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where M is the molar mass of the substance (usually given in SI units of grams per mole) and v is the valency of the ions. For Faraday's first law, M, F, v are constants; thus, the larger the value of Q, the larger m will be.
This equation is the equation of a straight line for as a function of pH with a slope of () volt (pH has no units). This equation predicts lower E h {\displaystyle E_{h}} at higher pH values. This is observed for the reduction of O 2 into H 2 O, or OH − , and for reduction of H + into H 2 .
The Hammett equation predicts the equilibrium constant or reaction rate of a reaction from a substituent constant and a reaction type constant. The Edwards equation relates the nucleophilic power to polarisability and basicity. The Marcus equation is an example of a quadratic free-energy relationship (QFER). [citation needed]
For example, in a collision between electrons and molecules, there may be tens or hundreds of particles involved. But the phenomenon may be reduced to a two-body problem by describing all the molecule constituent particle potentials together with a pseudopotential. [5] In these cases, the Lippmann–Schwinger equations may be used.
Taking a hydrogen molecule-like system (i.e. one with two electrons), one may attempt to model the state of each electron by first assuming the electrons behave independently (that is, as if the Pauli exclusion principle did not apply), and taking wave functions in position space of () for the first electron and () for the second electron.
In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction (half-cell or full cell reaction) from the standard electrode potential, absolute temperature, the number of electrons involved in the redox reaction, and activities (often approximated by concentrations) of the chemical species undergoing ...
In a semiconductor with an arbitrary density of states, i.e. a relation of the form = between the density of holes or electrons and the corresponding quasi Fermi level (or electrochemical potential) , the Einstein relation is [11] [12] =, where is the electrical mobility (see § Proof of the general case for a proof of this relation).
The Bethe formula is only valid for energies high enough so that the charged atomic particle (the ion) does not carry any atomic electrons with it. At smaller energies, when the ion carries electrons, this reduces its charge effectively, and the stopping power is thus reduced. But even if the atom is fully ionized, corrections are necessary.