Tables fundamental constants

Atomic and molecular physicists commonly express energies in units of and distances in units of Uq, because they absorb all the values of the fundamental constants h, m, and e. These are examples of atomic units, units derived from multiplicative combinations of the fundamental constants. Table 1.1 shows how these and other quantities can be obtained by appropriate combinations. 

The system of atomic units was developed to simplify mathematical equations by setting many fundamental constants equal to 1. This is a means for theorists to save on pencil lead and thus possible errors. It also reduces the amount of computer time necessary to perform chemical computations, which can be considerable. The third advantage is that any changes in the measured values of physical constants do not affect the theoretical results. Some theorists work entirely in atomic units, but many researchers convert the theoretical results into more familiar unit systems. Table 2.1 gives some conversion factors for atomic units. 

NEW The Fact Sheet at the back of the book provides students with a single source for most of the information they need to solve problems. The fact sheet includes a list of key equations for each chapter the periodic table and tables of the elements, SI prefixes, fundamental constants, and relations between units. 

A note on good practice To avoid overwhelming you with data we usually quote the values of fundamental constants to three decimal places. In actual calculations you should use the more precise values given in tables, including those inside the back cover. 

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. 

Four rather useful conversion factors (calculated from the fundamental constants below), which are not given in the tables, are... 

PERIODIC TABLE OF THE ELEMENTS, USEFUL CONVERSION FACTORS, AND FUNDAMENTAL CONSTANTS... 

A34 appendix d periodic table of the elements, useful conversion factors, and fundamental constants... 

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. 

Appendix IB). The symbols may be modified by attaching subscripts, as set out in Table 2. Fundamental constants are not included in the lists but can be found inside the back cover of the text. 

The constants C7, Q, Ch, Cj and Cv are related to fundamental constants and properties of the solvent. The relationships are given in Chapter 11. Values for these constants for aqueous solutions are given as a function of temperature and pressure in Table 18.1.b Below T — 373.15 K, the constants are the values at... 

Atomic weight values. These are fundamental constants available from IUPAC tables... 

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]... 

Numerical results (in kHz) for hydrogen and deuterium atoms and the helium-3 ion are collected in Table 2. One can see that the new corrections essentially shift the theoretical predictions. A comparison of the QED predictions (in kHz) against the experiments is summarized in Table 1. We take the values of the fundamental constants (like e. g. the fine structure constant a) from the recent adjustment (see Ref. [25]). 

In Table II are given the three fundamental constants for a number of atom pairs which are of interest in chemical kinetics. From these constants Morse curves can be constructed as just shown for bromine, and these, in turn, are necessary for the calculation of activation energies of chemical reactions. 

A new best set of the fundamental constants has been compiled by NIST at Gaithersburg in 1999. A selected set is given in the following table. 

The relation of atomic units to the corresponding SI units involves the values of the fundamental physical constants, and is therefore not exact. The numerical values in the table are based on the estimates of the fundamental constants given in chapter 5. The numerical results of calculations in theoretical chemistry are frequently quoted in atomic units, or as numerical values in the form (physical quantity)/(atomic unit), so that the reader may make the conversion using the current best estimates of the physical constants. 

These figures are obtained from the set of consistent fundamental constants recommended by Birge (1941) slightly different values are given in the International Critical Tables. 

Numerous new and revised thermochemical tables are included in this collection. However, this Third Edition is primarily a rewriting and a recalculation of all the tables no attempt has been made to reanalyze the data for all tables. The rewritten tables adhere more closely to the current lU-PAC recommendations on symbols and notation. The recalculated tables are all based on the current lUPAC and CODATA recommendations for relative molecular masses and fundamental constants. As a result, a comparison of a table in this Third Edition and its previously published form (i.e., same revision date) will reveal differences however, these result from the adjustments mentioned above rather than from a reanalysis of the data. 

The thermal functions at 298.15 K agree with recent CODATA recommendations ( 1) except for two minor differences. First, the entropy differs by 0.1094 J k" mol because this table uses a standard state pressure of 1 bar, whereas the CODATA recommendations are based on 1 atm. Second, an entropy difference of 0.001 J K" mol arises due to the use of slightly different values for the fundamental constants. 

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