Magnetism Pauli exclusion principle

Hund s rule, like the Pauli exclusion principle, is based on experiment It is possible to determine the number of unpaired electrons in an atom. With solids, this is done by studying their behavior in a magnetic field. If there are unpaired electrons present the solid will be attracted into the field. Such a substance is said to be paramagnetic. If the atoms in the solid contain only paired electrons, it is slightly repelled by the field. Substances of this type are called diamagnetic. With gaseous atoms, the atomic spectrum can also be used to establish the presence and number of unpaired electrons. 

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 Pauli Exclusion Principle. No two electrons in an atom may have the same four quantum numbers n, t, m, ms where m and ms are respectively the magnetic and spin quantum numbers. 

The hydrogen nucleus is classified as a Eermi particle with nuclear spin I = 1/2. Because of Pauli exclusion principle, hydrogen molecule is classified into two species, ortho and para. Erom the symmetry analysis of the wave functions, para-hydrogen is defined to have even rotational quantum number J with a singlet nuclear spin function, and ortho-hydrogen is defined to have odd J with a triplet nuclear spin function. The interconversion between para and ortho species is extremely slow without the existence of external magnetic perturbation. 

Nonrelativistic quantum mechanics, extended by the theory of electron spin and by the Pauli exclusion principle, provides a reliable theory for the computation of atomic spectral frequencies and intensities, of cross sections for scattering or capture of electrons by atomic systems, of chemical bonds and many properties of solids, including magnetic properties, although with much more complicated systems it has not always proved possible to develop with adequate accuracy the consequences of the theory. Quantum mechanics has also had a limited success in nuclear theory although m this field it is possible that a more fundamental system of mechanics is required. 

FJectron correlations are intimately associated with two assumptions (1) a fourth quantum number, the electron-spin quantum number s, and ( ) the Pauli exclusion principle. In order to account for spectral data, it is necessary to postulate that electrons spin about their own axis to create a magnetic moment (G2o). Whereas the magnetic moment associated with the angular momentum may have (2Z + 1) components mi in the direction of an external magnetic field H, the spin moment may have only two components corresponding to s = ms = 1/2. Classically the magnitude of the moment fia associated with an angular momentum p is... 

Why is it that each orbital can contain only two electrons A hypothesis suggests that electrons spin around their own axes as they move around the nucleus, generating magnetic fields. They can spin either in a positive direction or in a negative direction. In 1925, Wolfgang Pauli proposed that only two electrons of opposite spin could occupy an orbital. This idea became known as the Pauli exclusion principle. 

A little further discussion on electron spin is in order now. Spin orbitals are necessary because an electron possesses a spin quantum number (-l-j or — ). In the absence of a magnetic held, the up and down spins are energetically degenerate, or indistinguishable. The Pauli exclusion principle says that electronic wave functions must be antisymmetric (they change sign) under the interchange of any two electrons. Because of this antisymmetry, two electrons are not allowed to occupy the same quantum state. 

This can be shown by writing down only those electronic arrangements of m and ms which do not violate the Pauli exclusion principle. For p electrons, the subsidiary quantum number 1=1, and the magnetic quantum number m may have values from + / 0 /, giving in this case values of m = + 1, 0 and -1. There are 15 possible combinations. 

The Pauli exclusion principle is one of the fundamental principles of quantum mechanics. It can be tested by a simple observation. If the two electrons in the lx orbital of a helium atom had the same, or parallel, spins or ), their net magnetic fields would reinforce each other. Such an arrangement would make the helium atom paramagnetic [Figure 7.24(a)]. Paramagnetic substances are those that are attracted by a... 

Some of the statements are vague and misleading. Even apart from the fact that the three real p functions cannot be defined in a single coordinate system for the purpose of linear combination, a more serious objection is that each of them has the same magnetic quantum number m = 0. In addition they also have n = 2 and 1=1. The assumption therefore violates the Pauli exclusion principle, emphasized in statement 2. However, the sp carbon has three electrons with = 2, / = 1 and m = 0, and there are only two possible spin values, Wj = 5. The exclusion principle is widely recognized to be as ruthless as the second law of thermodynamics. The idea of sp hybridization is therefore as ludicrous as perpetual motion. 

The Pauli exclusion principle states that no two electrons in the same atom are identical, that is, no two electrons in the same atom have an identical set of quantum numbers. Each electron of an electron pair differs only by their spin orientation they have identical principal, orbital and magnetic quantum numbers. One electron has a... 

Electrons have an intrinsic property called electron spin, which is quantized. The spin magnetic quantum number, in can have two possible values, + and — which can be envisioned as the two directions of an electron spinning about an axis. The Pauli exclusion principle states that no two electrons in an atom can have the same values for it, I, ni), and nig. This principle places a limit of two on the number of electrons that can occupy any one atomic orbitaL These two electrons differ in their value of nig. 

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