Magnetic quantum number mt

The quantum number, m , originating from the 0(6) and P(0) functions of the Schrodinger wave equation, indicates how the orbital angular momentum is oriented relative to some fixed direction, particularly in a magnetic field. Thus, ml roughly characterizes the directions of maximum extension of the electron 

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An operator Op is assumed to cause a transition from a state with angular momentum Jj and magnetic quantum number Mt to a state with quantum numbers JtMt. The ensemble is assumed to be randomly oriented in the initial state, and no observation with respect to the quantum number Mf is made in the final state. Under these conditions the transition rate P can be calculated from... 

The magnetic quantum number mt describes how the various orbitals are oriented in space. The value of m, depends on the value of /. The values allowed are Integers from -/ to 0 to +/. For example, if the value of / = 1 (p orbital — see Table 34), you can write three values for m/ -1,0, and +1. This means that there are three different p subshells for a particular orbital. The subshells have the same energy but different orientations in space. 

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... 

The valence electron for the cesium atom is in the 6s orbital. In assigning quantum numbers, n = principal energy level = 6. The quantum number l represents the angular momentum (type of orbital) with s orbitals = 0, p orbitals = 1, d orbitals = 2, and so forth. In this case, l = 0. The quantum number m is known as the magnetic quantum number and describes the orientation of the orbital in space. For, v orbitals (as in this case), mt always equals 0. For p orbitals, mt can take on the values of -1, 0, and +1. For d orbitals, can take on the values -2, -1, 0, +1, and +2. The quantum number ms is known as the electron spin quantum number and can take only two values, +1/2 and -1/2, depending on the spin of the electron. 

The energy states of atoms are expressed in terms of four quantum numbers j it, the principal quantum number /, the azimuthal quantum number m, the magnetic quantum number and mt or s, the spin quantum number. According to Pauli s exclusion principle, no two electrons can have the same values for all the four quantum numbers. 

The partial solution of the equation that contains the angular dependence results in the introduction of another quantum number, mt. This number is called the magnetic quantum number. The magnetic quantum number gives the quantized lengths of the projection of the l vector along the z-axis. Thus, this quantum number can take on values +/, (/ - 1),. ..,... 

The magnetic quantum number mi or m may have integer values from -/ to /. mi is a measure of how an individual orbital responds to an external magnetic field, and it often describes an orbital s orientation. A subscript—either the value of /r / or a function of the x-, y-, and z-axes—is used to designate a specific orbital. See Skill 1.2a for images of electron density regions for a few orbitals of hydrogen. n=3,1=2, and mt=0 for the Zdo orbital. Each orbital may hold up to two electrons. 

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... 

The third quantum number, mb describes the orientation of the electron orbital relative to an arbitrary direction. Because an external magnetic field (such as might be induced by a neighboring atom) provides a convenient reference direction, mt is usually called the magnetic orbital quantum number. It can take an integral value from —l to /. 

As long as there is no external magnetic field for nuclei for which the nuclear spin quantum number I = Yi, the number of nuclei with mt Vi equals the number of nuclei with nij = +3/2 there is a dynamic equilibrium... 

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