Definition and Characteristics of Atomic Orbitals
– Atomic orbitals describe the location and wave-like behavior of electrons in an atom.
– Each orbital is characterized by quantum numbers n, ℓ, and m, which represent energy, angular momentum, and magnetic quantum number, respectively.
– Orbitals are labeled as s, p, d, and f, corresponding to angular momentum quantum numbers 0, 1, 2, and 3.
– Each orbital can hold a maximum of two electrons.
– Orbitals describe the probability of finding an electron in a specific region around the nucleus.
– Each orbital can hold a maximum of 2 electrons with opposite spins.
– Orbitals are labeled by their principal quantum number (n) and azimuthal quantum number (ℓ).
– The energy of an orbital increases as the principal quantum number increases.
– Orbitals with the same principal quantum number but different azimuthal quantum numbers have different shapes.
Wave-like Properties of Electrons
– Electrons exist as standing waves rather than orbiting the nucleus like planets.
– The lowest energy state of an electron is similar to the fundamental frequency of a wave.
– Higher energy states are like harmonics of the fundamental frequency.
– The probability of finding an electron at a specific point can be determined from its wave function.
– The charge of an electron is distributed in space according to the squared magnitude of its wave function.
Particle-like Properties of Electrons
– The number of electrons orbiting a nucleus is always an integer.
– Electrons jump between orbitals like particles when they absorb or emit energy.
– Only one electron changes state when struck by a photon.
– Each electron wave state has the same electric charge as its particle.
– Each wave state has a discrete spin, either spin up or spin down.
Electron Cloud Model
– Electrons cannot be described simply as solid particles.
– The electron cloud around the nucleus is analogous to a large and often oddly shaped atmosphere.
– Atomic orbitals describe the shape of the electron cloud when only one electron is present.
– Additional electrons tend to fill in the space around the nucleus more evenly, resulting in a generally spherical zone of probability.
– The uncertainty principle contributes to the electron cloud’s probability distribution.
Formal Quantum Mechanical Definition
– Atomic orbitals are approximate solutions to the Schrödinger equation for electrons bound to the atom.
– They are expansion terms in the configuration interaction expansion of the atomic state.
– Atomic orbitals are spatial components of one-electron functions.
– They are used to label quantum states and electron configurations.
– Atomic orbitals are key for visualizing excitation processes and transitions in atomic spectroscopy. Source: https://en.wikipedia.org/wiki/Electron_cloud
In atomic theory and quantum mechanics, an atomic orbital (/ˈɔːrbɪtəl/) is a function describing the location and wave-like behavior of an electron 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. The term atomic orbital may also refer to the physical region or space where the electron can be calculated to be present, as predicted by the particular mathematical form of the orbital.
Each orbital in an atom is characterized by a set of values of the three quantum numbers n, ℓ, and ml, which respectively correspond to the electron's energy, its angular momentum, and an angular momentum vector component (magnetic quantum number). As an alternative to the magnetic quantum number, the orbitals are often labeled by the associated harmonic polynomials (e.g., xy, x2 − y2). Each such orbital can be occupied by a maximum of two electrons, each with its own projection of spin . The simple names s orbital, p orbital, d orbital, and f orbital refer to orbitals with angular momentum quantum number ℓ = 0, 1, 2, and 3 respectively. These names, together with the value of n, are used to describe the electron configurations of atoms. They are derived from the description by early spectroscopists of certain series of alkali metal spectroscopic lines as sharp, principal, diffuse, and fundamental. Orbitals for ℓ > 3 continue alphabetically (g, h, i, k, ...), omitting j because some languages do not distinguish between the letters "i" and "j".
Atomic orbitals are the basic building blocks of the atomic orbital model (or electron cloud or wave mechanics model), a modern framework for visualizing the submicroscopic behavior of electrons in matter. In this model the electron cloud of an atom may be seen as being built up (in approximation) in an electron configuration that is a product of simpler hydrogen-like atomic orbitals. The repeating periodicity of blocks of 2, 6, 10, and 14 elements within sections of the periodic table arises naturally from the total number of electrons that occupy a complete set of s, p, d, and f orbitals, respectively, though for higher values of quantum number n, particularly when the atom bears a positive charge, the energies of certain sub-shells become very similar and so the order in which they are said to be populated by electrons (e.g., Cr = [Ar]4s13d5 and Cr2+ = [Ar]3d4) can be rationalized only somewhat arbitrarily.
