Energy level in the context of Metastable state

Fluorescence is one of two kinds of photoluminescence, the emission of light by a substance that has absorbed light or other electromagnetic radiation. When exposed to ultraviolet radiation, many substances will glow (fluoresce) with colored visible light. The color of the light emitted depends on the chemical composition of the substance. Fluorescent materials generally cease to glow nearly immediately when the radiation source stops. This distinguishes them from the other type of light emission, phosphorescence. Phosphorescent materials continue to emit light for some time after the radiation stops.This difference in duration is a result of quantum spin effects.

Fluorescence occurs when a photon from incoming radiation is absorbed by a molecule, exciting it to a higher energy level, followed by the emission of light as the molecule returns to a lower energy state. The emitted light may have a longer wavelength and, therefore, a lower photon energy than the absorbed radiation. For example, the absorbed radiation could be in the ultraviolet region of the electromagnetic spectrum (invisible to the human eye), while the emitted light is in the visible region. This gives the fluorescent substance a distinct color, best seen when exposed to UV light, making it appear to glow in the dark. However, any light with a shorter wavelength may cause a material to fluoresce at a longer wavelength. Fluorescent materials may also be excited by certain wavelengths of visible light, which can mask the glow, yet their colors may appear bright and intensified. Other fluorescent materials emit their light in the infrared or even the ultraviolet regions of the spectrum.

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the University of Manchester based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively charged nucleus, with a cloud of negatively charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force.

The diameter of the nucleus is in the range of 1.70 fm (1.70×10 m) for hydrogen (the diameter of a single proton) to about 11.7 fm for uranium. These dimensions are much smaller than the diameter of the atom itself (nucleus + electron cloud), by a factor of about 26,634 (uranium atomic radius is about 156 pm (156×10 m)) to about 60,250 (hydrogen atomic radius is about 52.92 pm).

An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on the fact that atoms have quantised energy levels, and transitions between such levels are driven by very specific frequencies of electromagnetic radiation. This phenomenon serves as the basis for the SI definition of the second:

This definition underpins the system of TAI, which is maintained by an ensemble of atomic clocks around the world. The system of UTC — the basis of civil time — implements leap seconds to allow clock time to stay within one second of Earth's rotation.

The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in an atom. The classification of the series by the Rydberg formula was important in the development of quantum mechanics. The spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen and calculating red shifts.

Fermi–Dirac statistics is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac, each of whom derived the distribution independently in 1926. Fermi–Dirac statistics is a part of the field of statistical mechanics and uses the principles of quantum mechanics.

Fermi–Dirac statistics applies to identical and indistinguishable particles with half-integer spin (1/2, 3/2, etc.), called fermions, in thermodynamic equilibrium. For the case of negligible interaction between particles, the system can be described in terms of single-particle energy states. A result is the Fermi–Dirac distribution of particles over these states where no two particles can occupy the same state, which has a considerable effect on the properties of the system. Fermi–Dirac statistics is most commonly applied to electrons, a type of fermion with spin 1/2.

In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting identical particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles obeying Bose–Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium. The theory of this behaviour was developed (1924–25) by Satyendra Nath Bose, who recognized that a collection of identical and indistinguishable particles could be distributed in this way. The idea was later adopted and extended by Albert Einstein in collaboration with Bose.

Bose–Einstein statistics apply only to particles that do not follow the Pauli exclusion principle restrictions. Particles that follow Bose-Einstein statistics are called bosons, which have integer values of spin. In contrast, particles that follow Fermi-Dirac statistics are called fermions and have half-integer spins.

A phosphor is a substance that exhibits the phenomenon of luminescence; it emits light when exposed to some type of radiant energy. The term is used both for fluorescent or phosphorescent substances which glow on exposure to ultraviolet or visible light, and cathodoluminescent substances which glow when struck by an electron beam (cathode rays) in a cathode-ray tube.

When a phosphor is exposed to radiation, the orbital electrons in its molecules are excited to a higher energy level; when they return to their former level they emit the energy as light of a certain color. Phosphors can be classified into two categories: fluorescent substances which emit the energy immediately and stop glowing when the exciting radiation is turned off, and phosphorescent substances which emit the energy after a delay, so they keep glowing after the radiation is turned off, decaying in brightness over a period of milliseconds to days.

In atomic physics and chemistry, an atomic electron transition (also called an atomic transition, quantum jump, or quantum leap) is an electron changing from one energy level to another within an atom or artificial atom. The time scale of a quantum jump has not been measured experimentally. However, the Franck–Condon principle binds the upper limit of this parameter to the order of attoseconds.

Electrons can relax into states of lower energy by emitting electromagnetic radiation in the form of a photon. Electrons can also absorb passing photons, which excites the electron into a state of higher energy. The larger the energy separation between the electron's initial and final state, the shorter the photons' wavelength.

In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.

In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum. Richard Feynman called it "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen. It is the most precise and stringently tested theory in physics.

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands).

Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.).

The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum.

If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator that acts non-trivially on a ground state and commutes with the Hamiltonian of the system.

Positronium (Ps) is a system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom, specifically an onium. Unlike hydrogen, the system has no protons. The system is unstable: the two particles annihilate each other to predominantly produce two or three gamma-rays, depending on the relative spin states. The energy levels of the two particles are similar to that of the hydrogen atom (which is a bound state of a proton and an electron). However, because of the reduced mass, the frequencies of the spectral lines are less than half of those for the corresponding hydrogen lines.

In chemistry, chemical stability is the thermodynamic stability of a chemical system, in particular a chemical compound or a polymer. Colloquially, it may instead refer to kinetic persistence, the shelf-life of a metastable substance or system; that is, the timescale over which it begins to degrade.

Thermodynamic stability occurs when a system is in its lowest energy state, or in chemical equilibrium with its environment. This may be a dynamic equilibrium in which individual atoms or molecules change form, but their overall number in a particular form is conserved. This type of chemical thermodynamic equilibrium will persist indefinitely unless the system is changed. Chemical systems might undergo changes in the phase of matter or a set of chemical reactions.

In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy.A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation. Higher energy isomers are long lived because they are prevented from rearranging to their preferred ground state by (possibly large) barriers in the potential energy.

During a metastable state of finite lifetime, all state-describing parameters reach and hold stationary values. In isolation: