Magnetic quantum, number

The negative sign in equation (b 1.15.26) implies that, unlike the case for electron spins, states with larger magnetic quantum number have smaller energy for g O. In contrast to the g-value in EPR experiments, g is an inlierent property of the nucleus. NMR resonances are not easily detected in paramagnetic systems because of sensitivity problems and increased linewidths caused by the presence of unpaired electron spins. 

According to quantum mechanics, the maximum observable component of the angular momentum is Ih/lir, where h is Planck s constant. A nucleus can assume only 21+1 energy states. Associated with each of these states is a magnetic quantum number m. where m has the values I, I — I, I —2,, —1+ 1, —I. 

The third quantum number m is called the magnetic quantum number for it is only in an applied magnetic field that it is possible to define a direction within the atom with respect to which the orbital can be directed. In general, the magnetic quantum number can take up 2/ + 1 values (i.e. 0, 1,. .., /) thus an s electron (which is spherically symmetrical and has zero orbital angular momentum) can have only one orientation, but a p electron can have three (frequently chosen to be the jc, y, and z directions in Cartesian coordinates). Likewise there are five possibilities for d orbitals and seven for f orbitals. 

The bound states (where < 0) are characterized by the three quantum numbers n (the principal quantum number), I (the azimuthal quantum number) and mi (the magnetic quantum number). 

The third quantum number required to specify an orbital is mh the magnetic quantum number, which distinguishes the individual orbitals within a subshell. This quantum number can take the values... 

The spins of two electrons are said to be paired if one is T and the other 1 (Fig. 1.43). Paired spins are denoted Tl, and electrons with paired spins have spin magnetic quantum numbers of opposite sign. Because an atomic orbital is designated by three quantum numbers (n, /, and mt) and the two spin states are specified by a fourth quantum number, ms, another way of expressing the Pauli exclusion principle for atoms is... 

For each orbital listed in Exercise 1.51, give the possible values for the magnetic quantum number. 

Among atomic orbitals, s orbitals are spherical and have no directionality. Other orbitals are nonspherical, so, in addition to having shape, every orbital points in some direction. Like energy and orbital shape, orbital direction is quantized. Unlike footballs, p, d, and f orbitals have restricted numbers of possible orientations. The magnetic quantum number (fflj) indexes these restrictions. 

The magnetic quantum number derives its name from the fact that different orbital orientations generate different behaviors in... 

The magnetic quantum number (fni) can have any positive or negative integral value between 0 and 1 ... 

C07-0075. List the values for the quantum numbers for a 3d electron that has spin up and the largest possible value for its magnetic quantum number. 

Transverse magnetization represents a particular type of coherence involving a change in quantum number p of 1. Each coherence a is equal to the difference in magnetic quantum numbers of the nuclei r and 5, i.e., the coherence order is M,—M and pulses cause transitions to occur... 

Coherence order, p The difference in the magnetic quantum number, of the two energy levels connected by the same coherence. 

Double-quantum coherence Coherence between states that are separated by magnetic quantum numbers of 2. This coherence cannot be detected directly, but must be converted to single-quantum coherence before detection. 

The third solution to Schrodinger s equation produces the magnetic quantum number, usually designated as m. Allowable values of this quantum number range from -f to +f. A summary of... 

Magnetic quantum number One solution to Schrodinger s wave equation produces the magnetic quantum number. It specifies how the s, p, d, and/orbitals are oriented in space. 

The Hamiltonian operator for the electric quadrupole interaction, 7/q, given in (4.29), coimects the spin of the nucleus with quantum number I with the EFG. In the simplest case, when the EFG is axial (y = Vyy, i.e. rf = 0), the Schrddinger equation can be solved on the basis of the spin functions I,mi), with magnetic quantum numbers m/ = 7, 7—1,. .., —7. The Hamilton matrix is diagonal, because... 

The eigenfunctions for nonaxial nuclear quadrupole interaction are mixtures of the 7, mj) basis functions and thus do not possess well-defined magnetic quantum numbers. Strictly speaking, the states should not be labeled with pure quantum numbers m/. ... 

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