# The Work Function

The work function is the minimum amount of energy required for an electron to be emitted from the surface of a metal plate.

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Up Learn – A Level physics (aqa)

## Quantum

Einstein’s transformative theory was that light consists of packets of energy called photons.

We call Einstein’s photon theory of light… (click 1 time)… the particle theory of light.

And to begin with… we can use the particle theory of light to explain why certain types of light emit photoelectrons… but others don’t!

Now, we’ve seen before that electrons at the surface of a metal are weakly attracted to the metal.

So, they can be removed.

But, these don’t just pop out of the surface of their own accord… it does take some energy.

One way to visualise that… is like this

Where, if you had a ball… stuck in a ditch…

Then, the ball would need to get some energy in order to get out (click 1 time, dead trigger)

So if we gave the ball this amount of energy, then it wouldn’t leave the ditch

Whereas, if we gave the ball this amount of energy, then it would leave the ditch

Likewise, we can represent electrons bound to the metal surface like this

Where electrons need to gain enough energy… to escape from this ditch.

Now, electrons need to absorb a minimum amount of energy to escape…

For instance, here… this photon … doesn’t give the electron enough energy to escape…

But, here… this new photon..

does give the electron enough energy to escape…

And, here… again, the photon does give the electron enough energy to escape

An electron requires a minimum amount of energy to be emitted from a metal plate.

We call this minimum amount of energy the work function.

And so, which of these electrons gained enough energy to overcome the work function of the metal?

These electrons gained enough energy to overcome the work function of the metal…

Whereas, this electron did not.

So, electrons absorb packets of energy known as photons… if a photon gives an electron enough energy… then it’ll overcome the work function of the metal that it’s bound to.

Next, when we talk about the work function… we use this symbol.

And, that’s just the Greek letter phi…

Finally, we’ve previously seen that each electron only interacts with…

Each electron only interacts with one photon at a time.

For example, if this photon doesn’t give the electron enough energy to escape…

Then another photon with the same energy…

Or another one thousand photons with the same energy…

Won’t help the electron escape from the metal plate.

Instead, the fate of the electron is entirely dependent on the energy of a single photon.

To sum up…

The work function is the minimum amount of energy required for an electron to be emitted from the surface of a metal plate.

Next, photoelectrons are emitted only when they interact with…

Photoelectrons are only emitted when they interact with one photon that can give it enough energy to overcome the work function.