# How to find the work function of a metal without knowing the threshold-frequency?

As the title says it, I want to know how people find the work function of a metal without knowing the threshold frequency.

Yes I've already searched on Google but I didn't find anything really relevant. I just found how to calculate Work function with threshold frequency.

• Do you know the kinetic energy of an ejected electron? – ODP Oct 15 '16 at 12:30
• Isn't it : KE = hf - W ( where W is work function ). But let's say you just have the metal in your hand and you have to find it's work function ; how you'll do that? – Lulzsec Oct 15 '16 at 12:32
• en.wikipedia.org/wiki/Work_function this provides some useful information. – ODP Oct 15 '16 at 12:38
• Do you think that the Wikipedia article is not relevant? It describes a few methods for measuring work function. Is that not what you want? – garyp Oct 15 '16 at 14:13

Say we also know the frequency of the photons that we aimed at the metal. Then the energy of the photon that ejected the electron is $hf$, where $h$ is Planck's constant and $f$ is the frequency of the incident photon.
Well then it follows that the difference between the energy of the photon and the kinetic energy of the electron (i.e. the amount of energy that the photon transferred to the electron) will of course be the work function. In mathematical terms, $$\phi=hf-K,$$ where $\phi$ is the work function and $K$ is the kinetic energy of the electron. Thus the work function has been calculated without having to know the threshold frequency.