# Why is the 'work function' called a function?

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• spareine

#### spareine

The work function is the energy required to remove an electron from a solid to a point outside, it is a single value. Why is it called a function, instead of a single value? The word function suggests it is a function of some variable x.

.. is a function of ..

I agree the wikipedia article says the value of W depends on the surface of the material and surface condition, but in that statement it does not replace the general word dependence by the rather mathematical term function. It seems odd to me to call something in physics a function if nobody expresses it in a mathematical equation in the form W=f(x), with x a real valued number.

I googled for examples of how the 'work function' was used in old books, and it is almost always used as a single value for a particular material, not a mathematical function. Also, other languages like German and French do not use the obscure name 'work function', but 'exit work' (Austrittsarbeit, Travail de sortie), which is clearly a single value. I am wondering if the name 'work function' was introduced as a specific mathematical function f(x) by a someone, and then hijacked by others, who applied it to a single value.

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I see no problem.
The output value of a function is dependent on the input values.
A function can have more than one argument, but it returns only one value.
The arguments may be implied by the context.

W( Se ) = 5.9 eV.
On the subject of selenium, the work function, W() = 5.9 eV.

As Baluncore doesn't seem to have much sympathy for your complaint, I wanted to say I agree with you. It is a strange use of the word “function”. The energy for removing one electron from an atom or molecule is the ionization energy, not the ionization function. The energy to overcome a barrier potential is the activation energy not the activation function.

That being said, the reason you haven’t received many responses is because language is much harder to explain than physics. People work very hard trying to unravel the origins of quirks in the language and often arrive at only the barest conjectures. You would have to go through the earliest literature and find the first usages and see if it made more sense in context of what those coiners of the phrase were doing.

I did some further googling. The term work function seems to have been introduced by Richardson in 1914.(link) He proposed that the emission law should have the mathematical form ##J = A T^2 \mathrm{e}^{- W \over k T}##, where W is the 'work function'. A comment on Richardson's work says: "a common error in the application of equation to thermionic emission is the assumption that the true work function W is a constant."(link) W not being constant would explain why it is called a function, instead of a value.

As Baluncore doesn't seem to have much sympathy for your complaint,
I'm sorry if I appear to lack sympathy while presenting the counterargument.

If one member presents the argument that W() is not a function, then I will offer a reasoned defence. That it really is a function and hopefully, that it all makes sense. We inherited the work function term from posterity and I believe now, W is being misused. That does explain why the OP is unhappy with it's current use. In any debate, only a closed mind can be certain.

According to your "definition" all properties of materials are "functions" because their values, of course, depend on materials. :)
So density, resistivity, susceptibility, etc are all functions.
But of course, this is just of matter of definition so you can call them whatever you want as long as it's clear what you mean.

As for inheriting "from posterity", this will require a redefinition of posterity to make inheritance possible. Or some time machine. :)

I did some further googling. The term work function seems to have been introduced by Richardson in 1914.(link) He proposed that the emission law should have the mathematical form ##J = A T^2 \mathrm{e}^{- W \over k T}##, where W is the 'work function'. A comment on Richardson's work says: "a common error in the application of equation to thermionic emission is the assumption that the true work function W is a constant."(link) W not being constant would explain why it is called a function, instead of a value.

I find all of this as a mole hill being turned into a mountain. And I'm speaking on this as someone who spent almost my entire career as a physicist working on photoemission, field emission, and photocathodes.

First of all, there is such a thing as an effective work function, if you include such things as applied electric field and temperature. This quantity varies with respect to those two parameters. However, the "intrinsic" work function for a particular material is often a constant, which is why you can look up a table of values associated with various types of material (including different crystal structures).

So to the question on whether a "work function" stays constant or changes as a function of something, the answer is "yes". In the end, you can call it whatever you like, as long as you understand the physics.

Zz.

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