Other Fundamental Constants

If the SI units were redefined as described above, other fundamental constants, which are functions of the constants used in the new definitions, would also be exact. A partial list is  

The effect of these new SI definitions would be to decrease the uncertainties of many other fundamental constants not used in the new definitions. For example, the relative uncertainty of the mass of the electron in kilograms me would change from 2 X 10 to 2 x 10 . Of course, the mass of the current kilogram artifact mass would no longer be exactly one kilogram, but rather would be determined by experiment, with its uncertainty being of the order of a few parts in 10.  

---

Other vital components of the traceability chain are atomic mass values, other fundamental constants, and associated physical measurements, such as mass, volume, etc. The results can be expressed in moles, moles per mole (mole fraction), or moles per kg, or if pre-... 

We assume here that the Bohr magneton /zb is a positive quantity. The numerical value of the Bohr magneton and some other fundamental constants, as recommended by CODATA, the Committee on Data for Science and Technology of the international Council of Scientific Unions, are presented in Table 4.1 [103]... 

The status of the constant changed dramatically when Niels Bohr crafred his model of the hydrogen atom. Specifically, Bohr s theory revealed that the Rydberg constant was not just a number, but was a combination of other fundamental constants. Here is the result that emerged from Bohr s work ... 

I low is it determined "> What other fundamental constants depend on Planck s constant What are the current values t>f these constants, and what are their uncertainties ... 

Decades of work have led to a profusion of LEERs for a variety of reactions, for both equilibrium constants and reaction rates. LEERs were also established for other observations such as spectral data. Furthermore, various different scales of substituent constants have been proposed to model these different chemical systems. Attempts were then made to come up with a few fundamental substituent constants, such as those for the inductive, resonance, steric, or field effects. These fundamental constants have then to be combined linearly to different extents to model the various real-world systems. However, for each chemical system investigated, it had to be established which effects are operative and with which weighting factors the frmdamental constants would have to be combined. Much of this work has been summarized in two books and has also been outlined in a more recent review [9-11]. 

Other SI electrical units are determined from the first four via the fundamental constants eo and tiQ, the permittivity and permeability of free space respectively. The ampere is defined in terms of the force between two straight parallel infinitely long conductors placed a metre apart, and once this has been defined the coulomb must be such that one coulomb per second passes along a conductor if it is carrying a current of one ampere. 

Fredkin points out that even if a preferred frame, or underlying lattice, is found, its implications are in one sense only philosophical the integrity of the theory of relativity remains intact, it is only our philosophical perspective that changes. Similarly, if a deterministic RUCA-like rule is the basis of the real physics, it does not mean that we should all throw away our quantum mechanics texts. On the other, if the finite nature hypothesis is correct and a RUCA-like rule exists and can be found, it should in principle be able to supply us with values of all of the fundamental constants of physics. 

These energy levels have exactly the form suggested spectroscopically, but now we also have an expression for S( in terms of more fundamental constants. When the fundamental constants are inserted into the expression for the value obtained is 3.29 X 10,s Hz, the same as the experimental value of the Rydberg constant. This agreement is a triumph for Schrodinger s theory and for quantum mechanics it is easy to understand the thrill that Schrodinger must have felt when he arrived at this result. A very similar expression applies to other one-electron ions, such as He1 and even C5+, with atomic number Z ... 

The relationship (equation (5.81)) between M and L depends only on fundamental constants, the electronic mass and charge, and does not depend on any of the variables used in the derivation. Although this equation was obtained by applying classical theory to a circular orbit, it is more generally valid. It applies to elliptical orbits as well as to classical motion with attractive forces other than dependence. For any orbit in any central force field, the angular... 

The virial isotherm equation, which can represent experimental isotherm contours well, gives Henry s law at low pressures and provides a basis for obtaining the fundamental constants of sorption equilibria. A further step is to employ statistical and quantum mechanical procedures to calculate equilibrium constants and standard energies and entropies for comparison with those measured. In this direction moderate success has already been achieved in other systems, such as the gas hydrates 25, 26) and several gas-zeolite systems 14, 17, 18, 27). In the present work AS6 for krypton has been interpreted in terms of statistical thermodynamic models. 

After in the foregoing chapter thermodynamic properties at high pressure were considered, in this chapter other fundamental problems, namely the influence of pressure on the kinetic of chemical reactions and on transport properties, is discussed. For this purpose first the molecular theory of the reaction rate constant is considered. The key parameter is the activation volume Av which describes the influence of the pressure on the rate constant. The evaluation of Av from measurement of reaction rates is therefor outlined in detail together with theoretical prediction. Typical value of the activation volume of different single reactions, like unimolecular dissociation, Diels-Alder-, rearrangement-, polymerization- and Menshutkin-reactions but also on complex homogeneous and heterogeneous catalytic reactions are presented and discussed. 

In recent years, great progress has been made in quantum-mechanical calculations of the properties of small organic molecules by so-called ab initio methods, which means calculations from basic physical theory using only fundamental constants, without calibration from known molecular constants. Calculations that are calibrated by one or more known properties and then used to compute other properties are called semiempirical calculations. 

For this wavefunction, the angular wavefunction Y is a constant, l/2ir1/2, independent of the angles, and the radial wavefunction decays exponentially toward 0 as r increases. The quantity a0 is called the Bohr radius when the values of the fundamental constants are inserted, we find a0 = 52.9 pm. The expressions for a number of other atomic orbitals are shown in Table 1.2. 

Over the years, several computational methods have been developed. The variational theory can be used either without using experimental data other than the fundamental constants (i.e., ab initio methods) or by using empirical data to reduce the needed amount of numerical work (i.e., semiempirical data methods). There are various levels of sophistication in both ab initio [HF(IGLO), DFT GIAO-MP2, GIAO-CCSD(T)] and semiempirical methods. In the ab initio methods, various kinds of basic sets can be employed, while in the semiempirical methods, different choices of empirical parameters and parametric functions exist. The reader is referred to reviews of the subject.18,77... 

Such approaches rely on so-called relative sensitivity coefficients (RSFs), ratios of the difference between the sensitivity of various elements, and these cannot be considered as fundamental constants. In fact, they provide no more than a quantitative measurement of the deviation of the method s result from the amount of substance, as issued from primary methods (if available). Other near-equilibrium plasma methods for the analysis of solids (glow discharge, sputtered neutrals secondary ion mass spectrometry) produce quite acceptable results for analytical practice. 

Determination of the amount of substance is thus in direct relation to basic units of the SI system and does not need a RM for comparison. The Faraday constant is one of the fundamental constants (it can be expressed as the product of the electron charge and the Avogadro constant). It enables the attainment of high precision and accuracy and is independent of the atomic weights of the elements in the sample. Its drawback is lower selectivity, a feature common to titration methods. This makes coulometry especially suitable for determination of relatively pure substances used as standards by other (relative) methods. The Faraday constant has been proposed as an ultimate standard in chemistry [3],... 

Tetrazoles, compared with the other azoles, possess an abnormally high acidity and very weak basicity. Nowadays, a sufficiently large experimental and theoretical database covers the acid-base characteristics of tetrazoles. Not only have dozens of fundamental constants inherent to the compounds of this series been determined by various methods, but also the effect of different factors on these constants has been analyzed. 

The resonance Raman spectrum of K4[Mo2C18] has been reinvestigated using 488.0 and 514.5 nm excitation. An enormous enhancement of the intensity of the Mo—Mo stretching mode relative to the intensity of other fundamentals was observed and an overtone progression in Vj to 5vj identified. From these data the harmonic frequency and anharmonicity constant X, were calculated as 347.1 + 0.5 cm -1... 

On the other hand, ab initio (meaning from the beginning in Latin) methods use a correct Hamiltonian operator, which includes kinetic energy of the electrons, attractions between electrons and nuclei, and repulsions between electrons and those between nuclei, to calculate all integrals without making use of any experimental data other than the values of the fundamental constants. An example of these methods is the self-consistent field (SCF) method first introduced by D. R. Hartree and V. Fock in the 1920s. This method was briefly described in Chapter 2, in connection with the atomic structure calculations. Before proceeding further, it should be mentioned that ab initio does not mean exact or totally correct. This is because, as we have seen in the SCF treatment, approximations are still made in ab initio methods. 

The GGA made simple [7], which we employ in this work, arises from two different non-empirical derivations [7,8]. All its parameters (other than those in LSD) are fundamental constants. 

It is the interplay between particle physics and QED phenomena in the muonium atom which cause increasing understanding of fundamental forces and increasing reliability of extracted fundamental constants. None of both sides could reach significant results without the other. With the significant improvement expected for muon beam rates at various places we can look forward to further insights and maybe hints why there are particle generations. 

The 1998 adjustment of the values of the fundamental physical constants has been carried out by the authors under the auspices of the CODATA Task Group on Fundamental Constants [1,2]. The purpose of the adjustment is to determine best values of various fundamental constants such as the fine-structure constant, Rydberg constant, Avogadro constant, Planck constant, electron mass, muon mass, as well as many others, that provide the greatest consistency among the most critical experiments based on relationships derived from condensed matter theory and quantum electrodynamics (QED) theory. The 1998 CODATA recommended values of the constants also may be found on the Web at physics.nist.gov/constants. 

---