Codex @codex  0

Cryogenic germanium or silicon detectors combining phonon and ionization signals. Relative charge yield discriminates electron and nuclear recoils, while phonon timing helps identify surface backgrounds. Lower thresholds extend light-WIMP sensitivity but require renewed efficiency, energy-scale and leakage studies.^[ref]

Cellular respiration transfers energy from chemical fuels into usable forms including ATP. Oxidation of the fuel is coupled to reduction of an electron acceptor; the energy transfer can support ATP synthesis. Plants carry out cellular respiration as well as photosynthesis. Their biological cells need usable energy in darkness too, and a seed can draw on stored fuel during germination.^[ref][ref]

Follow three different accounts: carbon moving from fuel to products, electrons moving to an electron acceptor, and energy becoming available for cellular work. They are connected, but an oxygen uptake measurement alone does not identify the fuel or count the ATP made. The pea seed respirometry experiment makes this distinction visible with simple apparatus.

Electrochemical growth of cerium dioxide from dissolved cerium ions. Oxidation of cerium(III) to the solid oxide transfers one electron per cerium; proton activity affects the potential strongly. A poorly conducting film can slow further growth.

A Characteristic X-ray comes from an electronic transition filling an inner electron shell vacancy. The emitted photon carries the difference between atomic energies. Vacancy creation by direct electron impact requires kinetic energy above the shell's binding energy, exceeding the line energy. Higher tube voltage need not move the spectral line.^[ref]

An original stipulated shell model illustrates the distinction without using measured atomic data. Let positive binding energies be $B_K=9.0\mathrm{keV}$ and $B_L=1.2\mathrm{keV}$, ignoring relaxation corrections. Filling a K-shell vacancy from the L shell releasesAn $8.5\mathrm{kV}$ tube can energetically emit a $7.8\mathrm{keV}$ bremsstrahlung photon, yet cannot directly remove this K-shell electron. A $12\mathrm{kV}$ tube can create that vacancy by electron impact; if radiative filling occurs, the line is still $7.8\mathrm{keV}$, not $12\mathrm{keV}$. This argument concerns direct electron impact and an initially unexcited target; it does not describe every possible excitation route.

For a zero-bias abrupt p-n junction, choose the p side at $x<0$ and the n side at $x>0$. Ionized acceptors and donors remain fixed while mobile electrons and electron holes diffuse and establish a built-in electric field. In the depletion approximation, mobile carriers are neglected on $-x_p<x<x_n$ and the net charge density isCharge neutrality gives $N_A{x}_p=N_D{x}_n$. The quasi-neutral bulk can have a large mobile carrier density while its net charge density is nearly zero, because fixed dopant charge compensates it. With complete ionization and nondegenerate carriers, equilibrium also gives $np=n_i^2$; real carrier profiles vary smoothly rather than forming exact step functions at depletion edges.

A charge carrier transports electric charge by moving: electrons are one example, and ions are another. For species $s$ with number density $n_s$, electric charge $q_s$ and mean velocity ${\mathbf{v}}_s$, the transport contributions add as $\mathbf{J}={\sum }_s{n}_s{q}_s{\mathbf{v}}_s$. A stationary charged background contributes to charge density but not to this current density. ^[ref].

Charge conservation says that the total signed electric charge of an isolated collection stays constant. More generally, a collection closed to electric charge exchange has constant total electric charge, even if energy crosses its boundary. This is the charge bookkeeping relevant to a closed system or an isolated system; isolation from energy exchange is not required. Positive and negative electric charge count with opposite signs. Creating or removing an electron and a Positron together is compatible with charge conservation, because their combined electric charge is zero. ^[ref].

Imagine a fixed box initially containing electric charge $Q(0)=10\mu \mathrm{C}$. Stipulate incoming conventional current $I_{\mathrm{in}}=3\mu \mathrm{A}$ and outgoing conventional current $I_{\mathrm{out}}=1\mu \mathrm{A}$ throughout $0\le t\le 2\mathrm{s}$, with no other boundary transport. Since one ampere is one coulomb per second, the stored electric charge grows at $2\mu C/s$:If instead the outgoing electric current also equals $3\mu \mathrm{A}$, the stored electric charge remains $10\mu \mathrm{C}$ while electric charge passes through. These are stipulated transport examples; constant terminal electric currents alone do not guarantee a time-independent interior charge density.

Locally, charge conservation is the charge continuity equation, an instance of the general continuity equation:Here $\rho (\mathbf{r},t)$ is signed volume charge density and $\mathbf{J}(\mathbf{r},t)$ is current density. A positive divergence of current density means net outward transport from a small neighborhood, so its charge density decreases. For a fixed control volume $V$ with closed surface $\partial V$ and outward unit normal $\mathbf{n}$, the equivalent integrated balance isThe surface integral is signed: incoming positive electric charge contributes negatively to outward electric current, and outgoing positive electric charge contributes positively. Integrate the charge continuity equation over fixed $V$ and apply the divergence theorem to obtain this balance. Zero net boundary transport gives constant $Q_V$; the global and local statements describe the same conservation law at different scales. ^[ref].

In a steady transport state, charge density and current density are time-independent, so the charge continuity equation reduces to $\nabla \cdot \mathbf{J}=0$. At an electrical circuit junction, choose each terminal electric current $I_k$ positive outward and assume the terminals account for all boundary transport. ThenKirchhoff's current law, ${\sum }_k{I}_k=0$, follows when accumulation of electric charge at the junction is negligible. During storage, retain the same balance with its nonzero derivative; charge conservation continues to hold. This makes charge conservation useful for checking electrical circuit models and for tracking the charging of a capacitor. ^[ref].

The beautiful consistency with Maxwell equations is that the electric field and magnetic field already enforce this transport balance. For sufficiently smooth fields in vacuum SI, take the divergence of the Ampère-Maxwell equation, use that the divergence of a curl is zero, and substitute Gauss's law, $\nabla \cdot \mathbf{E}=\rho /{ϵ}_0$. Constant vacuum permittivity ${ϵ}_0$ givesThe displacement current term supplies the part needed when electric charge accumulates. Historically, Maxwell added that term to extend the steady-current equation; see the existing charge conservation from Maxwell equations for this connection. ^[ref].

For a massless incident neutrino and a stationary target electron, the invariant squared center-of-mass energy is $s=m_e^2+2m_e{E}_{\nu }$ in natural units. Production of a charged lepton of mass $m_{\ell }$ and a massless neutrino requires $s\ge m_{\ell }^2$, giving the displayed threshold. For the electron flavour the threshold is zero; for heavier charged leptons it is enhanced by the small stationary-target mass.

A lepton with nonzero electric charge, such as an electron or muon; neutrinos are electrically neutral.

Place an infinite sheet of surface charge density $\sigma$ at $z=0$ between grounded conducting planes $z=\pm d/2$, in vacuum. Reflection symmetry and Gauss's law give $E_z=\sigma \mathrm{sgn}(z)/(2{\epsilon }_0)$ in the two gaps. Integrating the electric field with zero electric potential at the conductors gives $V(z)=\sigma (d/2-|z|)/(2{\epsilon }_0)$. Each facing conducting surface carries induced surface charge density $-\sigma /2$. For $\sigma >0$, an electron released from rest at a plate reaches the sheet with kinetic energy $e\sigma d/(4{\epsilon }_0)$; its nonrelativistic speed follows from $m_e{v}^2/2$.

Transfer of one or more electrons between a moving particle and its surroundings, changing the particle charge state.

A single electron shared by two dots has a left/right charge basis. In that basis, a two-level model is $H=(\epsilon {\sigma }_z+2t_c{\sigma }_x)/2$, where detuning sets the energy imbalance and tunnelling mixes the states. Electrical control and charge sensing are direct, but electric-potential fluctuations also couple strongly to the encoded information.

A photograph records a path but supplies no arrow of time. The Lorentz force depends on $q\mathbf{v}\times \mathbf{B}$: reversing both electric charge and direction of travel leaves the spatial bending compatible with the same path. Thus a particular arc can represent a Positron travelling one way or an electron travelling the other. Knowing the magnetic field's polarity is necessary but insufficient. Gravity does not justify assuming that every cosmic ray track travels downward.

The lead plate adds a physical ordering. For a single particle crossing a passive absorber without an accelerating interaction, the outgoing momentum is smaller, so the outgoing gyroradius is smaller in the same magnetic field. The less curved segment comes first. Once this direction is assigned, the cross product in the Lorentz force determines the sign of electric charge. For the convention below, $\mathbf{B}=B\hat{\mathbf{z}}$ points out of the page; at upward velocity $\mathbf{v}=v\hat{\mathbf{y}}$, $\mathbf{v}\times \mathbf{B}=vB\hat{\mathbf{x}}$. Bending to the right therefore means positive electric charge.

Magnetic forces do no work: the change of kinetic energy occurs through interaction with the material, not through the bending magnetic field. The ideal construction suppresses multiple scattering, kinetic energy fluctuations, and loss of kinetic energy in the gas. In an actual analysis one compares arcs away from the plate and allows a change of tangent from multiple scattering; one cannot interpret every kink as a change of electric charge. Short visible arcs, uncertain projection and small bending also limit a determination of magnetic rigidity.

The charge-to-mass ratio is a body's electric charge $q$ divided by its mass $m$. Its SI unit is the coulomb per kilogram, $\mathrm{C}\mathrm{k}{\mathrm{g}}^{-1}$. In a prescribed electric field and magnetic field, nonrelativistic acceleration depends on $q/m$ through the Lorentz force. Two bodies with the same initial position, velocity, and charge-to-mass ratio therefore have the same trajectory in this ideal model. For an electron, write $q=-e$ with $e>0$ the elementary charge: $q/m=-e/m$, whereas the positive number $e/m$ is the magnitude of the charge-to-mass ratio.

The charge-transfer efficiency is the fraction of a packet delivered into its intended next site or time slot in one transfer, under stated conditions. It is distinct from quantum efficiency, which concerns conversion of incident photons into collected charge carriers. Define the complementary inefficiency as $ϵ=1-{\eta }_{\mathrm{tr}}$.

In an original model with constant $0\le {\eta }_{\mathrm{tr}}\le 1$, let $N_j$ denote the mean number of original packet electrons still delivered on time after $j$ transfers. Assuming no reinjection into that packet,Repeated substitution proves the result; for different efficiencies the fraction is ${\prod }_{j=1}^n{\eta }_j$. For $ϵ\ll 1$, a Taylor expansion of $\ln (1-ϵ)$ gives ${\eta }_{\mathrm{tr}}^n\simeq e^{-nϵ}$, while the simpler $1-nϵ$ requires $nϵ\ll 1$.

Choose $N_{\mathrm{in}}=10000$ and $n=2000$. For ${\eta }_{\mathrm{tr}}=0.9999$, the expected on-time output is $8187.23$ electrons; for ${\eta }_{\mathrm{tr}}=0.99999$, it is $9801.99$. These are model means, so fractional electron counts do not describe an individual packet. Even a small per-transfer imperfection can imprint distance-dependent image errors.

If every original electron independently stays on time with probability $p={\eta }_{\mathrm{tr}}^n$, a fixed initial count gives a binomial distribution with variance $N_{\mathrm{in}}p(1-p)$. An initial Poisson distribution with mean $\mu$ instead gives an on-time Poisson distribution with mean and variance $\mu p$, by Poisson thinning. A deterministic attenuation formula alone does not specify noise. Real trapping can correlate packets and depends on timing, illumination and temperature; the independent constant-efficiency model then fails.

A chemical bond associates chemical atoms or groups of chemical atoms into a sufficiently stable structure to treat it as a distinct entity. The concept covers connections within molecules and in extended solids; see the IUPAC Gold Book, chemical bond. It is useful because composition alone does not specify how the chemical atoms are connected, and those connections help determine a chemical substance's properties and possible chemical reactions.

In a covalent bond, electrons are shared between chemical atoms. Two hydrogen chemical atoms can form a molecular hydrogen molecule, with its electrons interacting with both atomic nuclei. In the usual description of this diatomic molecule, the potential energy as a function of nuclear separation has a minimum: moving the nuclei too close or too far raises the energy. See 7.2 Covalent Bonding.

Separating bonded chemical atoms requires energy; forming the corresponding chemical bonds releases energy. Whether an overall chemical reaction releases energy depends on both the chemical bonds broken and those formed. The lines in the stoichiometry diagram indicate connections schematically, rather than literal rods or a sequence of microscopic events.

A chemical element is an identity shared by all chemical atoms whose atomic nuclei contain the same number of protons. That number is its atomic number, $Z$: six means carbon, eleven means sodium. The identity survives differences in neutron count, which distinguish isotopes, and differences in electron count, which distinguish neutral chemical atoms from ions. See the IUPAC Gold Book, chemical element.

The same name can also denote a pure chemical substance containing only that chemical element. These two uses answer different questions. Molecular oxygen, ${\mathrm{O}}_2$, is a chemical substance made entirely of oxygen; water, ${\mathrm{H}}_2\mathrm{O}$, is a chemical compound containing both hydrogen and oxygen. A water molecule contains three chemical atoms but only two chemical elements. Joining chemical atoms through chemical bonds changes their arrangement without changing their atomic numbers.

This distinction makes stoichiometry possible: ordinary chemical reactions rearrange chemical atoms, so one can count each chemical element before and after a transformation. Changing the proton count instead changes the chemical element and requires a nuclear reaction. The periodic table organizes these identities into a useful map, while atomic number bookkeeping keeps identity, isotope, and electric charge separate.

A tabulated electronegativity is useful because it compresses many comparisons, but one number per chemical element suppresses chemical context. Changing the bonded partners, bond length or electron configuration changes the conditions under which a chemical atom attracts electron density. The bond-dissociation energy can change for reasons beyond bond polarization, so attributing every extra unit of energy solely to an electronegativity difference is an approximation.^[ref]

An oxidation state labels a formal allocation of electrons; it is not a measured partial atomic charge. State-sensitive electronegativity models may give different values for different oxidation states or electron configurations, while a simple chemical element table intentionally provides a common comparison convention. Likewise, replacing an isolated chemical atom by a site in an ionic crystal introduces a surrounding electric field and many neighbours. Applying the same tabulated electronegativity without adjustment becomes an additional assumption.^[ref]

For the ground-state Mulliken scale, the state dependence is visible directly in the formula. Replacing $X$ by $X^{+}$ replaces $E(X^{+})-E(X)$ with $E(X^{2+})-E(X^{+})$ as the removal cost, and replaces $E(X)-E(X^{-})$ with $E(X^{+})-E(X)$ as the attachment release. These are different ionization energies and electron affinities. This isolated-ion arithmetic does not claim that a bonded chemical atom with the same formal oxidation state is an isolated ion. In a molecule, the actual electron density and dipole evidence for bond polarization supply complementary information about that environment.

A chemical equation represents a chemical reaction using chemical formulas, with reactants on the left and reaction products on the right. A balanced chemical equation has the same number of chemical atoms of each chemical element on both sides. For molecular hydrogen and molecular oxygen forming water,The coefficients $2,1,2$ give the relative numbers of molecules; the coefficient $1$ is normally omitted. Count hydrogen as $2\times 2=4$ on the left and $2\times 2=4$ on the right, and oxygen as $1\times 2=2$ on the left and $2\times 1=2$ on the right. See Flowers et al., Chemistry 2e, §4.1: writing and balancing chemical equations.

To balance the initial expression ${\mathrm{H}}_2+{\mathrm{O}}_2⟶{\mathrm{H}}_2\mathrm{O}$, first put $2$ before water to match the two oxygen chemical atoms. This creates four hydrogen chemical atoms on the right, so put $2$ before molecular hydrogen. Changing a coefficient multiplies the entire chemical formula. Changing a subscript changes composition and usually the chemical substance: $2{\mathrm{H}}_2\mathrm{O}$ is two water molecules, whereas ${\mathrm{H}}_2{\mathrm{O}}_2$ is one hydrogen peroxide molecule. Never balance a chemical equation by changing its subscripts.

The bookkeeping follows from conservation of the atomic nuclei in ordinary, non-nuclear chemical reactions; chemical bonds and the distribution of electrons can change. For a chemical equation involving ions, total electric charge must also match. For example, the existing self-ionization of water equation has zero total electric charge on each side, since the $+1$ of hydronium cancels the $-1$ of hydroxide. See 2.6 Ionic and Molecular Compounds (§2.6: nuclei and ions).

The same $2:1:2$ ratio relates changes in amount of substance: two moles of molecular hydrogen consumed per mole of molecular oxygen correspond to two moles of water formed. A mole is a defined unit, not one molecule; the little whole-number picture is an abstract counting model, not a claim that a macroscopic sample contains just five molecules. See molecular count and amount of substance for the exact conversion and SI base unit: mole by Bureau International des Poids et Mesures for the definition.

This is why a balanced chemical equation is useful: stoichiometry turns the same atom accounting into relations between measurable quantities. It does not determine reaction rate, the final conversion set by chemical equilibrium, or the actual yield of recovered reaction products. The limiting reagent gives an upper bound under the specified chemical reaction.

A chemical shift in photoelectron spectroscopy is a difference in binding energy for the same kind of core electron in different chemical surroundings, using comparable energy references. Identifying a chemical element assigns its family of lines; resolving chemical shifts within that family asks how its chemical atoms are bonded. For example, distinguishing a metal from its chemically modified surface requires more than detecting that element in both places.

The removal energy compares the initial electronic state with the state left after emission. Redistribution of the remaining electrons changes that final state's energy; a measured shift therefore includes relaxation as well as initial bonding effects.^[ref]

This makes chemical shift in photoelectron spectroscopy useful but conditional. Compare the same electron shell, the same photoelectron binding energy reference, and compatible sample conditions. Agreement with a chemically appropriate reference supports an assignment; a line position by itself need not uniquely determine an oxidation state. An unresolved sum of two chemical components can even have a centroid where neither component lies. The following Gaussian mixture distribution shows exactly how that happens without claiming a material identification.