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Charge carrier density, also known as carrier concentration, denotes the number of charge carriers per volume. In SI units, it is measured in m −3. As with any density, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material.
Hund's first rule states that the lowest energy atomic state is the one that maximizes the total spin quantum number for the electrons in the open subshell. The orbitals of the subshell are each occupied singly with electrons of parallel spin before double occupation occurs.
The maximum number of electrons in any shell is 2n 2, where n is the principal quantum number. The maximum number of electrons in a subshell is equal to 2(2 l + 1), where the azimuthal quantum number l is equal to 0, 1, 2, and 3 for s, p, d, and f subshells, so that the maximum numbers of electrons are 2, 6, 10, and 14 respectively.
In quantum chemical calculations, the electron density, ρ(r), is a function of the coordinates r, defined so ρ(r)dr is the number of electrons in a small volume dr. For closed-shell molecules, ρ ( r ) {\displaystyle \rho (\mathbf {r} )} can be written in terms of a sum of products of basis functions, φ:
The maximum number of electrons that can be placed in a subshell is given by 2(2 l + 1). This gives two electrons in an s subshell, six electrons in a p subshell, ten electrons in a d subshell and fourteen electrons in an f subshell.
If the group is of the [d] or [f], type, an amount of 1.00 for each electron "closer" to the nucleus than the group. This includes both i) electrons with a smaller principal quantum number than n and ii) electrons with principal quantum number n and a smaller azimuthal quantum number l. In tabular form, the rules are summarized as:
As a result, when filling up atomic orbitals, the maximum number of unpaired electrons (and hence maximum total spin state) is assured. The valence orbitals of the oxygen atom (sides of diagram) and the dioxygen molecule (middle) in the ground state. In both atom and molecule, the electrons in singly occupied orbitals have their spins parallel.
In chemistry, electron counting is a formalism for assigning a number of valence electrons to individual atoms in a molecule. It is used for classifying compounds and for explaining or predicting their electronic structure and bonding. [1] Many rules in chemistry rely on electron-counting: