Stability of atom

TABLE 4. Orbital energies and relative stabilities of atomic states for sulphur ... 

The goodness of the PP representation can be checked by comparing the all-electron and PP orbital energies and relative stability of atomic states. The comparison is shown in Table 4, and is seen to be very satisfying. For a balanced treatment, also the carbon and oxygen atoms were treated by a PP, as described in previous work5.3d functions were not introduced in the sulphur basis set, mainly because they were not deemed necessary for the illustrative purposes of this chapter. Also, the derivation of a PP representation for polarization functions is not a straightforward matter. The next section is devoted to the discussion of this point. 

The colors of fireworks depend on the energies of the atomic orbitals of the various atomic ions, but orbital energy levels have consequences that are much more far-reaching. Orbital energies determine the stabilities of atoms and how atoms react. The structure of the periodic table is based on orbital energy levels. In this chapter we explore the details of orbital energies and relate them to the form and structure of the periodic table. This provides the foundation for interpreting chemical behavior patterns. 

The stability of atoms - their property of being steadfast and remaining unchanged - is determined by the nature of their nuclei (see Textbox 12). Nuclei in which the number of neutrons is smaller than or equal to the number of protons are stable, while those in which the number of neutrons is larger than the number of protons are unstable. Unstable nuclei have a tendency to adjust the disparity between the number of neutrons and protons and become stable they may do so by one of two processes, by radioactive decay or nuclear fission. 

The inert pair concept has sometimes been advanced to account for the extra stability of atoms or ions which contain a lone pair of s-electrons (e.g.,... 

The ratio of the number of neutrons to protons determines the stability of atomic nuclei. As the number of protons in the nucleus increases, the number of neutrons must increase at a greater rate to be stable. 

One may rightfully raise the question as to why some products of nuclear reactions are radioactive while others are not. The answer concerns the stability of atomic nuclei. Essentially, any radioactive element, whether artificial or natural, can be considered abnormal. A nucleus that undergoes radioactive decay is in an unstable condition, and the process of decay always leads to stable isotopes. This tendency toward the achievement of stability is illustrated by the stepwise decay of naturally radioactive uranium to form a stable isotope of lead and the formation of stable carbon by the decay of artificial radioactive nitrogen. Although the conditions resulting in the instability of atomic nuclei are fairly well understood, further consideration of these factors is beyond the scope of this discussion. 

W. Harkins, The constitution and stability of atom nuclei, Philosophical Magazine 42 (1921) 305-339, on 310. See also W. Harkins, Isotopes Their number and classification," Nature 107 (1921) 202-203, which includes what is probably the first diagram of the abundance of isotopes as a function of the atomic number. Like all other physicists at the time, Harkins believed that atomic nuclei consisted of protons and electrons. The number of electrons corresponds to the quantity A-Z, later identified with the neutron number. 

Not always emphasised in discussions of Bohr s theory <19131 is its success in accounting for the stability of atoms. We should be in trouble, should we not, if there were no stationary states. Right at the beginning of his famous paper [37] BOHR discusses this question of stability Thomson s model (which is to be discarded) is actually superior to Rutherford s (until Bohr quantizes it) because it allows certain configurations and motions of elections for which the system is in stable equilibrium. 

Quantum theory was developed primarily to find an explanation for the stability of atomic matter, specifically the planetary model of the hydrogen atom. In the Schrodinger formulation the correct equation was obtained by recognizing the wave-like properties of an electron. The first derivation by Schrodinger [30] was done by analogy with the relationship that was known to exist between wave optics and geometrical optics in the limit where the index of refraction, n does not change appreciably over distances of order A. This condition leads to the eikonal equation (T3.15)... 

See Issac F. Silvera and Jook Walraven, The Stabilization of Atomic Hydrogen, Scientific American (January) 66-74 (1982). 

Thus, 222kcalmol must be transferred to HOH to produce atomic oxygen, which is a measure of the deactivation and stabilization of atomic oxygen in the formation of a water molecule. Another important and unique characteristic of water molecules is their tendency to cluster through intermolecular hydrogen bonds (more properly hydrogen-oxygen bonds) (equation 2). In contrast, for ambient conditions, BH3, CH4, NH3, and HF are monomeric gas molecules (as are CO, CO2, H2S, and SO2). 

The incompatibility of Rutherford s planetary model, based soundly on experimental data, with the principles of classical physics was the most fundamental of the conceptual challenges facing physicists in the early 1900s. The Bohr model was a temporary fix, sufficient for the interpretation of hydrogen (H) atomic spectra as arising from transitions between stationary states of the atom. The stability of atoms and molecules finally could be explained only after quantum mechanics had been developed. 

V. QUANTUM PHASE TRANSITIONS AND STABILITY OF ATOMIC AND MOLECULAR SYSTEMS... 

In this section we will apply the FSS method to obtain critical parameters for few-body systems with Coulombic interactions. Thus, FSS approach can be used to explain and predict stability of atomic and molecular systems. 

The stability of atoms (V = —Za r l) including an external magnetic field has been demonstrated for Z 68 (Bach et al. 1998). In a following paper (Bach et al. 1999) the stability of matter has finally been proved. For the atomic problem an inequality for the moduli of Dirac operators,... 

We have already had before us (Chap. IV, 2, p. 69) a series of arguments to prove that the classical laws of motion cease to hold good ill the interior of atoms. We recall in particular the existence of sharp spectral lines, and the great stability of atoms, phenomena which from the classical standpoint are perfectly unintelligible. 

There are two particular aspects of radiative corrections in atomic physics that will be emphasized here. One has to do with the correct implementation of QED to many-electron atoms and ions, a subject also discussed by Labzowsky and Goidenko in Chapter 8 of this book. While QED has been tested quite stringently over the years, and is unlikely to be fundamentally incorrect, to actually carry out bound state calculations is a highly nontrivial task. Even the introduction of relativity has raised serious questions about the stability of atoms, referred to as the Brown-Ravenhall wasting disease [2] or continuum dissolution [3]. While the problem is, in a practical sense, still open for neutral systems, we will show that a particular way of applying QED to atoms, use of the Furry representation [4], allows a consistent and accurate treatment of these questions for highly charged ions. 

Bohr has succeeded in overcoming these difficulties by rejecting the classical principles in favour of the quantum principles discussed in 1 and 2. He postulates the existence of discrete stationary states, fixed by quantum conditions, the exchange of energy between these states and the radiation field being governed by his frequency condition (1), 2. The existence of a stationary state of minimum energy, which the atom cannot spontaneously abandon, provides for the absolute stability of atoms which is required by experience. Further,... 

We give in conclusion a brief formulation of the ideas which have led to Bohr s atomic theory. There are two observations which are fundamental firstly the stability of atoms, secondly the validity of the classical mechanics and electrodynamics for macroscopic processes. The application of the classical theory to atomic processes... 

The fundamental postulate of the stability of atoms referred to in the introduction is satisfied by the two principles of atomic mechanics given in 10. We now inquire to what extent they are in agreement with the other fundamental postulate, that the classical theory shall appear as a limiting case of the quantum theory. 

The d-orbital occupation of a central sulphur atom increases with its degree of valency due to a combination of spatial polarization needs in the molecule and the stabilization of atomic spectroscopic states. However, hypervalency depends more on size and geometric factors than on d-orbital occupancy. The S=0 bond generally has the S + —O structure as its major resonance component. 

---