Eermi-Dirac Statistics

Similar principles apply to ortho- and para-deuterium except that, as the nuclear spin quantum number of the deuteron is 1 rather than as for the proton, the system is described by Bose-Einstein statistics rather than the more familiar Eermi-Dirac statistics. Eor this reason, the stable low-temperature form is orriio-deuterium and at high temperatures the statistical weights are 6 ortho 3 para leading to an upper equilibrium concentration of 33.3% para-deuterium above about 190K as shown in Eig. 3.1. Tritium (spin 5) resembles H2 rather than D2. 

Eermi-Dirac statistics. Eor this we require to calculate tEe number of electrons striking one square centimetre of tbe boundary in tbe metal per second, suck that tbe kinetic energy of tbeir motion normal to tbe boundary is sufficient to carry tbe electron over tbe energy barrier of beigbt wbicb represents tbe boundary. We bave therefore to determine, on tbe basis of tbe distribution law, tbe number of electrons for wbicb, e.g.,... 

The second intrusion of the electron spin came through a non-energetic, symmetry requirement, the so-called Eermi-Dirac statistics for systems of identical, half-integer spin particles, which results in total antisymmetry of the Schrbdinger wave function in a combined space and spin coordinate domain. This entails the Pauli exclusion principle (1925) in the framework of the independent-particle, Slater-determinantal model. The expression of atomic and molecular wave functions as iinear combinations of Slater determinants has been the basis of most of the subsequent methodologies of quantum chemistry, thermodynamics, and spectroscopy. 

TEe proof of tEe fact tEat tEe quantity occurring in statistics is inversely proportional to tbe absolute temperature can be presented in tbe same form for all tbree types of statistics, tbe Boltzmann (B.), tEe Bose-Einstein (B.E.), and tbe Eermi-Dirac (F.D.). TEe fimdamental formulae for tbe probability of a state for all three statistics, can be unified by introducing tbe symbol... 

This modified equation predicted the existence and properties of the positron. Dirac also invented, independently of Enrico Eermi, the form of quantum statistics known as Fermi-Dirac statistics. 

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