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What is an atomic orbital?

What is an atomic orbital? Here are some definitions.

Noun
  1. (chemistry) A mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus.
  2. The physical region or space where an electron can be calculated to be present, as defined by the particular mathematical form of the orbital.
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It also enables a discussion of the bonding in the system in terms of bond orders and atomic orbital contributions to a given bond.
The scheme for atomic orbital radii is further generalized by chemical descriptors in the frame of density functional theory.
Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.
Each atomic orbital has a characteristic shape and energy and occupies a characteristic volume of space, which is predicted by the Schrodinger equation.
It can be an electric current in a conductor or charged particles moving through space, or it can be the motion of an electron in an atomic orbital.
The PDOSs of nitrogen atoms and their p orbitals for complex E have also been displayed in Fig. 15, indicating a high overlap between the PDOS of nitrogen atom with p1 atomic orbital compared to the other orbitals.

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