Richardson–Dushman equation
E835820
The Richardson–Dushman equation is a fundamental formula in thermionic emission theory that relates the current density of electrons emitted from a heated metal surface to its temperature and material-specific constants.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Richardson equation | 1 |
| Richardson–Dushman equation canonical | 1 |
| Richardson–Dushman law | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10003219 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Richardson–Dushman equation Context triple: [Edison effect, relatedTo, Richardson–Dushman equation]
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A.
Butler–Volmer equation
The Butler–Volmer equation is a fundamental relation in electrochemistry that describes how the rate of an electrode reaction (current density) depends on the electrode potential and reaction kinetics.
-
B.
Nernst–Planck equation
The Nernst–Planck equation is a fundamental relation in electrochemistry that describes the flux of charged species under the combined influence of diffusion, electric fields, and, in extended forms, convection.
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C.
Randles–Ševčík equation
The Randles–Ševčík equation is a fundamental electrochemical relationship that links peak current in cyclic voltammetry to the concentration and diffusion coefficient of a redox-active species.
-
D.
Fick's first law of diffusion
Fick's first law of diffusion is a fundamental physical law that relates the diffusive flux of particles to the spatial gradient of their concentration, describing how substances move from regions of high to low concentration.
-
E.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Richardson–Dushman equation Target entity description: The Richardson–Dushman equation is a fundamental formula in thermionic emission theory that relates the current density of electrons emitted from a heated metal surface to its temperature and material-specific constants.
-
A.
Butler–Volmer equation
The Butler–Volmer equation is a fundamental relation in electrochemistry that describes how the rate of an electrode reaction (current density) depends on the electrode potential and reaction kinetics.
-
B.
Nernst–Planck equation
The Nernst–Planck equation is a fundamental relation in electrochemistry that describes the flux of charged species under the combined influence of diffusion, electric fields, and, in extended forms, convection.
-
C.
Randles–Ševčík equation
The Randles–Ševčík equation is a fundamental electrochemical relationship that links peak current in cyclic voltammetry to the concentration and diffusion coefficient of a redox-active species.
-
D.
Fick's first law of diffusion
Fick's first law of diffusion is a fundamental physical law that relates the diffusive flux of particles to the spatial gradient of their concentration, describing how substances move from regions of high to low concentration.
-
E.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
equation
ⓘ
physical law ⓘ |
| alsoKnownAs |
Richardson equation
ⓘ
linked to:
Richardson–Dushman equation
Richardson–Dushman law ⓘ
linked to:
Richardson–Dushman equation
|
| appliesTo |
electron emission from heated cathodes
ⓘ
electron emission from heated metal surfaces ⓘ |
| assumes |
clean metal surface
ⓘ
no space-charge limitation ⓘ thermally equilibrated electron gas in metal ⓘ |
| canBeModifiedBy | Schottky correction for electric field ⓘ |
| category |
electron emission theory
ⓘ
statistical mechanics applications ⓘ |
| dependsOn |
Boltzmann constant
ⓘ
absolute temperature ⓘ material work function ⓘ |
| derivedFrom |
Fermi–Dirac statistics
ⓘ
classical emission over a potential barrier ⓘ |
| describes | thermionic emission current density ⓘ |
| domainOfValidity | high-temperature operation of metals ⓘ |
| field |
solid-state physics
ⓘ
surface physics ⓘ thermionic emission ⓘ vacuum electronics ⓘ |
| hasHistoricalSignificance | foundation of early vacuum tube theory ⓘ |
| hasMathematicalForm | J = A T^2 exp(-\phi / k_B T) ⓘ |
| hasUnitForJ | ampere per square meter ⓘ |
| ignores | Schottky effect unless modified ⓘ |
| includesParameter |
Richardson constant
ⓘ
metal work function ⓘ |
| namedAfter |
Irving Langmuir Dushman
ⓘ
linked to:
Irving Langmuir
Owen Willans Richardson ⓘ |
| predicts |
exponential dependence of emission on work function
ⓘ
quadratic dependence of emission on temperature ⓘ |
| relatedTo |
Child–Langmuir law
ⓘ
Fowler–Nordheim equation ⓘ |
| relates |
thermionic current density to absolute temperature
ⓘ
thermionic current density to work function ⓘ |
| temperatureDependence | strongly temperature dependent ⓘ |
| usedIn |
analysis of hot electron emitters
ⓘ
design of thermionic cathodes ⓘ electron gun design ⓘ vacuum tube engineering ⓘ |
| usesSymbol |
A for Richardson constant
ⓘ
J for current density ⓘ T for absolute temperature ⓘ \phi for work function ⓘ k_B for Boltzmann constant ⓘ |
| validFor | thermionic emission in vacuum ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Richardson–Dushman equation Description of subject: The Richardson–Dushman equation is a fundamental formula in thermionic emission theory that relates the current density of electrons emitted from a heated metal surface to its temperature and material-specific constants.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Richardson–Dushman equation
linked to: Richardson–Dushman equation