An orbital describes a probability region for finding an electron at a certain energy level, distance, and orientation as related to the atomic nucleus. Orbitals are described by a set of quantum numbers that describe their location shape and electron capacity. In accord with wave-particle duality, the high probability regions for finding electrons also describe the wavelike motion of electrons in the three-dimensional region of space surrounding an atomic nucleus.
Within each orbital beyond the first orbital there are suborbitals that reflect particular orientations in space (e.g., p orbitals directed along the x, y, or z axis). Each suborbital orbital can hold up to two electrons. Electrons occupy different energy levels in atoms and have different wave properties. The Schrödinger equation relates the energy of a system to its wave properties. This equation employs the three orbital quantum numbers, which describe an orbital, as well as a fourth quantum number, the electron spin quantum number. The shapes of different kinds of orbitals are different because of the interaction of the quantum effects between the different atomic particles.
In 1911, New Zealand-born English physicist Ernest Rutherford (1871-1937) developed a picture explaining the structure of the atom in terms of a positively charged nucleus surrounded by negatively charged electrons in orbits. Later, in 1913, Danish physicist Niels Bohr (1885-1962) developed a theory that explained why electrons can remain in orbits and do not collapse onto the nucleus. Quantum theory, developed during the 1920s, explained all phenomena concerning electrons and their role in atoms. The theory showed that all particles have certain associated wave properties and that electrons cannot be pictured as localized particles in space, but rather should be thought of as clouds of negative charge spread out over the entire orbit. These clouds represent orbits, the regions around the nucleus where the electrons are most likely found.
The exact physical manifestation of each orbital depends on many factors that are described by the quantum numbers associated with a particular energy state. The three quantum numbers that determine the shapes are n, the principle quantum number, l, the angular momentum quantum number, and m, the magnetic quantum number. The principle quantum number, n, determines the distance, size and general energy level of the orbital. It can be any positive integer (1, 2, 3, 4, etc.) with the higher number indicating a larger, less energetic orbital located progressively farther from the nucleus. The angular momentum quantum number, l, determines the shape of the orbital and its value takes on all positive integral values from 0 to n-1. Therefore, for any orbital there can be many shapes (i.e., orientation in space) for the associated suborbitals. The first angular momentum quantum numbers are designated as s, p, d, and f orbitals. The third of the quantum numbers, m the magnetic quantum number, determines the orientation with respect to an applied magnetic field. All values of the magnetic quantum number are integral and can range in value from -3 to 3.
The s orbital is spherical. The p orbital is dumb-bell shaped with two parts separated by a nodal plane where the probability of finding the electron approaches zero. Because of the range of possible values of magnetic quantum numbers associated with this orbital, there are three possible orientations of the p orbital, along the x-axis, along the y-axis or along the z-axis. The d orbital has four lobes with nodal planes at the intersection of the four lobes. There are five possible orientations for these orbitals because of the range of possible magnetic quantum numbers associated with this orbital. f orbitals have still more complicated shapes. There are seven possible orientations for these orbitals described by the magnetic quantum numbers. There is a fourth quantum number that describes the spin of the electron in an orbital. This quantum number is called the spin quantum number and can have a value of either 1/2 or -1/2 since an electron can orient in two ways in an applied magnetic field.
The electronic configuration of atoms is determined by application of the rules for placing electrons in orbitals. The electronic configuration for any atom is governed by the Aufbau principle (electrons occupy the lowest-energy orbitals available, the Hund principle (all sub orbitals receive an electron before electrons are paired) and the Pauli exclusion principle (no two electrons can have the same four quantum numbers). To build an electronic configuration of an atom, electrons are placed in the lowest energy orbitals first.
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