query: who said electrons occupy specific energy levels or shells

pos: Energy level a box and the quantum harmonic oscillator. The first evidence of quantization in atoms was the observation of spectral lines in light from the sun in the early 1800s by Joseph von Fraunhofer and William Hyde Wollaston. The notion of energy levels was proposed in 1913 by Danish physicist Niels Bohr in the Bohr theory of the atom. The modern quantum mechanical theory giving an explanation of these energy levels in terms of the Schrödinger equation was advanced by Erwin Schrödinger and Werner Heisenberg in 1926. In the formulas for energy of electrons at various levels given below in an

pos: Photoinduced charge separation electrical force the proton applied to the electron. Once the electron spiralled into the nucleus the electron would combine with a proton to form a neutron, and the atom would cease to exist. This model is clearly wrong. In 1913 Niels Bohr refined the Rutherford model by stating that the electrons existed in discrete quantized states called energy levels. This meant that the electrons could only occupy orbits at certain energies. The laws of quantum physics apply here, and they don't comply with the laws of classical newtonian mechanics. An electron which is completely free from the atom has an

neg: Electron spectroscopy electrons in the atoms of the sample, the physics of typical electron-electron collisions apply, such that sample electrons having less energy in their orbital shells than the energy setting of the SEM (kev setting), will be displaced from their orbits by the higher energy SEM electrons. This leaves the atom in an unstable state, which is remediated by higher energy electrons in the sample "dropping" down to occupy the electron shells previously ejected by the higher energy SEM electrons. In order to accomplish this, the higher energy electrons within the atom must relinquish the excess energy that exists between the

neg: Energy level fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the "n"th shell can in principle hold up to 2("n") electrons. Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: atoms may have two or even

neg: Energy level three incomplete outer shells. (See Madelung rule for more details.) For an explanation of why electrons exist in these shells see electron configuration. If the potential energy is set to zero at infinite distance from the atomic nucleus or molecule, the usual convention, then bound electron states have negative potential energy. If an atom, ion, or molecule is at the lowest possible energy level, it and its electrons are said to be in the "ground state". If it is at a higher energy level, it is said to be "excited", or any electrons that have higher energy than the ground

neg: Project Excalibur of a nucleus and a number of electrons orbiting in shells around it. These particles can be found in any one of a number of discrete energy states, defined by quantum mechanics. The energy levels depend on the structure of the nucleus, so they vary from element to element. Electrons can gain or lose energy by absorbing or emitting a photon with the same energy as the difference between two allowable energy states. This is why different elements have unique spectrums and gives rise to the science of spectroscopy. Electrons will naturally release photons if there is an unoccupied lower

neg: Dubnium are lower than the other six. (The three 6d electrons normally occupy the lowest energy levels, 6d.) A singly ionized atom of dubnium (Db) should lose a 6d electron compared to a neutral atom; the doubly (Db) or triply (Db) ionized atoms of dubnium should eliminate 7s electrons, unlike its lighter homologs. Despite the changes, dubnium is still expected to have five valence electrons; 7p energy levels have not been shown to influence dubnium and its properties. As the 6d orbitals of dubnium are more destabilized than the 5d ones of tantalum, and Db is expected to have two 6d,

neg: Energy-dispersive X-ray spectroscopy specimen, a high-energy beam of charged particles such as electrons or protons (see PIXE), or a beam of X-rays, is focused into the sample being studied. At rest, an atom within the sample contains ground state (or unexcited) electrons in discrete energy levels or electron shells bound to the nucleus. The incident beam may excite an electron in an inner shell, ejecting it from the shell while creating an electron hole where the electron was. An electron from an outer, higher-energy shell then fills the hole, and the difference in energy between the higher-energy shell and the lower energy shell

neg: Principal quantum number same "n" value are often referred to as electron shells or energy levels. The minimum energy exchanged during any wave-matter interaction is the product of the wave frequency multiplied by Planck's constant. This causes the wave to display particle-like packets of energy called quanta. The difference between energy levels that have different "n" determine the emission spectrum of the element. In the notation of the periodic table, the main shells of electrons are labeled: based on the principal quantum number. The principal quantum number is related to the radial quantum number, "n", by: where "ℓ" is the azimuthal quantum number

neg: Light-dependent reactions the excited electron can move from the initial molecule to the acceptor. This process results in the formation of a positive charge on the special pair (due to the loss of an electron) and a negative charge on the acceptor and is, hence, referred to as photoinduced charge separation. In other words, electrons in pigment molecules can exist at specific energy levels. Under normal circumstances, they exist at the lowest possible energy level they can. However, if there is enough energy to move them into the next energy level, they can absorb that energy and occupy that higher energy level.

neg: Pauli exclusion principle the higher-energy 2s states instead. Similarly, successively larger elements must have shells of successively higher energy. The chemical properties of an element largely depend on the number of electrons in the outermost shell; atoms with different numbers of occupied electron shells but the same number of electrons in the outermost shell have similar properties, which gives rise to the periodic table of the elements. In conductors and semiconductors, there are very large numbers of molecular orbitals which effectively form a continuous band structure of energy levels. In strong conductors (metals) electrons are so degenerate that they cannot even contribute much

neg: Photoemission spectroscopy used to study the energy levels of atomic core electrons, primarily in solids. Siegbahn referred to the technique as "electron spectroscopy for chemical analysis" (ESCA), since the core levels have small chemical shifts depending on the chemical environment of the atom that is ionized, allowing chemical structure to be determined. Siegbahn was awarded the Nobel Prize in 1981 for this work. XPS is sometimes referred to as PESIS (photoelectron spectroscopy for inner shells), whereas the lower-energy radiation of UV light is referred to as PESOS (outer shells) because it cannot excite core electrons. In the ultraviolet and visible region, the

neg: Hückel method below: The theory predicts two energy levels for ethylene with its two π electrons filling the low-energy HOMO and the high energy LUMO remaining empty. In butadiene the 4 π-electrons occupy 2 low energy molecular orbitals, out of a total of 4, and for benzene 6 energy levels are predicted, two of them degenerate. For linear and cyclic systems (with "N" atoms), general solutions exist: The energy levels for cyclic systems can be predicted using the mnemonic (named after the American chemist ). A circle centered at α with radius 2β is inscribed with a polygon with one vertex pointing

neg: Hund's rules stronger than any other remaining interactions. This is referred to as the LS coupling regime. Full shells and subshells do not contribute to the quantum numbers for total , the total spin angular momentum and for , the total orbital angular momentum. It can be shown that for full orbitals and suborbitals both the residual electrostatic energy (repulsion between electrons) and the spin–orbit interaction can only shift all the energy levels together. Thus when determining the ordering of energy levels in general only the outer valence electrons must be considered. Due to the Pauli exclusion principle, two electrons cannot share

neg: Energy level as σ or π depending on the situation. Corresponding anti-bonding orbitals can be signified by adding an asterisk to get σ* or π* orbitals. A non-bonding orbital in a molecule is an orbital with electrons in outer shells which do not participate in bonding and its energy level is the same as that of the constituent atom. Such orbitals can be designated as n orbitals. The electrons in an n orbital are typically lone pairs. In polyatomic molecules, different vibrational and rotational energy levels are also involved. Roughly speaking, a molecular energy state, i.e. an eigenstate of the molecular Hamiltonian,

neg: Degenerate matter In neutron stars, the degenerate particles are neutrons. A fermion gas in which all quantum states below a given energy level are filled is called a fully degenerate fermion gas. The difference between this energy level and the lowest energy level is known as the Fermi energy. In an ordinary fermion gas in which thermal effects dominate, most of the available electron energy levels are unfilled and the electrons are free to move to these states. As particle density is increased, electrons progressively fill the lower energy states and additional electrons are forced to occupy states of higher energy even

neg: Extended periodic table is larger due to the fact that 32 electrons are filled in the deeply buried 5g and 6f shells, instead of just 14 electrons being filled in the 4f and 5f shells in the lanthanides and actinides respectively. Pekka Pyykkö divides these superactinides into three series: a 5g series (elements 121 to 138), an 8p series (elements 139 to 140), and a 6f series (elements 141 to 155), also noting that there would be a great deal of overlapping between energy levels and that the 6f, 7d, or 8p orbitals could well also be occupied in the early superactinide atoms

neg: Atomic spectroscopy can potentially fail. Because optical spectroscopy is often less expensive and has performance adequate for many tasks, it is far more common Atomic absorption spectrometers are one of the most commonly sold and used analytical devices. Electrons exist in energy levels (i.e. atomic orbitals) within an atom. Atomic orbitals are quantized, meaning they exist as defined values instead of being continuous (see: atomic orbitals). Electrons may move between orbitals, but in doing so they must absorb or emit energy equal to the energy difference between their atom's specific quantized orbital energy levels. In optical spectroscopy, energy absorbed to move an

neg: Pauli exclusion principle has been shown that the Pauli exclusion principle is responsible for the fact that ordinary bulk matter is stable and occupies volume. This suggestion was first made in 1931 by Paul Ehrenfest, who pointed out that the electrons of each atom cannot all fall into the lowest-energy orbital and must occupy successively larger shells. Atoms therefore occupy a volume and cannot be squeezed too closely together. A more rigorous proof was provided in 1967 by Freeman Dyson and Andrew Lenard, who considered the balance of attractive (electron–nuclear) and repulsive (electron–electron and nuclear–nuclear) forces and showed that ordinary matter would collapse

neg: History of Solar System formation and evolution hypotheses electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles which satisfy the Pauli exclusion principle. At zero temperature, therefore, electrons could not all occupy the lowest-energy, or "ground", state; some of them had to occupy higher-energy states, forming a band of lowest-available energy states, the "Fermi sea". This state of the electrons, called "degenerate", meant that a white dwarf could cool to zero temperature and still possess high energy. Planetary nebulae are generally faint objects, and none are

neg: Metallic bonding they still experience the potential of the metal atoms, sometimes quite strongly. They require a more intricate quantum mechanical treatment (e.g., tight binding) in which the atoms are viewed as neutral, much like the carbon atoms in benzene. For - and especially -electrons the delocalization is not strong at all and this explains why these electrons are able to continue behaving as unpaired electrons that retain their spin, adding interesting magnetic properties to these metals. Metal atoms contain few electrons in their valence shells relative to their periods or energy levels. They are electron deficient elements and the communal sharing

neg: Atom equation. Electrons jump between orbitals in a particle-like fashion. For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon; see Electron properties. The energy of an emitted photon is proportional to its frequency, so these specific energy levels appear as distinct bands in the electromagnetic spectrum. Each element has a characteristic spectrum that can depend on the nuclear charge, subshells filled by electrons, the electromagnetic interactions between the electrons and other factors. When a continuous spectrum of energy is passed through a gas or plasma, some of the photons are

neg: Hund's rules of formula_17 changes from plus to minus for shells greater than half full. This term gives the dependence of the ground state energy on the magnitude of formula_5. The formula_19 lowest energy term of Si consists of three levels, formula_20. With only two of six possible electrons in the shell, it is less than half-full and thus formula_21 is the ground state. For sulfur (S) the lowest energy term is again formula_22 with spin–orbit levels formula_20, but now there are four of six possible electrons in the shell so the ground state is formula_24. If the shell is half-filled then

neg: Hund's rule of maximum multiplicity Hund's rule of maximum multiplicity Hund's rule of maximum multiplicity is a rule based on observation of atomic spectra, which is used to predict the ground state of an atom or molecule with one or more open electronic shells. The rule states that for a given electron configuration, the lowest energy term is the one with the greatest value of spin multiplicity. This implies that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs. The rule, discovered by Friedrich Hund in 1925, is of important use in atomic chemistry,

neg: Stimulated emission on the basis of stimulated emission. Electrons and their interactions with electromagnetic fields are important in our understanding of chemistry and physics. In the classical view, the energy of an electron orbiting an atomic nucleus is larger for orbits further from the nucleus of an atom. However, quantum mechanical effects force electrons to take on discrete positions in orbitals. Thus, electrons are found in specific energy levels of an atom, two of which are shown below: When an electron absorbs energy either from light (photons) or heat (phonons), it receives that incident quantum of energy. But transitions are only allowed

neg: Laser and shape of the beam. Electrons and how they interact with electromagnetic fields are important in our understanding of chemistry and physics. In the classical view, the energy of an electron orbiting an atomic nucleus is larger for orbits further from the nucleus of an atom. However, quantum mechanical effects force electrons to take on discrete positions in orbitals. Thus, electrons are found in specific energy levels of an atom, two of which are shown below: When an electron absorbs energy either from light (photons) or heat (phonons), it receives that incident quantum of energy. But transitions are only allowed

neg: Energy level Energy level A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels. The term is commonly used for the energy levels of electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized. In chemistry

neg: Mesoscopic physics terms of energy levels, potential well, valence bands, conduction band, and electron energy band gaps. Electrons in bulk dielectric material (larger than 10 nm) can be described by energy bands or electron energy levels. Electrons exist at different energy levels or bands. In bulk materials these energy levels are described as continuous because the difference in energy is negligible. As electrons stabilise at various energy levels, most vibrate in valence bands below a forbidden energy level, named the band gap. This region is an energy range in where no electron states exist. A smaller amount have energy levels above the

neg: Nanowire are composed of repeating molecular units either organic (e.g. DNA) or inorganic (e.g. MoSI). Typical nanowires exhibit aspect ratios (length-to-width ratio) of 1000 or more. As such they are often referred to as one-dimensional (1-D) materials. Nanowires have many interesting properties that are not seen in bulk or 3-D (three-dimensional) materials. This is because electrons in nanowires are quantum confined laterally and thus occupy energy levels that are different from the traditional continuum of energy levels or bands found in bulk materials. Peculiar features of this quantum confinement exhibited by certain nanowires manifest themselves in discrete values of the electrical

neg: Energy level lowest possible energy level, it and its electrons are said to be in the "ground state". If it is at a higher energy level, it is said to be "excited", or any electrons that have higher energy than the ground state are "excited". Such a species can be excited to a higher energy level by absorbing a photon whose energy is equal to the energy difference between the levels. Conversely, an excited species can go to a lower energy level by spontaneously emitting a photon equal to the energy difference. A photon's energy is equal to Planck's constant () times

neg: Franck–Hertz experiment any binding energy should also be possible for electrons. However, Bohr assumed that only a specific series of binding energies occur, which correspond to the "quantum energy levels" for the electron. An electron is normally found in the lowest energy level, with the largest binding energy. Additional levels lie higher, with smaller binding energies. Intermediate binding energies lying between these levels are not permitted. This was a revolutionary assumption. Franck and Hertz had proposed that the 4.9 V characteristic of their experiments was due to ionization of mercury atoms by collisions with the flying electrons emitted at the cathode. In

neg: Excimer excimer is very short, on the order of nanoseconds. Binding of a larger number of excited atoms form Rydberg matter clusters, the lifetime of which can exceed many seconds. Under the molecular orbital formalism, a typical ground-state molecule has electrons in the lowest possible energy levels. According to the Pauli principle, at most two electrons can occupy a given orbital, and if an orbital contains two electrons they must be in opposite spin states. The highest occupied molecular orbital is called the HOMO and the lowest unoccupied molecular orbital is called the LUMO; the energy gap between these two states

neg: Electron shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the "n"th shell can in principle hold up to 2("n") electrons. Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: atoms may

neg: Quantum cascade laser electromagnetic waves in a semiconductor with a superlattice" by R.F. Kazarinov and R.A. Suris in 1971. Within a bulk semiconductor crystal, electrons may occupy states in one of two continuous energy bands - the valence band, which is heavily populated with low energy electrons and the conduction band, which is sparsely populated with high energy electrons. The two energy bands are separated by an energy band gap in which there are no permitted states available for electrons to occupy. Conventional semiconductor laser diodes generate light by a single photon being emitted when a high energy electron in the conduction band

neg: Effective atomic number an atom as being 'stacked' by energy outside the nucleus; the lowest energy electrons (such as the 1s and 2s electrons) occupy the space closest to the nucleus, and electrons of higher energy are located further from the nucleus. The binding energy of an electron, or the energy needed to remove the electron from the atom, is a function of the electrostatic interaction between the negatively charged electrons and the positively charged nucleus. In Iron, atomic number 26, for instance, the nucleus contains 26 protons. The electrons that are closest to the nucleus will 'see' nearly all of them. However,

neg: Fermi point point, the break of symmetry can be explained by assuming a vortex or singularity will appear as a result of the spin of a fermi particle (quasiparticle, Fermion) in one dimension of the three-dimensional momentum space. The Fermi point is one particular electron state. The Fermi point refers to an event chirality of electrons is involved and the diameter of a carbon nanotube for which the nanotube becomes metallic. As the structure of a carbon nanotube determines the energy levels that the carbon's electrons may occupy, the structure affects macroscopic properties of the nanotube structure, most notably electrical and thermal

neg: Thomas–Fermi screening cases, see the article: Lindhard theory. The internal chemical potential (closely related to Fermi level, see below) of a system of electrons describes how much energy is required to put an extra electron into the system, neglecting electrical potential energy. As the number of electrons in the system increases (with fixed temperature and volume), the internal chemical potential increases. This consequence is largely because electrons satisfy the Pauli exclusion principle, only one electron may occupy an energy level and lower-energy electron states are already full, so the new electrons must occupy higher and higher energy states. The relationship is described

neg: Internal conversion cannot happen if the decay energy of the nucleus is less than a certain threshold. There are a few radionuclides in which the decay energy is not sufficient to convert (eject) a 1s (K shell) electron, and these nuclides, to decay by internal conversion, must decay by ejecting electrons from the L or M or N shells (i.e., by ejecting 2s, 3s, or 4s electrons) as these binding energies are lower. Although s electrons are more likely for IC processes due to their superior nuclear penetration compared to electrons with orbital angular momentum, spectral studies show that p electrons (from

neg: Nuclear structure shell structure of nucleons (protons and neutrons) within the nucleus, like that of electrons within atoms. Indeed, nucleons are quantum objects. Strictly speaking, one should not speak of energies of individual nucleons, because they are all correlated with each other. However, as an approximation one may envision an average nucleus, within which nucleons propagate individually. Owing to their quantum character, they may only occupy "discrete" energy levels. These levels are by no means uniformly distributed; some intervals of energy are crowded, and some are empty, generating a gap in possible energies. A shell is such a set of levels separated

neg: White dwarf allowed by electron orbitals limited by normal matter. Eddington wondered what would happen when this plasma cooled and the energy to keep the atoms ionized was no longer sufficient. This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics. Since electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles which satisfy the Pauli exclusion principle. At zero temperature, therefore, electrons can not all occupy the lowest-energy, or "ground", state;

neg: Electronic band structure absorption, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.). The electrons of a single, isolated atom occupy atomic orbitals each of which has a discrete energy level. When two or more atoms join together to form into a molecule, their atomic orbitals overlap. The Pauli exclusion principle dictates that no two electrons can have the same quantum numbers in a molecule. So if two identical atoms combine to form a diatomic molecule, each atomic orbital splits into two molecular orbitals of different energy, allowing the electrons in the former atomic orbitals to occupy

neg: Dirac equation of successively lower energy. Real electrons obviously do not behave in this way, or they would disappear by emitting energy in the form of photons. To cope with this problem, Dirac introduced the hypothesis, known as hole theory, that the vacuum is the many-body quantum state in which all the negative-energy electron eigenstates are occupied. This description of the vacuum as a "sea" of electrons is called the Dirac sea. Since the Pauli exclusion principle forbids electrons from occupying the same state, any additional electron would be forced to occupy a positive-energy eigenstate, and positive-energy electrons would be forbidden from

neg: Metal is made up of the central atom plus one-eight of each of the eight corner atoms. The electronic structure of metals means they are relatively good conductors of electricity. Electrons in matter can only have fixed rather than variable energy levels, and in a metal the energy levels of the electrons in its electron cloud, at least to some degree, correspond to the energy levels at which electrical conduction can occur. In a semiconductor like silicon or a nonmetal like sulfur there is an energy gap between the electrons in the substance and the energy level at which electrical conduction

neg: Pauli exclusion principle article "The Atom and the Molecule" by Gilbert N. Lewis, for example, the third of his six postulates of chemical behavior states that the atom tends to hold an even number of electrons in any given shell, and especially to hold eight electrons which are normally arranged symmetrically at the eight corners of a cube (see: cubical atom). In 1919 chemist Irving Langmuir suggested that the periodic table could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set of electron shells around the nucleus. In

neg: Ion is called "ionization". Atoms can be ionized by bombardment with radiation, but the more usual process of ionization encountered in chemistry is the transfer of electrons between atoms or molecules. This transfer is usually driven by the attaining of stable ("closed shell") electronic configurations. Atoms will gain or lose electrons depending on which action takes the least energy. For example, a sodium atom, Na, has a single electron in its valence shell, surrounding 2 stable, filled inner shells of 2 and 8 electrons. Since these filled shells are very stable, a sodium atom tends to lose its extra electron and

neg: Two-dimensional electron gas semiconductors. The most commonly encountered 2DEG is the layer of electrons found in MOSFETs. When the transistor is in inversion mode, the electrons underneath the gate oxide are confined to the semiconductor-oxide interface, and thus occupy well defined energy levels. For thin-enough potential wells and temperatures not too high, only the lowest level is occupied (see the figure caption), and so the motion of the electrons perpendicular to the interface can be ignored. However, the electron is free to move parallel to the interface, and so is quasi-two-dimensional. Other methods for engineering 2DEGs are high-electron-mobility-transistors (HEMTs) and rectangular quantum wells.

neg: Density of states with wavelengths and propagation directions dictated by the system. For example, in some systems, the interatomic spacing and the atomic charge of a material could allow only electrons of certain wavelengths to exist. In other systems, the crystalline structure of a material could allow waves to propagate in one direction, while suppressing wave propagation in another direction. Often, only specific states are permitted. Thus, it can happen that many states are available for occupation at a specific energy level, while no states are available at other energy levels . For example, the density of states of electrons at the bandedge

neg: Energy level the situation more stable for the involved atoms, which generally means the sum energy level for the involved atoms in the molecule is lower than if the atoms were not so bonded. As separate atoms approach each other to covalently bond, their orbitals affect each other's energy levels to form bonding and antibonding molecular orbitals. The energy level of the bonding orbitals is lower, and the energy level of the antibonding orbitals is higher. For the bond in the molecule to be stable, the covalent bonding electrons occupy the lower energy bonding orbital, which may be signified by such symbols

neg: Atomic orbital atomic orbitals. The repeating "periodicity" of the 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 atomic orbitals, respectively, although for higher values of the quantum number , particularly when the atom in question 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]4"s"3"d" and Cr = [Ar]3"d") can only be rationalized somewhat arbitrarily. With the

neg: Chronology of the universe radiation they emit reionizes much of the surrounding universe; splitting the neutral hydrogen atoms back into a plasma of free electrons and protons for the first time since recombination and decoupling. Reionization is evidenced from observations of quasars. Quasars are a form of active galaxy, and the most luminous objects observed in the universe. Electrons in neutral hydrogen have a specific patterns of absorbing photons, related to electron energy levels and called the Lyman series. Ionized hydrogen does not have electron energy levels of this kind. Therefore, light travelling through ionized hydrogen and neutral hydrogen shows different absorption lines. In

neg: Electrical resistivity and conductivity quantum mechanics, an electron in an atom or crystal can only have certain precise energy levels; energies between these levels are impossible. When a large number of such allowed energy levels are spaced close together (in energy-space)—i.e. have similar (minutely differing) energies— we can talk about these energy levels together as an "energy band". There can be many such energy bands in a material, depending on the atomic number {number of electrons (if the atom is neutral)} and their distribution (besides the size of the crystal and external factors like environmental modification of the energy bands). The material's electrons seek

neg: Upconverting nanoparticles difference between the intermediate state and the excited emission state. This minimizes non-radiative energy loss and facilitates both absorption and energy transfer. Generally, UCNPs contain some combination of rare-earth elements (Y, Sc, and the lanthanides), such as Er, Tm, and Ho ions, since they have several levels that follow this "ladder" pattern especially well. Lanthanide dopants are used as activator ions because they have multiple 4f excitation levels and completely filled 5s and 5p shells, which shield their characteristic 4f electrons, thus producing sharp f-f transition bands. These transitions provide substantially longer lasting excited states, since they are Laporte forbidden,

neg: Mesoscopic physics in bulk materials. As a result, the bandgap asserts itself: there is a small and finite separation between energy levels. This situation of discrete energy levels is called "quantum confinement". In addition, quantum confinement effects consist of isolated islands of electrons that may be formed at the patterned interface between two different semiconducting materials. The electrons typically are confined to disk-shaped regions termed quantum dots. The confinement of the electrons in these systems changes their interaction with electromagnetic radiation significantly, as noted above. Because the electron energy levels of quantum dots are discrete rather than continuous, the addition or subtraction

neg: Quantum well Quantum well A quantum well is a potential well with only discrete energy values. The classic model used to demonstrate a quantum well is to confine particles, which were originally free to move in three dimensions, to two dimensions, by forcing them to occupy a planar region. The effects of quantum confinement take place when the quantum well thickness becomes comparable to the de Broglie wavelength of the carriers (generally electrons and holes), leading to energy levels called "energy subbands", i.e., the carriers can only have discrete energy values. Quantum wells are formed in semiconductors by having a material, like

neg: Energy level is the sum of the electronic, vibrational, rotational, nuclear, and translational components, such that: where is an eigenvalue of the electronic molecular Hamiltonian (the value of the potential energy surface) at the equilibrium geometry of the molecule. The molecular energy levels are labelled by the molecular term symbols. 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. There are various types of energy level diagrams for bonds between atoms in a molecule. Electrons in atoms

neg: Periodic table a nonmetallic noble gas yet has some cationic chemistry that is characteristic of metals. Other classification schemes are possible such as the division of the elements into mineralogical occurrence categories, or crystalline structures. Categorizing the elements in this fashion dates back to at least 1869 when Hinrichs wrote that simple boundary lines could be placed on the periodic table to show elements having shared properties, such as metals, nonmetals, or gaseous elements. The electron configuration or organisation of electrons orbiting neutral atoms shows a recurring pattern or periodicity. The electrons occupy a series of electron shells (numbered 1, 2, and

neg: Atomic physics very large numbers of atoms. Electrons form notional shells around the nucleus. These are normally in a ground state but can be excited by the absorption of energy from light (photons), magnetic fields, or interaction with a colliding particle (typically ions or other electrons). If the electron absorbs a quantity of energy less than the binding energy, it will be transferred to an excited state. After a certain time, the electron in an excited state will "jump" (undergo a transition) to a lower state. In a neutral atom, the system will emit a photon of the difference in energy, since

neg: Nuclear reaction nucleus has a different atomic number, and thus the configuration of its electron shells is wrong. As the electrons rearrange themselves and drop to lower energy levels, internal transition X-rays (X-rays with precisely defined emission lines) may be emitted. In writing down the reaction equation, in a way analogous to a chemical equation, one may in addition give the reaction energy on the right side: For the particular case discussed above, the reaction energy has already been calculated as Q = 22.2 MeV. Hence: The reaction energy (the "Q-value") is positive for exothermal reactions and negative for endothermal reactions, opposite

neg: Nuclear structure the same state (Pauli exclusion principle). So the lowest-energy state of the nucleus is one where nucleons fill all energy levels from the bottom up to some level. A nucleus with full shells is exceptionally stable, as will be explained. As with electrons in the electron shell model, protons in the outermost shell are relatively loosely bound to the nucleus if there are only few protons in that shell, because they are farthest from the center of the nucleus. Therefore, nuclei which have a full outer proton shell will be more tightly bound and have a higher binding energy than

neg: Light-emitting diode holes existing in the p-region. Free electrons are in the conduction band of energy levels, while holes are in the valence energy band. Thus the energy level of the holes is lower than the energy levels of the electrons. Some portion of the energy must be dissipated to recombine the electrons and the holes. This energy is emitted in the form of heat and light. The electrons dissipate energy in the form of heat for silicon and germanium diodes, but in gallium arsenide phosphide (GaAsP) and gallium phosphide (GaP) semiconductors, the electrons dissipate energy by emitting photons. If the semiconductor

neg: Quantum well propagation paths confined within the multiple-quantum-well intrinsic layer. Quantum well A quantum well is a potential well with only discrete energy values. The classic model used to demonstrate a quantum well is to confine particles, which were originally free to move in three dimensions, to two dimensions, by forcing them to occupy a planar region. The effects of quantum confinement take place when the quantum well thickness becomes comparable to the de Broglie wavelength of the carriers (generally electrons and holes), leading to energy levels called "energy subbands", i.e., the carriers can only have discrete energy values. Quantum wells are

neg: Photoemission electron microscopy photoelectric effect is a quantum electronic phenomenon in which electrons (photoelectrons) are emitted from matter after the absorption of energy from electromagnetic radiation such as UV light or X-ray. When UV light or X-ray is absorbed by matter, electrons are excited from core levels into unoccupied states, leaving empty core states. Secondary electrons are generated by the decay of the core hole. Auger processes and inelastic electron scattering create a cascade of low-energy electrons. Some electrons penetrate the sample surface and escape into vacuum. A wide spectrum of electrons is emitted with energies between the energy of the illumination and

neg: Electron configuration shells and subshells despite the advances in understanding of the quantum-mechanical nature of electrons. An electron shell is the set of allowed states that share the same principal quantum number, "n" (the number before the letter in the orbital label), that electrons may occupy. An atom's "n"th electron shell can accommodate 2"n" electrons, "e.g." the first shell can accommodate 2 electrons, the second shell 8 electrons, the third shell 18 electrons and so on. The factor of two arises because the allowed states are doubled due to electron spin—each atomic orbital admits up to two otherwise identical electrons with opposite

neg: Hund's rules analogous to the behaviour of bus passengers who tend to occupy all double seats singly before double occupation occurs.) Two different physical explanations have been given for the increased stability of high multiplicity states. In the early days of quantum mechanics, it was proposed that electrons in different orbitals are further apart, so that electron–electron repulsion energy is reduced. However, accurate quantum-mechanical calculations (starting in the 1970s) have shown that the reason is that the electrons in singly occupied orbitals are less effectively screened or shielded from the nucleus, so that such orbitals contract and electron–nucleus attraction energy becomes greater

neg: Semiconductor if its energy is near the Fermi level (see Fermi–Dirac statistics). High conductivity in a material comes from it having many partially filled states and much state delocalization. Metals are good electrical conductors and have many partially filled states with energies near their Fermi level. Insulators, by contrast, have few partially filled states, their Fermi levels sit within band gaps with few energy states to occupy. Importantly, an insulator can be made to conduct by increasing its temperature: heating provides energy to promote some electrons across the band gap, inducing partially filled states in both the band of states beneath

neg: Pauli exclusion principle alkali metal spectra in an external magnetic field, where all degenerate energy levels are separated, is equal to the number of electrons in the closed shell of the noble gases for the same value of "n". This led Pauli to realize that the complicated numbers of electrons in closed shells can be reduced to the simple rule of "one" electron per state, if the electron states are defined using four quantum numbers. For this purpose he introduced a new two-valued quantum number, identified by Samuel Goudsmit and George Uhlenbeck as electron spin. The Pauli exclusion principle with a single-valued many-particle

neg: Hollow atoms Hollow atoms Hollow Atoms (discovered in 1990 by a French team of researchers around Jean-Pierre Briand) are short-lived multiply excited neutral atoms which carry a large part of their Z electrons (Z ... projectile nuclear charge) in high-n levels while inner shells remain (transiently) empty. This population inversion arises for typically 100 femtoseconds during the "interaction of a slow highly charged ion (HCI) with a solid surface". Despite this limited lifetime, the formation and decay of a hollow atom can be conveniently studied from ejected electrons and soft X-rays, and the trajectories, energy loss and final charge state distribution of

neg: Atom Irving Langmuir suggested that this could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set of electron shells about the nucleus. The Stern–Gerlach experiment of 1922 provided further evidence of the quantum nature of atomic properties. When a beam of silver atoms was passed through a specially shaped magnetic field, the beam was split in a way correlated with the direction of an atom's angular momentum, or spin. As this spin direction is initially random, the beam would be expected to deflect in a random

neg: Auger electron spectroscopy yield information about the chemical composition of a surface. Figure 1 illustrates two schematic views of the Auger process. The types of state-to-state transitions available to electrons during an Auger event are dependent on several factors, ranging from initial excitation energy to relative interaction rates, yet are often dominated by a few characteristic transitions. Because of the interaction between an electron's spin and orbital angular momentum (spin-orbit coupling) and the concomitant energy level splitting for various shells in an atom, there are a variety of transition pathways for filling a core hole. Energy levels are labeled using a number of

neg: Wide-bandgap semiconductor that allow electrons to be added or removed with little applied energy. When tightly packed together, electrons can easily move from atom to atom, making them excellent conductors. In comparison, most plastic materials have widely spaced energy levels that requires considerable energy to move electrons between their atoms, making them natural insulators. Semiconductors are those materials that have both types of bands, and at normal operational temperatures, some electrons are in both bands. In semiconductors, adding a small amount of energy pushes more electrons into the "conduction band", making them more conductive and allowing current to flow like a conductor.

neg: Period 5 element reactive as the alkali metals. Like rubidium, it has 5 electron shells or energy levels, and in accordance with the Madelung rule it has two electrons in its 5s subshell. Strontium is a soft metal and is extremely reactive upon contact with water. If it does come in contact with water, though, it will combine with the atoms of both oxygen and hydrogen to form strontium hydroxide and pure hydrogen gas which quickly diffuses in the air. In addition, strontium, like rubidium, oxidizes in air and turns a yellow color. When ignited, it will burn with a strong red flame.

neg: Periodic table so on). Each shell consists of one or more subshells (named s, p, d, f and g). As atomic number increases, electrons progressively fill these shells and subshells more or less according to the Madelung rule or energy ordering rule, as shown in the diagram. The electron configuration for neon, for example, is 1s 2s 2p. With an atomic number of ten, neon has two electrons in the first shell, and eight electrons in the second shell; there are two electrons in the s subshell and six in the p subshell. In periodic table terms, the first time an electron

neg: Electron microprobe by an electron from either a higher energy bound shell in the atom (producing another vacancy which is in turn filled by electrons from yet higher energy bound shells) or by unbound electrons of low energy. The difference in binding energy between the electron shell in which the vacancy was produced and the shell from which the electron comes to fill the vacancy is emitted as a photon. The energy of the photon is in the X-ray region of the electromagnetic spectrum. As the electron structure of each element is unique, the series X-ray line energies produced by vacancies in

neg: Shubnikov–de Haas effect level is substantially flat inside a sample (see Fig 1). At the edges of a sample, the work function bends levels upwards. Fig 1 shows the Fermi energy "E" located in between two Landau levels. Electrons become mobile as their energy levels cross the Fermi energy "E". With the Fermi energy "E" in between two Landau levels, scattering of electrons will occur only at the edges of a sample where the levels are bent. The corresponding electron states are commonly referred to as edge channels. The Landauer-Büttiker approach is used to describe transport of electrons in this particular sample. The

neg: Molecular orbital diagram The antibonding pi orbital (also asymmetrical) has four lobes pointing away from the nuclei. Both p and p orbitals form a pair of pi orbitals equal in energy (degenerate) and can have higher or lower energies than that of the sigma orbital. In diboron the 1s and 2s electrons do not participate in bonding but the single electrons in the 2p orbitals occupy the 2πp and the 2πp MO's resulting in bond order 1. Because the electrons have equal energy (they are degenerate) diboron is a diradical and since the spins are parallel the compound is paramagnetic. In certain diborynes

neg: Electrical resistivity and conductivity in that region. In contrast, the low energy states are rigidly filled with a fixed number of electrons at all times, and the high energy states are empty of electrons at all times. Electric current consists of a flow of electrons. In metals there are many electron energy levels near the Fermi level, so there are many electrons available to move. This is what causes the high electronic conductivity of metals. An important part of band theory is that there may be forbidden bands of energy: energy intervals that contain no energy levels. In insulators and semiconductors, the number of

neg: Electrodeless lamp of the liquid mercury or the mercury in the amalgam vaporizes to provide the mercury vapor. The electric field ionizes some of the mercury atoms to produce free electrons, and then accelerates those free electrons. When the free electrons collide with mercury atoms, some of those atoms absorb energy from the electrons and are “excited” to higher energy levels. After a short delay, the excited mercury atoms spontaneously relax to their original lower energy state and emit a UV photon with the excess energy. As in a conventional fluorescent tube, the UV photon diffuses through the gas to the inside

neg: Landau quantization the gauge transformation we get Consider an operator formula_64 such that formula_65 from above relation we deduce that from this we conclude Landau quantization Landau quantization in quantum mechanics is the quantization of the cyclotron orbits of charged particles in magnetic fields. As a result, the charged particles can only occupy orbits with discrete energy values, called Landau levels. The Landau levels are degenerate, with the number of electrons per level directly proportional to the strength of the applied magnetic field. Landau quantization is directly responsible for oscillations in electronic properties of materials as a function of the applied magnetic

neg: Planetary nebula of the Sun's spectrum in 1868. While helium was isolated on Earth soon after its discovery in the spectrum of the Sun, "nebulium" was not. In the early 20th century, Henry Norris Russell proposed that, rather than being a new element, the line at 500.7 nm was due to a familiar element in unfamiliar conditions. Physicists showed in the 1920s that in gas at extremely low densities, electrons can occupy excited metastable energy levels in atoms and ions that would otherwise be de-excited by collisions that would occur at higher densities. Electron transitions from these levels in nitrogen and oxygen

neg: Superatom Superatom A superatom is any cluster of atoms that seem to exhibit some of the properties of elemental atoms. Sodium atoms, when cooled from vapor, naturally condense into clusters, preferentially containing a magic number of atoms (2, 8, 20, 40, 58, etc.). The first two of these can be recognized as the numbers of electrons needed to fill the first and second shells, respectively. The superatom suggestion is that free electrons in the cluster occupy a new set of orbitals that are defined by the entire group of atoms, i.e. cluster, rather than each individual atom separately (non-spherical or doped

neg: History of chemistry a planetary model in which the negatively charged electrons orbit a small, positively charged nucleus similar to the planets orbiting the Sun (except that the orbits are not planar) - the gravitational force of the solar system is mathematically akin to the attractive Coulomb (electrical) force between the positively charged nucleus and the negatively charged electrons. In the Bohr model, however, electrons orbit the nucleus in orbits that have a set size and energy - the energy levels are said to be "quantized", which means that only certain orbits with certain radii are allowed; orbits in between simply don't exist.

neg: Electron shell found to correspond to the "n" values 1, 2, 3, etc. They are used in the spectroscopic Siegbahn notation. The physical chemist Gilbert Lewis was responsible for much of the early development of the theory of the participation of valence shell electrons in chemical bonding. Linus Pauling later generalized and extended the theory while applying insights from quantum mechanics. The electron shells are labeled K, L, M, N, O, P, and Q; or 1, 2, 3, 4, 5, 6, and 7; going from innermost shell outwards. Electrons in outer shells have higher average energy and travel farther from the nucleus

neg: Valley of stability which implies that the atomic nucleus is built up in "shells" in a manner similar to the structure of the much larger electron shells in atoms. In both cases, shells are just groups of quantum energy levels that are relatively close to each other. Energy levels from quantum states in two different shells will be separated by a relatively large energy gap. So when the number of neutrons and protons completely fills the energy levels of a given shell in the nucleus, the binding energy per nucleon will reach a local maximum and thus that particular configuration will have a

neg: L-shell the electron energy decreases to the VHF regime and the magnetosphere eventually gives way to the solar wind. Because Jupiter's trapped electrons contain so much energy, they more easily diffuse across L-shells than trapped electrons in Earth's magnetic field. One consequence of this is a more continuous and smoothly-varying radio-spectrum emitted by trapped electrons in gyro-resonance. L-shell The L-shell, L-value, or McIlwain L-parameter (after Carl E. McIlwain) is a parameter describing a particular set of planetary magnetic field lines. Colloquially, L-value often describes the set of magnetic field lines which cross the Earth's magnetic equator at a number of Earth-radii

neg: Spark gap equipment from high-voltage transients. The light emitted by a spark does not come from the current of electrons itself, but from the material medium fluorescing in response to collisions from the electrons. When electrons collide with molecules of air in the gap, they excite their orbital electrons to higher energy levels. When these excited electrons fall back to their original energy levels, they emit energy as light. It is impossible for a visible spark to form in a vacuum. Without intervening matter capable of electromagnetic transitions, the spark will be invisible (see vacuum arc). Spark gaps are essential to the

neg: H-alpha H-alpha H-alpha (Hα) is a specific deep-red visible spectral line in the Balmer series with a wavelength of 656.28 nm in air; it occurs when a hydrogen electron falls from its third to second lowest energy level. H-alpha light is important to astronomers as it is emitted by many emission nebulae and can be used to observe features in the Sun's atmosphere, including solar prominences and the chromosphere. According to the Bohr model of the atom, electrons exist in quantized energy levels surrounding the atom's nucleus. These energy levels are described by the principal quantum number "n" = 1, 2,

neg: Heat transfer physics of principal carriers (e.g.. momentum, energy) are derived from the Schrödinger equation (called first principle or "ab initio") and the interaction rates (for kinetics) are calculated using the quantum states and the quantum perturbation theory (formulated as the Fermi golden rule). Variety of "ab initio" (Latin for from the beginning) solvers (software) exist (e.g., ABINIT, CASTEP, Gaussian, Q-Chem, Quantum ESPRESSO, SIESTA, VASP, WIEN2k). Electrons in the inner shells (core) are not involved in heat transfer, and calculations are greatly reduced by proper approximations about the inner-shells electrons. The quantum treatments, including equilibrium and nonequilibrium "ab initio" molecular dynamics (MD), involving

neg: Energy level of atoms, there are 1st, 2nd, 3rd, etc. ionization energies for removing the 1st, then the 2nd, then the 3rd, etc. of the highest energy electrons, respectively, from the atom originally in the ground state. Energy in corresponding opposite quantities can also be released, sometimes in the form of photon energy, when electrons are added to positively charged ions or sometimes atoms. Molecules can also undergo transitions in their vibrational or rotational energy levels. Energy level transitions can also be nonradiative, meaning emission or absorption of a photon is not involved. If an atom, ion, or molecule is at the

neg: Landau quantization Landau quantization Landau quantization in quantum mechanics is the quantization of the cyclotron orbits of charged particles in magnetic fields. As a result, the charged particles can only occupy orbits with discrete energy values, called Landau levels. The Landau levels are degenerate, with the number of electrons per level directly proportional to the strength of the applied magnetic field. Landau quantization is directly responsible for oscillations in electronic properties of materials as a function of the applied magnetic field. It is named after the Soviet physicist Lev Landau. Consider a two-dimensional system of non-interacting particles with charge and spin confined

neg: 18-electron rule 18-electron rule when one considers only those valence electrons, which occupy metal–ligand bonding orbitals. 18-electron rule The 18-electron rule is a rule used primarily for predicting and rationalizing formulae for stable metal complexes, especially organometallic compounds. The rule is based on the fact that the valence shells of transition metals consist of nine valence orbitals (one s orbital, three p orbitals and five d orbitals), which collectively can accommodate 18 electrons as either bonding or nonbonding electron pairs. This means that, the combination of these nine atomic orbitals with ligand orbitals creates nine molecular orbitals that are either metal-ligand bonding

neg: Island of stability first proposed by Glenn T. Seaborg in the late 1960s. The hypothesis is based upon the nuclear shell model, which implies that the atomic nucleus is built up in "shells" in a manner similar to the structure of the much larger electron shells in atoms. In both cases, shells are just groups of quantum energy levels that are relatively close to each other. Energy levels from quantum states in two different shells will be separated by a relatively large energy gap, so when the number of neutrons and protons completely fills the energy levels of a given shell in the

neg: Photosynthetic reaction centre pigment molecules, or passed to them by resonance transfer from a surrounding light-harvesting complex, they release two electrons into an electron transport chain. Light is made up of small bundles of energy called photons. If a photon with the right amount of energy hits an electron, it will raise the electron to a higher energy level. Electrons are most stable at their lowest energy level, what is also called its ground state. In this state, the electron is in the orbit that has the least amount of energy. Electrons in higher energy levels can return to ground state in a

neg: Atomic orbital terms of electron shells and subshells which can each hold a number of electrons determined by the Pauli exclusion principle. Thus the "n" = 1 state can hold one or two electrons, while the "n" = 2 state can hold up to eight electrons in 2s and 2p subshells. In helium, all "n" = 1 states are fully occupied; the same for "n" = 1 and "n" = 2 in neon. In argon the 3s and 3p subshells are similarly fully occupied by eight electrons; quantum mechanics also allows a 3d subshell but this is at higher energy than the

neg: Electron paramagnetic resonance and spin quantum number formula_1, with magnetic components formula_2 and formula_3. In the presence of an external magnetic field with strength formula_4, the electron's magnetic moment aligns itself either parallel (formula_3) or antiparallel (formula_2) to the field, each alignment having a specific energy due to the Zeeman effect: where Therefore, the separation between the lower and the upper state is formula_11 for unpaired free electrons. This equation implies (since both formula_8and formula_10 are constant) that the splitting of the energy levels is directly proportional to the magnetic field's strength, as shown in the diagram below. An unpaired electron can move

neg: Aufbau principle the order of ionization of electrons in this and other transition metals far more intelligible, given that 4s electrons are invariably preferentially ionized. Aufbau principle The aufbau principle states that in the ground state of an atom or ion, electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. For example, the 1s shell is filled before the 2s subshell is occupied. In this way, the electrons of an atom or ion form the most stable electron configuration possible. An example is the configuration 1s 2s 2p 3s 3p for the phosphorus atom, meaning that the

neg: Transparency and translucency light wave absorption include: In electronic absorption, the frequency of the incoming light wave is at or near the energy levels of the electrons within the atoms which compose the substance. In this case, the electrons will absorb the energy of the light wave and increase their energy state, often moving outward from the nucleus of the atom into an outer shell or orbital. The atoms that bind together to make the molecules of any particular substance contain a number of electrons (given by the atomic number Z in the periodic chart). Recall that all light waves are electromagnetic in

neg: Density functional theory complete neglect of electron correlation. Teller (1962) showed that Thomas–Fermi theory cannot describe molecular bonding. This can be overcome by improving the kinetic energy functional. The kinetic energy functional can be improved by adding the Weizsäcker (1935) correction: The Hohenberg–Kohn theorems relate to any system consisting of electrons moving under the influence of an external potential. The many-electron Schrödinger equation can be very much simplified if electrons are divided in two groups: valence electrons and inner core electrons. The electrons in the inner shells are strongly bound and do not play a significant role in the chemical binding of atoms;

neg: Wide-bandgap semiconductor Reversing the polarity of this applied energy pushes the electrons into the more widely separated bands, making them insulators and stopping the flow. Since the amount of energy needed to push the electrons between these two levels is very small, semiconductors allow switching with very little energy input. However, this switching process depends on the electrons being naturally distributed between the two states, so small inputs cause the population statistics to change rapidly. As the external temperature changes, due to the Maxwell–Boltzmann distribution more and more electrons will normally find themselves in one state or the other, causing the switching

neg: Free electron model a zero-temperature pressure given by where formula_21 is the volume and formula_22 is the total energy, the derivative performed at temperature and chemical potential constant. This pressure is called the electron degeneracy pressure and does not come from repulsion or motion of the electrons but from the restriction that no more than two electrons (due to the two values of spin) can occupy the same energy level. This pressure defines the compressibility or bulk modulus of the metal This expression gives the right order of magnitude for the bulk modulus for alkali metals and noble metals, which show that this

neg: White dwarf some of them would have to occupy higher-energy states, forming a band of lowest-available energy states, the "Fermi sea". This state of the electrons, called "degenerate", meant that a white dwarf could cool to zero temperature and still possess high energy. Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, this will increase the kinetic energy of the electrons, thereby increasing the pressure. This "electron degeneracy pressure" supports a white dwarf against gravitational collapse. The pressure depends only on density and not on temperature. Degenerate matter is relatively compressible;

neg: Energy level to the nucleus, since its potential energy is negative and inversely dependent on its distance from the nucleus. Crystalline solids are found to have energy bands, instead of or in addition to energy levels. Electrons can take on any energy within an unfilled band. At first this appears to be an exception to the requirement for energy levels. However, as shown in band theory, energy bands are actually made up of many discrete energy levels which are too close together to resolve. Within a band the number of levels is of the order of the number of atoms in the