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Electromechanical conversion power balance applies conservation of energy to an electric machine's electrical and mechanical ports, internal storage and losses. In an electric motor sign convention, with electrical input positive and mechanical output positive,The internal term can include a changing magnetic field and rotational kinetic energy. Omitting it is justified only at the relevant steady operating point or after averaging over a cycle with no net storage change.

An original constant-field direct current motor model has winding electrical resistance $R$, inductance $L$, opposing induced electromotive force $e$, and current $i$:Multiplication by $i$ givesFor an ideal conversion coupling, $e=k_e\omega$ and electromagnetic torque ${\tau }_e=k_{t}i$ give $ei={\tau }_e\omega$ when the numerical constants agree in coherent SI units. The induced electrical term is converted power, not a resistive loss. DOE's motor analysis derives current from applied minus opposing induced electric potential difference and relates torque to field and armature current.^[ref]

Suppose $v=24\mathrm{V}$, $i=2\mathrm{A}$, $R=1\Omega$, $L=0.5\mathrm{H}$ and $di/dt=4\mathrm{A}{\mathrm{s}}^{-1}$. Then $e=20\mathrm{V}$ andThe terms are winding heating, increasing magnetic energy, and mechanical conversion. If $10\mathrm{W}$ is additionally going into rotational acceleration and mechanical losses are neglected, only $30\mathrm{W}$ reaches the shaft load at that instant. Calling all $40\mathrm{W}$ useful shaft output would omit a second storage term.

A proposed experiment records terminal electric potential difference, electric current, shaft speed and load torque during acceleration and after settling. The discrepancy between electrical input and load output can include storage as well as heating. For an electrical generator, reversing the port directions gives the corresponding mechanical-input balance; the physical energy accounting is unchanged.

Let an electron start with negligible kinetic energy and move through an increase $U>0$ in electric potential. Its electric charge is $q=-e$, where $e>0$ is the elementary charge, so the decrease in potential energy is $eU$. In a field-free region after acceleration,This is an electron formula, not a universal conversion from voltage to wavelength. It assumes negligible initial kinetic energy, negligible losses, and $eU\ll m_e{c}^2$, where $c$ is the speed of light. It describes the de Broglie wavelength outside the crystal; the potential energy inside a material can change the local kinetic momentum.

For $U=54\mathrm{V}$, take $h=6.62607015\times 10^{-34}\mathrm{J}\mathrm{s}$, $e=1.602176634\times 10^{-19}\mathrm{C}$, and $m_e\simeq 9.1093837\times 10^{-31}\mathrm{kg}$. The rounded electron mass is consistent with the 2022 recommended constants.^[ref]The electronvolt is an energy unit: $54\mathrm{eV}$ must be converted to joules before combining it with $m_e$ in SI units. Dimensional analysis checks both steps:The resulting velocity is about $4.3584\times 10^6\mathrm{m}{\mathrm{s}}^{-1}$, or $0.01454c$, so the nonrelativistic assumption is consistent. For a larger accelerating voltage, the relativistic energy-momentum relation gives $pc=\sqrt{K(K+2m_e{c}^2)}$, with $K=eU$, while $\lambda =h/p$ still holds. At $54\mathrm{V}$ the relativistic wavelength is shorter by about $0.00264\%$.

Explicitly, the exact special relativity formula and its nonrelativistic quantum mechanics limit areHere $K=eU$ is the gained kinetic energy; the total energy is $E=m_e{c}^2+K$. At $80\mathrm{kV}$, the nonrelativistic quantum mechanics expression gives $4.336\mathrm{pm}$, about $3.84\%$ larger than the exact $4.176\mathrm{pm}$. This difference matters when using electron diffraction ring positions to infer lattice plane spacings.

For free-electron recoil and a linear acoustic branch, $E_e(q)={\hslash }^2{q}^2/(2m_e)$ and $E_{\mathrm{ph}}(q)=\hslash c_{s}q$. Their ratio is $q\lambda$, so equality occurs at $q=1/\lambda$. This is a momentum/localization crossover scale, formally half a sound-speed analogue of the Reduced Compton wavelength. It does not replace the speed of light in electron relativity or determine a mean free path. A Fermi-surface electron emitting a phonon has fractional radial loss $\delta \simeq q/(2\lambda k_F^2)$ when the transferred energy is small.

Electron affinity measures how strongly an isolated neutral species binds an additional electron. In the spectroscopic convention used here, it is the positive energy required to detach that electron from a bound anion. With the free electron at rest assigned zero energy,The quantum states of $X$ and $X^{-}$ must be specified, usually their ground states. Positive $A_{\mathrm{ea}}$ means that attachment lowers the energy; a signed attachment energy is then negative. This convention agrees with the IUPAC definition and with the atomic tables used for Mulliken electronegativity.^[ref]

For chlorine, a published photodetachment threshold is $A_{\mathrm{ea}}/(hc)=29138.59(22)\mathrm{c}{\mathrm{m}}^{-1}$, approximately $3.612725\mathrm{eV}$ per chemical atom. Here $h$ is the Planck constant, $c$ the speed of light, and the inverse-length unit expresses an energy through a spectroscopic wavenumber. The parentheses give the reported uncertainty in the last digits, not a range of possible sign conventions.^[ref]

An electron affinity is neither an electronegativity nor a lattice energy. The first describes a specified isolated-species energy difference, electronegativity compares attraction for electron density in a chemical bond, and lattice energy refers to an entire ionic crystal and separated gaseous ions. A stable anion can therefore help explain ionic bonding without describing the full energy balance for making a salt.

An electron attachment enthalpy is the signed molar enthalpy change for a stated attachment reaction,For favourable attachment such as chlorine's first attachment, the electron attachment enthalpy is negative. Its leading isolated-ground-state energy contribution is $-N_{\mathrm{A}}{A}_{\mathrm{ea}}$, where $N_{\mathrm{A}}$ is the Avogadro constant. At finite temperature, consistent thermal populations, translational contributions and the $pV$ term in enthalpy must also be included, together with the same gaseous-electron reference used in the corresponding ionization energy term. Consequently a measured spectroscopic electron affinity is not automatically an exact $298.15\mathrm{K}$ attachment enthalpy with a minus sign. A Born-Haber cycle must use compatible enthalpies throughout.

An electron beam is a directed population of electrons with specified energy, current and spatial distribution. Electric fields accelerate or focus it, while magnetic fields bend trajectories through the Lorentz force.

In an electron microscope, the beam's interaction with a specimen produces signals carrying structural information. Its brightness, energy spread and angular spread matter independently of total current. A vacuum reduces collisions with background gas, and electron-electron repulsion can limit transport at high current. Treating it as a single trajectory omits this collective and statistical structure.

Adjustment of exposure dose or shape to compensate for energy deposited outside the intended write location.

Electron correlation concerns the dependence between electronic degrees of freedom that cannot be captured by treating each electron as moving independently. In a quantum-chemical use of the term, correlation usually means effects beyond the best single-Slater determinant Hartree-Fock method; that method already includes exchange associated with fermionic antisymmetry.

The distinction matters when comparing approximations. Dynamic electron correlation describes additional instantaneous avoidance even when one electronic configuration dominates. Static electron correlation becomes important when several configurations have comparable significance, as during some bond-dissociation processes. A correlation energy is therefore defined relative to a stated reference calculation, and the physical need for multiple configurations is different from merely allowing a single orbital to change shape.

Electronegativity describes a chemical atom's tendency to attract electron density towards itself in a chemical bond. It helps answer a useful question: when two different chemical atoms share electrons, which end of the chemical bond tends to be richer in electron density? For hydrogen chloride, the answer is chlorine: the covalent bond is a polar covalent bond, conventionally written ${\mathrm{H}}^{\delta +}-{\mathrm{Cl}}^{\delta -}$. The symbols indicate partial atomic charges, not isolated ions carrying whole elementary electric charges.^[ref]

Electronegativity is a comparison scheme, not the number of electrons on a chemical atom. A partial atomic charge depends on how the electron density is partitioned; formal charge instead follows an integer allocation in a Lewis structure. Neither is numerically equal to electronegativity. Nor is electronegativity identical to electron affinity, which concerns adding an electron to an isolated species. Different electronegativity scales use different measured inputs and conventions; compare numbers only after specifying the scale.^[ref]

For a concrete comparison, the Royal Society of Chemistry lists Pauling electronegativities ${\chi }_{\mathrm{P}}(\mathrm{H})=2.20$ and ${\chi }_{\mathrm{P}}(\mathrm{Cl})=3.16$. Their difference is $0.96$, so the electronegativity rule predicts bond polarization towards chlorine in hydrogen chloride. An isolated molecular hydrogen molecule has identical ends and zero electronegativity difference. These examples explain a direction of unequal sharing, not a quantitative partial atomic charge.^[ref][ref]

A larger electronegativity difference often suggests stronger bond polarization, but there is no universal numerical boundary where a covalent bond suddenly becomes ionic bonding. Tables of cutoffs are classification aids with exceptions. Hydrogen fluoride, for example, is described by a polar covalent bond even when its electronegativity difference exceeds a textbook's nominal ionic threshold. The actual electron density, physical setting, and chemical substance's structure matter.^[ref]

The distinction from ionization energy is equally useful: an ionization energy measures the cost of removing an electron from a specified isolated species, whereas electronegativity compares attraction for electron density in a bonded environment. Neither the removal cost alone nor the attachment release alone supplies a unique bonded-atom electronegativity. A scale combines selected measured inputs with a model and a convention.^[ref]

For an original relative comparison, stipulate fictitious bonded sites $A,B,C$ on one chosen dimensionless electronegativity scale:The electronegativity heuristic predicts bond polarization towards $B$ in $A-B$, towards $C$ in $B-C$, and towards $C$ in $A-C$. Shifting ${\chi }_0$ leaves every comparison unchanged. Although the $A-C$ difference is twice the $A-B$ difference, this does not make its partial atomic charge or bond dipole twice as large: those require additional information about electron density and bond length. These symbols describe a stipulated ordering, not a table of measured chemical elements.

Keep the chemical context attached to that ordering. A chemical atom in a molecule has neighbours and an electron configuration; an isolated-atom energy scale and a bonded-atom comparison are different constructions. The chemical environment dependence of electronegativity explains why a table is a useful approximation rather than an immutable property of every site. Furthermore, an applied electric field can induce bond polarization even between identical chemical atoms, through electric polarizability; equal tabulated electronegativity does not forbid that response.

An electron energy analyzer selects electrons by kinetic energy, allowing their count rate to be recorded as an energy scan.

Electron energy loss spectroscopy measures the energy transferred from incident electrons to a specimen. A transmitted-electron spectrometer separates nearly unscattered electrons from electrons that excited collective modes, atomic transitions or core-level processes.

The zero-loss feature supplies an energy reference, and losses can be reported as $E_{\mathrm{loss}}=E_{\mathrm{incident}}-E_{\mathrm{detected}}$. Element-specific edges and their energy-loss near-edge structure constrain composition and bonding. A thicker specimen can produce several losses in one trajectory, so the recorded electron energy loss spectroscopy response need not equal a single-interaction response. ^[ref]

For classical nondegenerate electrons, the free-particle Boltzmann occupancy has the form $z_e\exp [-p^2/(2mkT)]$, with chemical potential measured relative to its rest energy. Counting the two spin states in phase space gives $n_e=2z_e(2\pi mkT/h^2{)}^{3/2}$. A bound level of energy $-I_n$ has relative occupancy $(g_n/g_{+})z_e{e}^{I_n/kT}$ against its parent ion. Eliminating $z_e$ gives the level-specific Saha ionization equation.

The exact ground-state energy minus the minimum Hartree-Fock energy for the same Hamiltonian and variational constraints. It is nonpositive when compared with the unrestricted variational minimum. Correlations beyond a single determinant can substantially change phase boundaries at low density.

For number densities $n_{\uparrow },n_{\downarrow }$, $\zeta =(n_{\uparrow }-n_{\downarrow })/(n_{\uparrow }+n_{\downarrow })$. Uniform spin polarization raises kinetic energy by concentrating occupation in one Fermi sphere, while lowering exchange energy.

An electron gun creates, accelerates and shapes a directed electron beam. A source such as a heated cathode supplies electrons, an applied electric potential difference accelerates them toward an anode, and electrodes control the emitted current and beam geometry.

For an electron accelerated from rest through potential difference $V$, the ideal gained kinetic energy is $eV$, with the voltage sign chosen to accelerate it. Focusing optics then control beam position and convergence. Source size, energy spread and space charge affect the useful beam; increasing accelerating voltage alone does not guarantee a smaller probe or higher image resolution.

An electron hole is an unoccupied electron quantum state in an otherwise nearly full energy band, often the valence band. “Filled” refers to occupation of the allowed quantum states, not to filling all space with a continuous fluid of electrons. Each state, including its spin label, can hold at most one electron by the Pauli exclusion principle. The almost full energy band and its few missing occupants are therefore simpler to describe as a background plus a few electron holes. The electron hole is a quasiparticle, not a Positron inserted into the crystal.

Removing an electron of electric charge $-e$ changes the background's electric charge by $+e$. Thus an electron hole carries positive electric charge relative to that background. Promoting an electron into the conduction band creates an electron hole without changing the whole crystal's electric charge: $(-e)+(+e)=0$. An unbound pair still consists of two separate charge carriers; only a bound state of their relative motion is an exciton.

The local cartoon explains why a vacancy can move: when a neighboring electron fills it, another vacancy appears where that electron was. The vacancy has moved opposite to that particular transfer of an electron. In an extended Bloch state, use crystal momentum instead of imagining a permanently empty atomic site. For a completely filled energy band the summed electric current vanishes. Omitting one electron with group velocity ${\mathbf{v}}_v$ removes its contribution $-e{\mathbf{v}}_v$, leaving a contribution $+e{\mathbf{v}}_v$. This fixes both the positive electric charge and the velocity convention of the electron hole.

More precisely, near a parabolic valence band maximum, set its energy $E_v(0)$ as reference and define the electron hole wave vector by ${\mathbf{k}}_h=-{\mathbf{k}}_v$. ThenThe occupied electron branch has negative curvature there, while the electron hole branch has positive effective mass $m_h^{\ast }$. The velocity equality compares the electron hole with the missing Bloch state's group velocity; it does not contradict the opposite vacancy motion in a local transfer cartoon. The sign conventions are listed in Phys 460 Lecture 17.

An electron filling an electron hole removes both excitations relative to the filled-band background. Their electric charges cancel, consistent with charge conservation; the remaining electrons are still present. The released energy can leave through photon emission or other channels, including phonons. Formation of an exciton instead retains the excited electron and electron hole as a bound pair; recombination removes the pair. A valence band electron filling a nearby vacancy merely moves the electron hole and does not remove the total vacancy count.

Symmetry of the excitation spectrum under exchange of conduction band electrons and valence band holes, after choosing a central zero of energy. In a two-band model with equal effective masses and equal degeneracy factors, charge neutrality in an intrinsic semiconductor fixes the chemical potential at that central energy. Indeed the Fermi-Dirac distribution obeys $1-f(-E;\mu =0)=f(E;\mu =0)$, so excitation populations are equal at every positive energy.

An electronic amplifier uses an electrical power supply to increase a signal's amplitude or available output power. The input controls the transfer of supply energy to the load; it does not supply all the amplified output energy itself.

A voltage amplifier, a transimpedance amplifier and a charge amplifier relate different input and output quantities. To characterize one, vary the input around its operating point and measure gain, frequency response, noise and the range before saturation. A large gain does not by itself improve signal-to-noise ratio, since input noise and amplifier noise can both be amplified.

Separate geometry from electronic response in an original one-dimensional toy tunnel junction. Write the geometric surface height as $h(x)$, tip height as $z(x)$, and positive gap as $s(x)=z(x)-h(x)$. Assume low fixed tip-sample electric potential difference: the sampled energy window is narrow enough that the tip density of states is featureless and the sample local density of states varies little across that window. Neglect thermal broadening, changes of tip shape and lateral averaging. Let $\rho (x)>0$ be the effective sample local density of states divided by a positive reference value, so it is dimensionless. Choose a spatially constant effective barrier energy $\Phi >0$, a positive coefficient $C$ with units of electric current, andHere $m_e$ is the electron mass, $\hslash$ the reduced Planck constant, and $\kappa$ the tunnelling decay constant. This is an illustrative low-bias model, not a universal calibration formula. At fixed $I=I_0>0$, taking a logarithm givesThe logarithms have dimensionless arguments. Only constant $\rho$ makes the recorded height differ from geometric height by a constant. Multiplying $\rho$ by $r>0$ raises the apparent height by $\ln r/(2\kappa )$ without moving the geometric surface.

For a concrete ambiguity, choose $\kappa =10{\mathrm{nm}}^{-1}$, $a=0.020\mathrm{nm}$, lateral period $L=1\mathrm{nm}$, $s_0=0.50\mathrm{nm}$, and $q(x)=\cos (2\pi x/L)$. CompareBoth produce exactly $z(x)=s_0+aq(x)$ at $I_0=C{e}^{-2\kappa s_0}=C{e}^{-10}$. Substitution checks this without identifying $\rho$ with geometric height: case A has constant gap $s_0$, while case B has gap $s_0+aq(x)$ and a compensating electronic factor. The chosen ${\rho }_B$ ranges from $e^{-0.4}$ to $e^{0.4}$, approximately $0.6703$ to $1.4918$; every gap remains positive. The chosen $\kappa$ corresponds to $\Phi \simeq 3.81$ electronvolts, a positive effective barrier.

At fixed tip height $z_f=s_0$, both cases instead giveTheir maximum-to-minimum electric current ratio is $e^{0.8}\simeq 2.226$. Thus even adding this fixed-height scan at the same electric potential difference cannot distinguish these deliberately chosen surfaces within the toy model. Independent structural information or additional electronic measurements are required. Changing electric potential difference can supply such information, but also changes the assumptions used to define $C$ and $\rho$.