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The electronic structure of an atom refers not only to the number of electrons in an atom but also to their distribution around the nucleus and to their energies.

Most of our current understanding of the electronic structure of atoms comes from analysis of light, either emitted or absorbed by substances. The number of complete wavelengths that pass a given point each second is the frequency of the wave. If the wavelength is long, the frequency will be low; if the wavelength is short, the frequency will be high. In 1900, Max Planck proposed that energy can be either released or absorbed by atoms only in discrete "chunks" of some minimum size. Because it can be released only in specific amounts, energy is quantized - restricted to certain quantities. Planck's rules regarding the gain or loss of energy are always the same, no matter the size of the objects involved. In 1905, Albert Einstein described the photoelectric effect - the emission of electrons from metal surfaces on which light shines. If a photon strikes the surface of the metal with a specific amount of energy - called the work function - an electron in the metal can absorb that energy and use it to overcome the attractive forces that hold it in the metal. If the photon has less energy than the work function, electrons do not escape from the metal. If the photon has more energy than the work function, the excess energy appears as the kinetic energy of the emitted electrons. According to Einstein's theory, light must possess both wave-like and particle-like characteristics and, depending on the situation, will behave more like a wave or more like particles. Elements are known to produce their own characteristic spectra with colored lines separated by black regions, which correspond to wavelengths that are absent from the light. The first three spectra above are the emission spectra of the excited gases of hydrogen, mercury, and neon. Only orbits of certain radii, corresponding to certain definite energies, are permitted for an electron.

An electron in a permitted orbit has a specific energy and is in an "allowed" energy state. Energy is emitted or absorbed by the electron only as the electron changes from one allowed energy state to another. The lowest energy state of the electron is called the ground state, n = 1, When the electron is in a higher energy state, n = 2 or higher, the atom is said to be excited.

As n increases, the radius of the orbit increases by n2, until a point is reached when the electron is completely separated from the nucleus. Bohr's model of the hydrogen atom states that only the specific frequencies of light that satisfy the allowed energy states can be absorbed or emitted by the atom, thus explaining the discrete spectral lines. While Bohr's calculation explains the spectral lines of hydrogen, it does not fully explain observed behaviors of other atoms.

Electrons exist only in certain discrete energy levels, which are described by quantum numbers.

De Broglie proposed that the electron (or any other particle of matter) has associated with it a particular wavelength, represented by an equation in which λ is the wavelength, m is its mass, v is its velocity, and h is Planck's constant. Werner Heisenberg proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and the momentum of any object. When applied to the electrons in an atom, Heisenberg's Uncertainty Principle states that it is inherently impossible to know simultaneously both the exact momentum of the electron and its exact location in space. Combining de Broglie's hypothesis and Heisenberg's uncertainty principle, we get a model of the atom that precisely describes the energy of the electron while describing its location only in terms of probabilities. In 1926, Erwin Schrodinger proposed an equation, now known as Schrodinger's wave equation, that incorporates both the wave-like behavior and the particle-like behavior of the electron.

Solving Schrodinger's equation leads to a series of mathematical functions called wave functions that describe the electron. The square of the wave function, ψ2, at a given point in space represents the probability that the electron will be found at that location. In this diagram, representing a spherical s orbital, the regions with a high density of dots correspond to relatively large values for ψ2 and are regions where there is a high probability of finding the electron.

In orbitals with a more complex shape, the probability of finding the electron drops to zero, then begins to increase again.

The angular quantum number, l, can have integral values from 0 to n − 1 for each value of n.

The letters represent sharp, principal, diffuse, and fundamental, which described features of spectra before quantum mechanics was developed. The magnetic quantum number, m, can have integral values for −l and l, including zero. The shell with principal quantum number n will consists of exactly n subshells: 1s, 2s and 2p, 3s and 3p and 3d, etc. As scientists studied the line spectra of many-electron atoms (see aluminum below), they found that what were originally thought to be single lines were actually closely spaced pairs of lines. In 1925, the Dutch physicists George Uhlenbeck and Samuel Goudsmit proposed a solution to the problem.

With this knowledge, Wolfgang Pauli established the principle that governs the arrangements of electrons in many-electron atoms. The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers, n, l, m, and s. Orbitals are filled in order of increasing energy, with no more than two electrons per orbital - which must have opposite spins. Although the shapes of the orbitals in atoms with more than hydrogen's one electron (many-electron atoms) is the same, the presence of more than one electron greatly changes the energies of the orbitals. The exact energies of the orbitals and their spacings differ from one atom to another, but all orbitals of a given subshell (such as the 3d orbitals) still have the same energy as one another.

It is different from Newtonian mechanics, which is the physics describing macroscopic (normal-sized) objects.

Most of our current understanding of the electronic structure of atoms comes from analysis of light, either emitted or absorbed by substances. The number of complete wavelengths that pass a given point each second is the frequency of the wave. If the wavelength is long, the frequency will be low; if the wavelength is short, the frequency will be high. In 1900, Max Planck proposed that energy can be either released or absorbed by atoms only in discrete "chunks" of some minimum size. Because it can be released only in specific amounts, energy is quantized - restricted to certain quantities. Planck's rules regarding the gain or loss of energy are always the same, no matter the size of the objects involved. In 1905, Albert Einstein described the photoelectric effect - the emission of electrons from metal surfaces on which light shines. If a photon strikes the surface of the metal with a specific amount of energy - called the work function - an electron in the metal can absorb that energy and use it to overcome the attractive forces that hold it in the metal. If the photon has less energy than the work function, electrons do not escape from the metal. If the photon has more energy than the work function, the excess energy appears as the kinetic energy of the emitted electrons. According to Einstein's theory, light must possess both wave-like and particle-like characteristics and, depending on the situation, will behave more like a wave or more like particles. Elements are known to produce their own characteristic spectra with colored lines separated by black regions, which correspond to wavelengths that are absent from the light. The first three spectra above are the emission spectra of the excited gases of hydrogen, mercury, and neon. Only orbits of certain radii, corresponding to certain definite energies, are permitted for an electron.

An electron in a permitted orbit has a specific energy and is in an "allowed" energy state. Energy is emitted or absorbed by the electron only as the electron changes from one allowed energy state to another. The lowest energy state of the electron is called the ground state, n = 1, When the electron is in a higher energy state, n = 2 or higher, the atom is said to be excited.

As n increases, the radius of the orbit increases by n2, until a point is reached when the electron is completely separated from the nucleus. Bohr's model of the hydrogen atom states that only the specific frequencies of light that satisfy the allowed energy states can be absorbed or emitted by the atom, thus explaining the discrete spectral lines. While Bohr's calculation explains the spectral lines of hydrogen, it does not fully explain observed behaviors of other atoms.

Electrons exist only in certain discrete energy levels, which are described by quantum numbers.

De Broglie proposed that the electron (or any other particle of matter) has associated with it a particular wavelength, represented by an equation in which λ is the wavelength, m is its mass, v is its velocity, and h is Planck's constant. Werner Heisenberg proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and the momentum of any object. When applied to the electrons in an atom, Heisenberg's Uncertainty Principle states that it is inherently impossible to know simultaneously both the exact momentum of the electron and its exact location in space. Combining de Broglie's hypothesis and Heisenberg's uncertainty principle, we get a model of the atom that precisely describes the energy of the electron while describing its location only in terms of probabilities. In 1926, Erwin Schrodinger proposed an equation, now known as Schrodinger's wave equation, that incorporates both the wave-like behavior and the particle-like behavior of the electron.

Solving Schrodinger's equation leads to a series of mathematical functions called wave functions that describe the electron. The square of the wave function, ψ2, at a given point in space represents the probability that the electron will be found at that location. In this diagram, representing a spherical s orbital, the regions with a high density of dots correspond to relatively large values for ψ2 and are regions where there is a high probability of finding the electron.

In orbitals with a more complex shape, the probability of finding the electron drops to zero, then begins to increase again.

The angular quantum number, l, can have integral values from 0 to n − 1 for each value of n.

The letters represent sharp, principal, diffuse, and fundamental, which described features of spectra before quantum mechanics was developed. The magnetic quantum number, m, can have integral values for −l and l, including zero. The shell with principal quantum number n will consists of exactly n subshells: 1s, 2s and 2p, 3s and 3p and 3d, etc. As scientists studied the line spectra of many-electron atoms (see aluminum below), they found that what were originally thought to be single lines were actually closely spaced pairs of lines. In 1925, the Dutch physicists George Uhlenbeck and Samuel Goudsmit proposed a solution to the problem.

With this knowledge, Wolfgang Pauli established the principle that governs the arrangements of electrons in many-electron atoms. The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers, n, l, m, and s. Orbitals are filled in order of increasing energy, with no more than two electrons per orbital - which must have opposite spins. Although the shapes of the orbitals in atoms with more than hydrogen's one electron (many-electron atoms) is the same, the presence of more than one electron greatly changes the energies of the orbitals. The exact energies of the orbitals and their spacings differ from one atom to another, but all orbitals of a given subshell (such as the 3d orbitals) still have the same energy as one another.

It is different from Newtonian mechanics, which is the physics describing macroscopic (normal-sized) objects.

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