now that pulsed fourier-transform techniques have become generally available. 

All have zero nuclear spin except (33.8% abundance) which has a nuclear spin quantum number this isotope finds much use in nmr spectroscopy both via direct observation of the Pt resonance and even more by the observation of Pt satellites . Thus, a given nucleus coupled to Pt will be split into a doublet symmetrically placed about the central unsplit resonance arising from those species containing any of the other 5 isotopes of Pt. The relative intensity of the three resonances will be (i X 33.8) 66.2 ( x 33.8), i.e. 1 4 1. 

We often say that an electron is a spin-1/2 particle. Many nuclei also have a corresponding internal angular momentum which we refer to as nuclear spin, and we use the symbol I to represent the vector. The nuclear spin quantum number I is not restricted to the value of 1/2 it can have both integral and halfintegral values depending on the particular isotope of a particular element. All nuclei for which 7 1 also posses a nuclear quadrupole moment. It is usually given the symbol Qn and it is related to the nuclear charge density Pn(t) in much the same way as the electric quadrupole discussed earlier ... 

This equation is called the Curie law and relates the equilibrium magnetization M0 to the strength of the magnetic field B0. The constants have the following meaning I is the nuclear spin quantum number (see below), y is the gyromagnetic ratio specific for a given isotope, h is Planck s constant, kB is Boltzmann s constant, N is the number of nuclei and T is the temperature. 

Equation (2.3) describes line positions correctly for spectra with small hyperfine coupling to two or more nuclei provided that the nuclei are not magnetically equivalent. When two or more nuclei are completely equivalent, i.e., both instantaneously equivalent and equivalent over a time average, then the nuclear spins should be described in terms of the total nuclear spin quantum numbers I and mT rather than the individual /, and mn. In this coupled representation , the degeneracies of some multiplet lines are lifted when second-order shifts are included. This can lead to extra lines and/or asymmetric line shapes. The effect was first observed in the spectrum of the methyl radical, CH3, produced by... 

Quadrupolar nuclei, i.e., those with a nuclear spin quantum number 7 greater than or equal to one, outnumber their spin-1/2 counterparts by a factor of roughly 3 1 and are critically important in the study of many solid materials. For example, nB (spin 7 = 3/2, 80% natural abundance), 14N (7=1, 99.6%), 23Na (7 = 3/2, 100%), 170 (7 = 5/2, 0.04%) and 27A1 (7 = 5/2,100%) comprise some of the most important atomic nuclei in chemistry, materials science, and biology. As is well... 

Proceeding in the spirit above it seems reasonable to inquire why s is equal to the number of equivalent rotations, rather than to the total number of symmetry operations for the molecule of interest. Rotational partition functions of the diatomic molecule were discussed immediately above. It was pointed out that symmetry requirements mandate that homonuclear diatomics occupy rotational states with either even or odd values of the rotational quantum number J depending on the nuclear spin quantum number I. Heteronuclear diatomics populate both even and odd J states. Similar behaviors are expected for polyatomic molecules but the analysis of polyatomic rotational wave functions is far more complex than it is for diatomics. Moreover the spacing between polyatomic rotational energy levels is small compared to kT and classical analysis is appropriate. These factors appreciated there is little motivation to study the quantum rules applying to individual rotational states of polyatomic molecules. 

Nuclear magnetic resonance (NMR) is based on a phenomenon that nuclei which possess both magnetic and angular moments (i.e. have odd mass number or odd atomic number) interact with an applied magnetic field B0 yielding 21 + 1 (where 1 is the nuclear spin quantum number) energy levels with separation AE ... 

NUCLEAR SPIN. The intrinsic angular momentum of the atomic nucleus due to rotation about its own axis, It is usually designated I and has the magnitude, JI 1 + 1 )h/2iz /(/z/2jt), where I is the nuclear spin quantum number which has different (integral or half-integral) values... 

In defining the spin quantum number of an electron (5 = 1 /2), and the nuclear spin quantum number, I, of an atomic nucleus for example, 45Sc has I =... 

Figure 4.20 19F NMR spectrum of 4.44- (n-Bu)4N+F 0.5 1 after heating at 150 °C for 1 h in DMSO-c/6 followed by storage at 25 °C for 10 d. The resonances from left to right correspond to anion cryptates with respectively 0, 1, 2, 3, 4, 5 and 6 NH protons replaced by deuterium. The observed multiplicity follows the standard formula multiplicity = 2n/+ 1 where n is the number of H nuclei remaining and /is the nuclear spin quantum number of H, i.e. xh. (Reproduced with permission from [38] 2004 American Chemical Society).

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