# 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
Commented Oct 15, 2016 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? Commented Oct 15, 2016 at 12:32
• en.wikipedia.org/wiki/Work_function this provides some useful information.
– ODP
Commented Oct 15, 2016 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? Commented Oct 15, 2016 at 14:13

## 1 Answer

So the work function gives the minimum energy required from a photon to knock an electron out of the surface of a metal.

Say we know the velocity of the electron once ejected, or we know the kinetic energy of the electron.

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.

• Thank you for this well explained answer. Now, If I give you a piece of Nickel, how you'd do to find 5.04 eV ? Commented Oct 15, 2016 at 12:42
• Maybe you could set it up as part of an electric circuit and measure the resistance or potential difference across it (work done by one electron to get through 1eV), perhaps from there you could work out the energy of one delocalised electron by making estimates of the number of delocalised electrons from the atomic structure of nickel, and thus could find the minimum energy required to actually remove the electron from the metal (work function), something like that??
– ODP
Commented Oct 15, 2016 at 13:19