A Fundamental Physical Constants

The symbol h represents a fundamental physical constant that we now call Planck s constant h = 6.626 X 10 34 J s. For example, one quantum of red light... 

The Arrhenius equation describes reactions involving gases, as well as those occurring in solution or on the surface of a catalyst. and A are both constants characteristic of a particular reaction, R is a fundamental physical constant for all reactions and T and k are variables. None of the three constants change significantly with temperature. The expression (e a/ ) is known as the exponential factor and allows for the large effect of an increase in temperature in the Arrhenius equation. 

The absorptivity in Equation 5.1 is the proportionality constant between concentration and absorbance. For a given molecule and a given wavenumber of light, the absorptivity is a fundamental physical constant of a molecule, as invariant as its boiling point or molecular weight. For example, the absorptivity of water at... 

Molecular weight (relative molecular mass) is a fundamental physical constant that can be used in conjunction with other physical properties to characterize hydrocarbon mixtures. 

Section 2 combines the former separate section on Mathematics with the material involving General Information and Conversion Tables. The fundamental physical constants reflect values recommended in 1986. Physical and chemical symbols and definitions have undergone extensive revision and expansion. Presented in 14 categories, the entries follow recommendations published in 1988 by the lUPAC. The table of abbreviations and standard letter symbols provides, in a sense, an alphabetical index to the foregoing tables. The table of conversion factors has been modified in view of recent data and inclusion of SI units cross-entries for archaic or unusual entries have been curtailed. 

All equations given in this text appear in a very compact form, without any fundamental physical constants. We achieve this by employing the so-called system of atomic units, which is particularly adapted for working with atoms and molecules. In this system, physical quantities are expressed as multiples of fundamental constants and, if necessary, as combinations of such constants. The mass of an electron, me, the modulus of its charge, lei, Planck s constant h divided by lit, h, and 4jt 0, the permittivity of the vacuum, are all set to unity. Mass, charge, action etc. are then expressed as multiples of these constants, which can therefore be dropped from all equations. The definitions of atomic units used in this book and their relations to the corresponding SI units are summarized in Table 1-1. 

Max Planck (1858-1947 Nobel Prize for physics 1918) at first did not have the atom in his sights. He was more interested in thermodynamics, and especially in the laws of radiation. In 1900 he surprised the Physical Society of Berlin — and later the whole world — with an experimentally based realization that changed the world view. In contrast to time and space, energy is guantized. Thus it does not form a continuum, but is essentially "grainy". The smallest unit is the Planck constant, a fundamental natural constant. 

A convenient measure of the importance of relativistic corrections is given by the ratio Aei of Z to the fine-structure constant (e2/(hc) — 137, a dimensionless ratio of fundamental physical constants)... 

A list of some non-SI units, together with their SI values, and a table containing the best values of some fundamental physical constants are given in appendix A. 

Only a few relevant points about the atomic structures are summarized in the following. Table 4.1 collects basic data about the fundamental physical constants of the atomic constituents. Neutrons (Jn) and protons (ip), tightly bound in the nucleus, have nearly equal masses. The number of protons, that is the atomic number (Z), defines the electric charge of the nucleus. The number of neutrons (N), together with that of protons (A = N + Z) represents the atomic mass number of the species (of the nuclide). An element consists of all the atoms having the same value of Z, that is, the same position in the Periodic Table (Moseley 1913). The different isotopes of an element have the same value of Z but differ in the number of neutrons in their nuclei and therefore in their atomic masses. In a neutral atom the electronic envelope contains Z electrons. The charge of an electron (e ) is equal in size but of opposite sign to that of a proton (the mass ratio, mfmp) is about 1/1836.1527). 

A factor Avogadro s constant multiplied by 10 enters these expressions on condition that atomic and electronic masses be expressed, as is customary in spectral analyses, in unified atomic mass unit both Uifi and f/o,i contain mass in their units, despite their values being formally independent of atomic mass. The standard errors associated with values of k and in Table 1 include contributions from errors of pertinent fundamental physical constants [94]. 

An ab initio calculation uses the correct molecular electronic Hamiltonian (1.275) and does not introduce experimental data (other than the values of the fundamental physical constants) into the calculation. A semiempirical calculation uses a Hamiltonian simpler than the correct one, and takes some of the integrals as parameters whose values are determined using experimental data. The Hartree-Fock SCF MO method seeks the orbital wave function 0 that minimizes the variational integral <(4> //el initio method. Semiempirical methods were developed because of the difficulties involved in ab initio calculation of medium-sized and large molecules. We can... 

An important aspect of the photoelectric effect is that it requires a minimum frequency of light which depends on the material of the photocathode. This means that each particle of light or photon carries an energy E proportional to the frequency v E = hv. The factor h is known as Planck s constant , one of the most fundamental physical constants in all of nature. 

TABLE 11.1 Fundamental Physical Constants A. Defined values... 

The Curie constant C can be considered a magnetic parameter (MP) associated with the sample. Theory, however, tells us that such a phenomenological parameter could be made of fundamental physical constants and the magnetogyric-ratio parameter g in the following way ... 

Table A.3. 1986 recommended values of the fundamental physical constants.

The task of reconciling experimental measurements in many different laboratories to produce the best possible set of fundamental physical constants is assigned to CODATA (the Committee on Data for Science and Technology), established in 1966 by the International Council of Scientific Unions. Roughly every ten years this group releases a new set of constants. Appendix A presents the 1998 values. Each value also has associated error bars, which we will explain in more detail in Chapter 4. 

Perhaps a problem more important for applications is to eliminate the nuclear effects and to test the bound state QED precisely or use the bound state QED for the determination of some fundamental physical constants. There are a few ways to manage this problem [11] and to expand the accuracy of the tests of bound state QED beyond a level of our knowledge of the nuclear structure effects. 

Another metrological application of simple atoms is the determination of values of the fundamental physical constants. In particular, the use of the new frequency chain for the hydrogen and deuterium lines [6] provided an improvement of a value of the Rydberg constant (Roc)- But that is not the only the constant determined with help of simple atoms. A recent experiment on g factor of a bound electron [27,11] has given a value of the proton-to-electron mass ratio. This value now becomes very important because of the use of photon-recoil spectroscopy for the determination of the fine structure constant [41] (see also [8])-... 

Fundamental physical constants are universal and their values are needed for different problems of physics and metrology, far beyond the study of simple atoms. That makes the precision physics of simple atoms a subject of a general physical interest. The determination of constants is a necessary and important part of most of the so-called precision test of the QED and bound state QED and that makes the precision physics of simple atoms an important field of a general interest. 

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