Nucleus wave mechanics

It can be shown, from wave-mechanical calculations, that the Is orbital (quantum numbers n = 1, Z = 0, m = 0, corresponding to the classical K shell) is spherically symmetrical about the nucleus of the atom, and that the 2s orbital (quantum numbers n = 2, Z = 0, m = 0) is similarly spherically symmetrical, but at a greater distance from the nucleus there is a region between the two latter orbitals where the probability of finding an electron approaches zero (a spherical nodal surface). 

Take the Is electron as an example. In the Bohr theory, the electron moves in a fixed orbit of radius l o- On the other hand, in the wave mechanical treatment, the electron can in principle be found at any distance from the nucleus, and the most probable nucleus-electron separation is lao- Here we can see... 

In three dimensions a spatial wave group moves around an harmonic ellipsoid and remains compact, in contrast to the dispersive wave packets of classical optics. The distinction is ascribed to the fact that the quantum wave packet is built up from discrete harmonic components, rather than a continuum of waves. The wave mechanics of a hydrogen electron is conjectured to produce wave packets of the same kind. At small quantum numbers the wave spreads around the nucleus and becomes more particle-like, at high quantum numbers, as it approaches the ionization limit where the electron is ejected from the atom. 

The formulation of spatially separated a and 7r interactions between a pair of atoms is grossly misleading. Critical point compressibility studies show [71] that N2 has essentially the same spherical shape as Xe. A total wave-mechanical model of a diatomic molecule, in which both nuclei and electrons are treated non-classically, is thought to be consistent with this observation. Clamped-nucleus calculations, to derive interatomic distance, should therefore be interpreted as a one-dimensional section through a spherical whole. Like electrons, wave-mechanical nuclei are not point particles. A wave equation defines a diatomic molecule as a spherical distribution of nuclear and electronic density, with a common quantum potential, and pivoted on a central hub, which contains a pith of valence electrons. This valence density is limited simultaneously by the exclusion principle and the golden ratio. 

You should recall from your general chemistry course that electrons have some of the properties of waves. Chemists use the equations of wave mechanics to describe these electron waves. Solving these wave equations for an electron moving around the nucleus of an atom gives solutions that lead to a series of atomic... 

A theory of these wave numbers was worked out by Bohr before the discovery of wave mechanics or the wave particle theory. Bohr s theory was based on Einstein s idea that light consists of photons and on Rutherford s nucleus theory of the atom. 

In wave mechanics the quantum numbers / and m, are obtained directly from the theory. In the Bohr treatment, on the other hand, the value of / was associated with the magnitude of the minor axis of the elliptical orbit, and hence the lowest possible value of I was i, since when / is zero the ellipse degenerates into a straight line and the electron during its motion would pass through the nucleus. Before the introduction of wave mechanics and the theoretical proof that / may have the value zero, it had been necessary to modify the Bohr theory, by putting / = o in order to conform with spectroscopic evidence. 

In the atom, electrons move in the field of a single nucleus whereas in a molecule, the electrons exist in a field due to several nuclei and wave mechanics show that the latter state may be more favourable on the basis of energy considerations. Let us consider the simplest molecule viz the hydrogen molecule ion Hg+, formed by the combination of a hydrogen atom and a proton. In this molecule a single electron exists in the field of two nuclei. The existence of this molecule has been demonstrated spectroscopically and the heat of formation of the molecule from a hydrogen atom and a proton is 6i kcals/gm mol. the distance between the nuclei is I oGA. The ion is, however, very reactive and the energy liberated in the reaction = Hg is 354 kcals and it has therefore, a very limited... 

The probability of the transference of an electron from one nucleus to the other will increase as the nuclei approach each other and from the point of view of wave mechanics it is incorrect to locate the first electron at nucleus a and the second electron at nucleus b. The two electrons are indistinguishable and it is impossible to regard one electron as located at a certain nucleus. Therefore in addition to equation 3.71 we must consider a second expression in which the electrons have been transposed,... 

These diffraction experiments on whole atoms show that the wave structure is not a property peculiar to beams of electrons, but that there is a general principle in question classical mechanics is replaced by a new warn mechanics. For, in the case of an atom, it is clearly the centroid of all its particles (nucleus and electrons), i.e. an abstract point, which satisfies the same wave laws as the individual free electron. Wave mechanics in its developed form does actually render an account of this. 

The application of wave mechanics to the nucleus is met by the essential difficulty that the dimensions of the nucleus are of the same order of magnitude (10 cm.) as the diameter of the electron, which... 

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