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Cooling an ion beam through Coulomb interactions with a co-moving low-spread electron beam. Friction reduces ion motion relative to the electron guiding flow while diffusion and external heating determine the eventual equilibrium.

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.

Electron magnetohydrodynamics neglects ion motion and electron inertia while retaining transport of the magnetic field by the electron current. At constant electron number density, ${\mathbf{u}}_e=-\mathbf{J}/(en)=-c\nabla \times \mathbf{B}/(4\pi en)$. Flux freezing in this velocity givesFor a uniform guide field, the solenoidal linear equation implies ${\omega }^2=(c{B}_0/4\pi en{)}^2{k}_{\parallel }^2{k}^2$. With $v_A=B_0/\sqrt{4\pi n{m}_i}$ and $d_i=c\sqrt{m_i/(4\pi e^{2}n)}$, the coefficient is $c{B}_0/(4\pi en)=v_A{d}_i$.

An interaction between electric charges mediated by an electric field. In a uniform dielectric the pair potential energy is $q_1{q}_2/(4\pi ϵr)$; mobile ions can modify it through electrostatic screening.

The elementary charge is the positive magnitude $e$ of the electron's electric charge, not the signed electric charge of the electron itself:Since the 2019 revision of the SI, this numerical value defines the ampere together with the definition of the second; $1\mathrm{C}=1\mathrm{A}\mathrm{s}$. Thus today's numerical exactness is a choice of units, whereas measured electric charges still have experimental uncertainty. An oil drop experiment can test charge quantization and the apparatus calibration; it does not supply a new uncertain defining value of $e$ in today's SI. ^[ref].

For ordinary isolated chemical atoms, ions and charged objects whose net electric charge is counted through protons and electrons, charge quantization gives $Q=ne$ with signed integer $n$. A neutral chemical atom that loses two electrons becomes an ion of electric charge $+2e$. A toy object with $10^9$ excess electrons has $Q=-0.1602176634\mathrm{nC}$. Conversely, the scale $1\mathrm{nC}/e\simeq 6.24\times 10^9$ explains why laboratory electric charge often looks continuous: billions of microscopic increments fit into a small macroscopic amount. Averaged charge density is a continuum description, not a claim that each particle has an arbitrarily divisible electric charge.

The ordinary-matter qualifier matters. In the Standard Model, quarks have electric charges $+2e/3$ or $-e/3$, and antiquarks have the opposite signs. Confinement means these are constituents of hadrons, not isolated fractionally charged particles collected by an oil drop experiment. The usual valence quark sums give $2(2e/3)-e/3=e$ for a proton and $2e/3-2(e/3)=0$ for a neutron. Thus elementary charge should not be defined as the smallest nonzero electric charge of every constituent in particle theory. ^[ref].

The beautiful experimental idea behind the oil drop experiment is to determine a microscopic electric charge by watching a visible carrier move. In his 1913 paper, Millikan timed the descent and electrically driven ascent of individual oil drops, repeatedly changing a drop's electric charge through capture of air ions. His apparatus used parallel plates separated by $16\mathrm{mm}$, a roughly $5300\mathrm{V}$ source, and an optical scale to measure travel distances. He reported multiple relationships among a given drop's inferred electric charges. He also found that uncorrected Stokes's law gave a size-dependent inferred elementary unit, and introduced a pressure-dependent slip correction. These were measured relationships with calibration and model uncertainties, not exact readings of today's defined $e$. ^[ref].

A modern instructional implementation sprays low-volatility oil of known density through a plate aperture, illuminates the drops, and follows one through a calibrated optical scale. Measure the plate spacing $d$, electric potential difference $V$, air temperature and pressure. Time a fixed distance $L$ with the electric field off to get a terminal falling speed $v_f=L/t_f$. Then choose the field polarity to drive the same drop upward and measure $v_r=L/t_r$. Repeat timings at a fixed electric charge, and compare before and after an ion-capture event. The same drop is especially useful because its radius and mass need not be inferred anew for each charge state. ^[ref].

Here is the leading continuum model, retaining buoyancy. Assume a drop shaped as a sphere of radius $a$, oil and air densities ${\rho }_o$ and ${\rho }_a$, air dynamic viscosity $\eta$, and gravitational acceleration $g$. Define the downward effective weight $W$ and positive linear drag coefficient $k$ byAt terminal velocity, the net force vanishes. Falling with no electric field, the upward drag force balances weight minus buoyancy. Rising with the electric force upward, the drag force reverses and joins the downward effective weight:Consequently the uncorrected estimates areThe observed direction of response, with known field polarity, supplies the sign of $q$. A suspended drop gives the alternative balance $|q|E=W$, but it still requires a determination of $W$: balancing a drop alone does not determine its electric charge.

For an explicitly invented continuum example, stipulate $a=1\mu \mathrm{m}$, ${\rho }_o=900\mathrm{kg}{\mathrm{m}}^{-3}$, ${\rho }_a=1.2\mathrm{kg}{\mathrm{m}}^{-3}$, $\eta =1.8\times 10^{-5}\mathrm{Pa}\mathrm{s}$, $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$, $q=-5e$ and a downward $E=10^5\mathrm{V}{\mathrm{m}}^{-1}$. The balances predict $W\simeq 3.69\times 10^{-14}\mathrm{N}$, $v_f\simeq 0.109\mathrm{mm}{\mathrm{s}}^{-1}$ and $v_r\simeq 0.127\mathrm{mm}{\mathrm{s}}^{-1}$. Substituting those speeds recovers $|q|=5e$ within rounding. This checks the algebra; it is not a precision prediction for real micrometre drops, which need a slip correction.

The inference has two distinct parts. Compare inferred electric charges or charge changes with a common unit, seeking $q_i\simeq n_{i}e$ within uncertainty, rather than demanding exact ratios of rounded measurements. Then establish the absolute scale through electric field, density, dynamic viscosity and distance/time calibration. If the observed steps are all even multiples, their common spacing alone cannot exclude an unobserved smaller unit. Air motion, evaporation and mistimed crossings can alter inferred electric charge without an ion-capture event. Small Reynolds number supports Stokes's law, but does not by itself justify its no-slip continuum coefficient: a significant ratio of air mean free path to drop radius requires a slip correction. Millikan's comparison of different drop sizes and pressures addressed that systematic limitation; the modern PASCO manual also includes the correction. Agreement supports charge quantization for the observed carriers within experimental resolution, rather than proving a universal statement about every possible particle.

Multiplying $e$ by the Avogadro constant gives the Faraday constant, $F=N_{A}e$, the electric charge per mole of singly charged carriers. This connects counting individual electric charges with bulk electrochemistry. ^[ref].

An enzyme is a biological catalyst: it accelerates a chemical reaction and is regenerated after a successful catalytic cycle. Most enzymes are proteins, but catalytic RNA molecules, called ribozymes, also exist. Many reactions needed by a biological cell would proceed too slowly under its ordinary conditions without enzymes. See Cooper, The Cell: the central role of enzymes as biological catalysts.

The biological beauty is selective speed. A biological cell contains many possible reactants; its enzymes help determine which transformations happen on a useful timescale. In metabolism, one step's reaction product can become another step's substrate, so selective catalysts support an organized flow of material.

The ribosome is a striking biological example: the machinery that builds proteins has RNA at its catalytic centre. The complete ribosome contains both RNA and proteins, but its bond-forming active site is built from RNA. Structural evidence established this distinction in Nissen et al., The structural basis of ribosome activity in peptide bond synthesis, Science 289, 920–930 (2000).

Selection occurs at an active site, the region where substrate binding and catalytic chemistry take place. Shape and chemical interactions favour some substrates over others; binding can also reshape the enzyme, an induced fit. Recognition alone is insufficient: holding a substrate extremely tightly need not make it react quickly. Catalysis requires a favourable route through the transition state, the high-barrier configuration between reactants and reaction products. Positioning reactive groups and stabilizing this configuration relative to the bound substrate can lower that barrier. Specificity is often strong, but need not mean exactly one acceptable substrate. See Cooper, The Cell: mechanisms of enzymatic catalysis.

Read the diagram numerically. Its chosen Gibbs free energies are $0$ for the reactants and $-10\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ for the reaction products. The uncatalysed peak is $60\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, whereas the catalysed peak is $40\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$. The forward free-energy barriers are therefore $60$ and $40\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$; viewed from the reaction products, the reverse barriers are $70$ and $50\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$. Both decrease by $20\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, while the endpoint difference stays $-10\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$. These are constructed values, not measurements of a particular enzyme.

This separates chemical kinetics from chemical equilibrium. An enzyme changes how rapidly the system approaches chemical equilibrium; it does not change the equilibrium constant for the same overall chemical reaction under the same conditions. Faster catalysis therefore supplies no extra driving energy. In a biological cell, continuing supply of reactants and removal of reaction products can nevertheless sustain a net flow: the surroundings keep that system away from chemical equilibrium. See IUBMB, Symbolism and terminology in enzyme kinetics: basic definitions.

Some enzymes require a cofactor, an additional nonprotein component such as a metal ion or a small organic molecule. Organic helpers are often called coenzymes; they can assist transfers that the protein alone cannot readily perform. The cofactor may remain bound or exchange with the surroundings, depending on the system. A coenzyme can be chemically changed in one reaction and regenerated by another: regeneration of the enzyme does not mean every helper is unchanged in that individual reaction. Some enzymes need no additional cofactor. See Alberts et al., Molecular Biology of the Cell: small molecules associated with proteins and Alberts et al., activated carriers and their regeneration.

How much faster does adding substrate make a reaction? Enzyme kinetics gives a quantitative answer when a model's assumptions fit. For an illustrative reaction obeying Michaelis-Menten kinetics, use the Michaelis-Menten equation with substrate concentration $s$, limiting reaction rate $V_{\max }$ and Michaelis constant $K_M$. At $s/K_M=0.1$, substitution gives $v/V_{\max }=0.1/1.1=1/11\approx 0.0909$. At $s/K_M=1$, it gives $1/2$; at $s/K_M=10$, it gives $10/11\approx 0.9091$. Thus a hundredfold increase in substrate between the first and last examples yields only a tenfold increase in reaction rate.

For a chosen $V_{\max }=110\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$, those fractions mean reaction rates of $10$, $55$ and $100\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$. Doubling substrate from $10K_M$ to $20K_M$ raises the normalized rate only from $10/11$ to $20/21\approx 0.9524$, a relative increase of about $4.76\%$. In this simplest model, the catalytic machinery is already nearly fully occupied. Doubling the amount of active enzyme instead doubles $V_{\max }$ and the predicted reaction rates at fixed free substrate concentration, provided the other conditions are unchanged. This distinction helps decide whether additional substrate or additional catalytic capacity could improve throughput.

The interpretation has limits. The simplest Michaelis-Menten kinetics assumes a single substrate, fixed active enzyme amount, a suitable quasi-steady-state approximation, and initial measurements with negligible reverse reaction from accumulated reaction product. Substantial depletion, interacting binding sites, or inhibition by excess substrate can invalidate this model. Within it, $K_M$ is the substrate concentration giving half the limiting reaction rate; it is not generally the binding dissociation constant $K_d$. See IUBMB, enzyme kinetics: steady-state approximation and substrate dissociation and IUBMB, Michaelis-Menten and non-Michaelis-Menten kinetics. Measuring activity also requires specified temperature, pH and necessary cofactor availability: a weak signal can reflect unsuitable conditions rather than little enzyme. See Brooks et al., Assay Guidance Manual: basics of enzymatic assays for HTS.

For equal ion and neutral mass densities, let $\mu ={\mu }_{in}={\mu }_{ni}$, $a=k_{\parallel }{B}_0/\sqrt{4\pi {\rho }_i}$ and use Fourier time dependence $e^{-i\omega t}$. Solenoidal displacements obey ${\ddot{\xi }}_i=-a^2{\xi }_i-\mu ({\dot{\xi }}_i-{\dot{\xi }}_n)$ and ${\ddot{\xi }}_n=-\mu ({\dot{\xi }}_n-{\dot{\xi }}_i)$. For nonzero frequency, the neutral equation gives ${\xi }_i=(1-i\omega /\mu ){\xi }_n$. Substitution in the ion equation givesEquivalently, the growth rate $s=-i\omega$ obeys $s^3+2\mu s^2+a^{2}s+\mu a^2=0$. A time-independent neutral displacement with zero velocity is a relabeling of a uniform fluid, not an additional wave root of the velocity/magnetic-field system.

The Faraday constant is the electric charge associated with one mole of elementary charges, $F=N_{\mathrm{A}}e\approx 96485.33212\mathrm{C}\mathrm{mo}{\mathrm{l}}^{-1}$. The product of the Avogadro constant and elementary charge is exact under the SI definitions; the displayed decimal is rounded. For ions with signed charge number $z$, the molar electrical contribution to an electrochemical potential is $zF\psi$, where $\psi$ is electric potential. ^[ref].

For field amplitudes of order the guide field, the ion Lorentz-force response over time $\tau$ is $\Delta u/v_A=O(v_A\tau /l)\ll 1$. The electron-current velocity is of order $v_A{d}_i/l$, larger than a bulk velocity of order $v_A$. Thus the leading Hall magnetohydrodynamics induction equation becomes the closed electron magnetohydrodynamics equation, while ions remain fixed to leading order on this fast scale. The first nonzero ion response need not have zero acceleration. This limit retains the fast branch of incompressible Hall-MHD wave dispersion, not the slow branch; very oblique modes must separately satisfy the fast-time ordering.

Filtration separates suspended solid particles from a fluid using a porous barrier. Dissolved ions can pass with the fluid; the separation does not establish the filtrate's composition. Solubility product measurement by titration requires removal of undissolved calcium hydroxide before acid-base titration.

Prepare the same ideal monoprotic acid model at initial pH $5$, with appropriate accompanying ions to balance electric charge. To predict the new pH after a finite signed addition $\Delta b$, solve $Q({\mathrm{pH}}_1)-Q(5)=\Delta b$ using the chemical equilibrium expression above. For $\Delta b=0.002\mathrm{mol}{\mathrm{L}}^{-1}$ of added chemical base, the calculated final pH is $5.366798$ at $C=0.010\mathrm{mol}{\mathrm{L}}^{-1}$, but $5.034749$ at $C=0.100\mathrm{mol}{\mathrm{L}}^{-1}$. The initial local approximation gives changes of about $0.34605$ and $0.034730$, respectively; its accuracy decreases as the partner balance changes appreciably.

For the dilute example, additions beyond approximately $0.005\mathrm{mol}{\mathrm{L}}^{-1}$ in either direction exceed the initial inventory of one partner. The full chemical equilibrium calculation still produces a finite pH; an inventory-only Henderson-Hasselbalch equation calculation would attempt to use a negative partner quantity. At $+0.006\mathrm{mol}{\mathrm{L}}^{-1}$ the dilute example reaches pH $10.99564$, whereas the concentrated example reaches only $5.104698$. This demonstrates a finite operating range, not an abrupt cessation of all buffer capacity.

A molecule or material whose fluorescence changes when it binds a target ion.

A formula unit is a specified compositional accounting entity for a chemical substance that need not consist of discrete molecules. For ordinary crystalline $\mathrm{NaCl}$, one formula unit counts one sodium ion ${\mathrm{Na}}^{+}$ and one chlorine ion ${\mathrm{Cl}}^{-}$; it does not identify an isolated pair within the crystal. Cohen et al., IUPAC Green Book, 3rd ed., §2.10.1(iii)(b), p. 51 defines a formula unit as a specified group of chemical atoms, rather than a unit of measurement. An amount of substance of one mole of $\mathrm{NaCl}$ formula units therefore corresponds to one mole of each kind of ion.

Radiation from unbound charged particles during a scattering encounter, notably electrons accelerated by ions in a plasma. Both the initial and final electron states are free, distinguishing this process from emission involving an atomic bound state.

A galvanic cell supplies electrical work from a spontaneous redox chemical reaction under the specified conditions. In discharge through a passive load, oxidation occurs at its negative anode and reduction at its positive cathode. Separating the reacting compartments makes the electrons take an external route, where their transport can deliver useful work. See Flowers et al., Chemistry 2e, §17.2: separated reactions and electrical work.

In the metallic external electrical circuit, electrons move from anode to cathode, while conventional current goes from cathode through the load to anode. Inside the cell, net ionic conventional current closes the loop from the anode compartment toward the cathode compartment. Oppositely moving cations and anions can both contribute to that direction; see electrolyte for the signed current density calculation. A cell can maintain a nonzero terminal electric potential difference near open circuit while delivering almost no power; the Daniell cell voltage and load experiment makes this distinction concrete.

Coupled dissolution of a less noble solid metal and reduction/deposition of a more noble metal ion without an external power supply.

Adding sodium hydroxide to acidified glycine successively removes its two titratable protons. Two broad buffer solution regions appear around the two pKa values, separated by a steep pH rise near the isoelectric point. This is useful evidence for two separated acid-base chemistry steps even though the changing chemical species are invisible. In the approximation that added hydroxide only changes glycine protonation, $b=1-\bar{z}$ is the added base amount of substance per initial amount of substance of glycine. Then $b\approx 0.5$, $1$ and $1.5$ correspond to $\mathrm{p}{K}_{a1}$, $\mathrm{pI}$ and $\mathrm{p}{K}_{a2}$; endpoints are not exactly pure chemical species. ^[ref]

For the solid-curve model, start with $n_G=0.00200\mathrm{mol}$ of glycine in $V_0=0.0200\mathrm{L}$ and exactly $n_G$ of fully dissociated hydrochloric acid; this fixes the chloride inventory, but does not force every glycine molecule to remain $G^{+}$. Let the sodium hydroxide concentration be $C_B=0.100\mathrm{mol}{\mathrm{L}}^{-1}$ and $b=n_{\mathrm{NaOH}}/n_G$. Assume volume is additive and no other ions are present; stipulate $K_w=10^{-14}$ for self-ionization of water at a temperature of $25{}^{\circ }\mathrm{C}$. ThenBalancing all positive and negative electric charges requiresSolving this equation gives the solid curve. It remains finite at $b=0$ and beyond $b=2$, where ignoring free hydronium and hydroxide would fail. At the first pKa, the full model gives $b\approx 0.436$, rather than $0.5$: appreciable free hydronium makes that half-equivalent shortcut inaccurate. At the second pKa, $b\approx 1.502$. Known acid inventory, dilution, and thermodynamic activity assumptions are therefore part of any quantitative interpretation, not optional corrections inferred from the curve's shape.

A geometric heuristic favouring the largest coordination number compatible with neighbouring opposite-charge ions touching the central ion without overlap. A limiting radius ratio rule comes from additionally making the surrounding ions just touch. It is a hard-sphere model, not an exact stability criterion.

For a planar surface contacting a symmetric monovalent ideal electrolyte on one side, the Poisson-Boltzmann equation is ${\psi }^{\prime \prime }=(2e{n}_{\infty }/\epsilon )\sinh (e\psi /(k_{B}T))$. Multiplication by ${\psi }^{\prime }$ and integration using the zero field and zero potential in the bulk givesThe solution decays towards the bulk, and the boundary condition $\sigma =-\epsilon {\psi }^{\prime }(0^{+})$ therefore yields the displayed charge-potential relation, with ${\kappa }^2=2e^2{n}_{\infty }/(\epsilon k_{B}T)$. Its small-potential limit is the planar Debye-Hückel double layer. It is nonlinear but still a mean-field model with point-like ions and constant permittivity; it does not include a compact interfacial layer or finite-ion-size saturation.

Immanuel Estermann, O. C. Simpson and Otto Stern used gravitational deflection to measure atomic speeds. Stern describes scanning a hot-wire surface ionization detector through a cesium beam and recording ion electric current.^[ref] Their 1947 paper reports potassium and cesium beams; a deficit of slow arrivals increased with oven pressure, supporting a source-slit collision explanation.^[ref]

First consider an original point-launch model, with horizontal speed $v>0$, zero initial vertical velocity, flight distance $L$, and uniform gravitational acceleration $g$. Downward displacement $y$ follows from flight time $t=L/v$:Slow particles fall farther. However, a detector scan counts arrivals per interval of height, not per interval of speed. Change of variables for probability densities supplies the Jacobian determinant:Here $g(v)$ denotes the effusive beam speed distribution; the unadorned constant $g$ in $C$ denotes gravitational acceleration. The integral of $p_y$ is one: substituting $u=b/y$ reduces it to ${\int }_0^{\infty }u{e}^{-u}du=1$. Its mode is $y=b/3$. Simply mapping the most probable arrival speed into a fall distance instead gives $2b/3$. The peaks differ because equal height bins cover unequal speed intervals.

For those chosen parameters, $b\simeq 176.54\mu \mathrm{m}$, so the detector-height probability density peaks near $58.85\mu \mathrm{m}$. A detector covering only $0<y<Y$ accepts the fractionAt $Y=0.80\mathrm{mm}$ this is about $97.9\%$, even before allowing for imperfect detection. Discarding the remainder changes the observed normalization.

Real slits transmit a range of launch heights and vertical velocities. Their geometrical response must be combined with the gravitational deflection and detector width; the point-launch formula is not an exact reduction of the historical apparatus. In the point-launch model, an initial vertical velocity $w$ would add $wL/v$ to $y$. Source collisions, detector efficiency and alignment can also distort a profile. Varying oven pressure helps distinguish such source losses from an incorrect thermal distribution; inferring a source temperature from the peak alone ignores both selection and the detector's coordinate transformation.