Energy level

This article is about orbital (electron) energy levels. For compounds' energy levels, see chemical potential. In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical

A quantum mechanical system or particle that is bound, confined spacially, can only take on certain discrete values of energy, as opposed to classical particles, which can have any energy. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In Physics, a bound state is a composite of two or more building blocks ( particles or bodies) that behaves as a single object Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects These are called energy levels. The term is most commonly used for the energy levels (electron configuration) of electrons in atoms or molecules, which are bound by the electric field of the nucleus. In Atomic physics and Quantum chemistry, electron configuration is the arrangement of Electrons in an Atom, Molecule, or other The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by In other words, their energy spectrum can be quantized (see continuous spectrum for the more general case). In Physics, continuous spectrum refers to a range of values which may be graphed to fill a range with closely-spaced or overlapping intervals

If the potential energy is set to zero at infinity, the usual convention, then bound electron states have negative potential energy. Potential energy can be thought of as Energy stored within a physical system In Physics, a bound state is a composite of two or more building blocks ( particles or bodies) that behaves as a single object

Energy levels are said to be degenerate, if the same energy level is obtained by more than one quantum mechanical state. In Quantum physics, a quantum state is a mathematical object that fully describes a quantum system. They are then called degenerate energy levels. This article refers to physical states having the same energy

1 Explanation
2 Atoms
- 2.1 Intrinsic energy levels
- 2.2 Energy levels due to external fields
3 Molecules
4 Crystalline Materials
5 See also

Explanation

Quantized energy levels result from the relation between a particle's energy and its wavelength. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. For a confined particle, the waves have the form of standing waves. A standing wave, also known as a stationary wave, is a Wave that remains in a constant position Only stationary states with energies corresponding to integral numbers of wavelengths can exist; for other states the waves interfere destructively, resulting in zero probability density. In Quantum mechanics, a stationary state is an Eigenstate of a Hamiltonian, or in other words a state of definite energy Elementary examples that show how energy levels come about are the particle in a box and the quantum harmonic oscillator. In Physics, the particle in a box (also known as the infinite potential well or the infinite square well) is a problem consisting of a single particle inside The quantum harmonic oscillator is the quantum mechanical analogue of the classical harmonic oscillator.

The following sections give an overview of the most important factors that determine the energy levels of atoms and molecules.

Atoms

Intrinsic energy levels

Orbital state energy level

Assume an electron in a given atomic orbital. An atomic orbital is a Mathematical function that describes the wave-like behavior of an electron in an atom The energy of its state is mainly determined by the electrostatic interaction of the (negative) electron with the (positive) nucleus. The energy levels of an electron around a nucleus are given by :

$E_n = - h c R_{\infty} \frac{Z^2}{n^2} \$ ,

where $R_{\infty} \$ is the Rydberg constant (typically between 1 eV and 10³ eV), Z is the charge of the atom's nucleus, $n \$ is the principal quantum number, e is the charge of the electron, $h$ is Planck's constant, and c is the speed of light. The Rydberg Constant, named after the Swedish Physicist Johannes Rydberg, is a Physical constant relating to atomic spectra in the In Atomic physics, the principal quantum number symbolized as n is the first of a set of Quantum numbers (which includes the principal quantum The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta.

The Rydberg levels depend only on the principal quantum number $n \$ .

Fine structure splitting

Fine structure arises from relativistic kinetic energy corrections, spin-orbit coupling (an electrodynamic interaction between the electron's spin and motion and the nucleus's electric field) and the Darwin term (contact term interaction of s-shell electrons inside the nucleus). In Atomic physics, the fine structure describes the splitting of the Spectral lines of Atoms due to first order relativistic corrections In Quantum physics, the spin-orbit interaction (also called spin-orbit effect or spin-orbit coupling) is any interaction of a particle's spin In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin Typical magnitude $10 - 3$ eV.

Hyperfine structure

Spin-nuclear-spin coupling (see hyperfine structure). In Atomic physics, hyperfine coupling is the weak magnetic interaction between Electrons and nuclei. Typical magnitude $10 - 4$ eV.

Electrostatic interaction of an electron with other electrons

If there is more than one electron around the atom, electron-electron-interactions raise the energy level. These interactions are often neglected if the spatial overlap of the electron wavefunctions is low.

Energy levels due to external fields

Zeeman effect

Main article: Zeeman effect

The interaction energy is: $U = - μ B$ with $μ = q L / 2 m$

Zeeman effect taking spin into account

This takes both the magnetic dipole moment due to the orbital angular momentum and the magnetic momentum arising from the electron spin into account. The Zeeman effect (ˈzeɪmɑːn is the splitting of a Spectral line into several components in the presence of a static Magnetic field.

Due to relativistic effects (Dirac equation), the magnetic moment arising from the electron spin is $μ = - μ B g s$ with $g$ the gyro-magnetic factor (about 2). In Physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides $μ = μ l + g μ s$ The interaction energy therefore gets $U B = - μ B = μ B B (m l + g m s)$ .

Stark effect

Interaction with the external electric field causes:see Stark effect

Molecules

Roughly speaking, a molecular energy state, i. The Stark effect is the shifting and splitting of Spectral lines of atoms and molecules due to the presence of an external static Electric field. e. an eigenstate of the molecular Hamiltonian, is the sum of an electronic, vibrational, rotational, nuclear and translational component, such that:

$E = E_\mathrm{electronic}+E_\mathrm{vibrational}+E_\mathrm{rotational}+E_\mathrm{nuclear}+E_\mathrm{translational}\,$

where $E electronic$ is an eigenvalue of the electronic molecular Hamiltonian (the value of the potential energy surface) at the equilibrium geometry of the molecule. In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes In Atomic molecular and optical physics as well as in Quantum chemistry, molecular Hamiltonian is the name given to the Hamiltonian representing the In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes In Atomic molecular and optical physics as well as in Quantum chemistry, molecular Hamiltonian is the name given to the Hamiltonian representing the A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in Quantum mechanics and Statistical mechanics Molecular geometry or molecular structure is the three- Dimensional arrangement of the Atoms that constitute a Molecule.

The molecular energy levels are labelled by the molecular term symbols. In Molecular physics, the molecular term symbol is a shorthand expression of the Group representation and angular momenta that characterize the state of

The specific energies of these components vary with the specific energy state and the substance.

In molecular physics and quantum chemistry, an energy level is a quantized energy of a bound quantum mechanical state. Molecular physics is the study of the physical properties of Molecules and of the Chemical bonds between Atoms that bind them Quantum chemistry is a branch of Theoretical chemistry, which applies Quantum mechanics and Quantum field theory to address issues and problems in In Physics, a bound state is a composite of two or more building blocks ( particles or bodies) that behaves as a single object In Quantum physics, a quantum state is a mathematical object that fully describes a quantum system.

Crystalline Materials

Crystalline materials are often characterized by a number of important energy levels. The most important ones are the top of the valence band, the bottom of the conduction band, the Fermi energy, the vacuum level, and the energy levels of any defect states in the crystals. In Solids the valence band is the highest range of Electron energies where electrons are normally present at Absolute zero. In the Physics field of Semiconductors and insulators the conduction band is the range of Electron Energy, higher than that of the The Fermi energy is a concept in Quantum mechanics usually referring to the energy of the highest occupied Quantum state in a system of Fermions at

Dictionary

-noun

(physics) any of the discrete stable energies that a quantum mechanical system (such as the electrons of an atom) can have

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