Spin of an electron

According to the quantization mle this means that the spin projections onto the selected z-axis can have two values, namely. 

The quantum number m does not influence the electron wavefunction significantly however, it influences the electron distribution among the energy levels and quantum cells to a great extent. The Pauli principle is a consequence of these quantum mechanical rules. 

In full analogy with the orbital state, the spin magnetic moment can be determined through the gyromagnetic ratio g (Section 5.2.1). For spin g = 2 (in e/2 m units), the absolute value of spin magnetic moment is therefore equal to 

When chemists look at atomic and/or ionic electron states, and distribute electrons over the energy levels and/or fill in corresponding quantum cells by arrows in accordance with the Pauli exclusion principle (not more that two electrons into one quantum cell) and the Hund s rule, they bear in mind exactly these two projections of spin magnetic momenL Note that arrows are represented by schematically signs + and, since projections thonselves are not vector but algebraic values. 

---

A second approximation neglects coupling between the spin of an electron and its orbital momentum but assumes that coupling between orbital momenta is strong and that between spin momenta relatively weak but appreciable. This represents the opposite extreme to the 77-coupling approximation. It is known as the Russell-Saunders coupling approximation and serves as a useful basis for describing most states of most atoms and is the only one we shall consider in detail. 

Associated with the spin of an electron is a magnetic moment, which can be expressed by a quantum number of + or —5. According to the Pauli principle, any two electrons occupying the same orbital must have opposite spins, so the total magnetic moment is zero for any species in which all the electrons are paired. In... 

As mentioned in Section Wl, an electron has magnetism associated with a property called spin. Magnetism is directional, so the spin of an electron is directional, too. Like orbital orientation, spin orientation is quantized Electron spin has only two possible orientations, up or down. The spin orientation quantum number )... 

Quantum numbers are numbers used in Schrodinger s equation to describe the orbital size, shape, and orientation in space, and the spin of an electron. 

The principal quantum number, n, is related to the size of the orbital. A second quantum number, the angular momentum quantum number, I, is used to represent different shapes of orbital. The orientation of any non-spherical orbital is indicated by a third quantum number, the magnetic quantum number, m. A fourth quantum number, the spin quantum number, s, indicates the spin of an electron within an orbital. 

Spin-forbidden transitions. Transitions in which the spin of an electron changes are not allowed, because a change from one spin to the opposite involves a change in angular momentum and such a change would violate the law of conservation of angular momentum. 

The construction in this section generalizes. Any time there are two (or more) independent quantum-mechanical measurements, a tensor product is appropriate. We will see another example in Section 11.4, where we consider the independent measurements of position and spin of an electron. 

In this equation there has been introduced the symbol gy which is called the 0-factor, or sometimes the Land6 0-factor, after A. Land6, who introduced it. For orbital motion of an electron the 0-factor has the value 1, the ratio of magnetic moment to angular momentum being c/2w0c. For the spin of an electron, however, the 0-factor has the value 2. This value of the 0-factor cannot be explained in any simple way it has to be accepted as part of the nature of the electron. 

Figure 7.2 Coordinates for a plane wave. Having defined a reference point O (origin), an arbitrary spatial point of the wave travelling with wavenumber vector k into the K-direction is indicated by r. Cases (a) and (b) differ in the direction of the selected reference axis z (the quantization axis) which does or does not coincide with the direction of the wave, respectively. In case (c) the spin of an electron wave is also indicated it is shown as the double arrow pointing into the direction e against which the spin projection is assumed to...

The spin of an electron gives rise to a magnetic moment which can interact with effective magnetic field set up by its orbital motion about the nucleus. 

In Eq. 8.14, e is the electron charge and nif, is the electron mass. The quantity eh is the Bohr magneton, /Ab, which was aheady introduced. Equation 8.13 for the magnetic moment owing to the intrinsic spin of an electron can thus be rewritten as ... 

Electron spin quantum number (mg) The electron spin quantum number describes the spin of an electron. Magnetic fields have shown that the two electrons in an orbital have equal and opposite spins. The m values for these spins are - and... 

Electron spin quantum number The electron spin quantum number describes the spin of an electron. 

The electron may undergo intersystem crossing into a triplet state to go between a singlet and a triplet state, the spin of an electron is reversed. The triplet state is usually longer lived than the original excited state, and may decay radiatively to ground state in the process of phosphorescence. 

The spin quantum number, refers to the spin of an electron and the orientation of the magnetic field produced by this spin. For every set of n, , and values, m, can take the value +1 or — i ... 

---