# What happens when work function = hf

What happens when the photon which hits a metal surface has energy equal to the work function of that surface? $$\phi = hf$$ I realise the emitted electron will have no kinetic energy after escape, but then what does it do? Hover above the surface? Or does it have momentum from escaping? I also don't understand what the work function is caused by - is it the electrostatic attraction between nuclei and the electrons?

• Electron is trapped in potential barrier when it "orbits" nucleus, and it needs some amount of energy $E_0$ (which is same as work function $\phi$) to overcome that barrier and escape it, when photon comes with frequency $f$ (energy of that photon is $E=hf$) and hits the electron, it gives energy to it, and if it's greater than $\phi$ electron can escape (overcome) the potential barrier. and using work function you can calculate minimum frequency light needs to have so when it hits electron, electron will overcome barrier ($\phi = hf_0$ where $f_0$ is minimum frequency, $f_0 = \frac{\phi}{h}$) – Giorgi Butbaia Jun 8 '14 at 8:31
• When work function is same as energy of a photon which hits electron, then electron won't be able to escape nucleus, it will just "go up" to the top of potential barrier and then it will "go down" back to the bottom of potential barrier. – Giorgi Butbaia Jun 8 '14 at 8:38

Electron needs some energy $E_0$ to escape (overcome) that barrier ($E_0$ is same as work function $\phi$), When photon with frequency $f$ (Energy of that photon is $E=hf$) comes and hits electron, it gives it energy ($E=hf$), and if it's greater than $\phi$ then electron can escape the nucleus (overcome the potential barrier):
and it will have some kinetic energy ($KE$) too. So in order to electron escape the nucleus photon which will hit it must have greater energy than $\phi$ (it's same as greater frequency than $f_0$ (where $f_0$ is minimum frequency for photon which will hit electron so it will escape the nucleus and you can calculate it using this equation $\phi = hf_0$ and $f_0=\frac{\phi}{h}$)). But when photon which will hit electron has same energy as minimum energy required for electron to escape the nucleus ($\phi = E$ or $f=f_0$) then electron will just "go up" to the top of potential barrier and then it will "go down" back to the bottom of the potential barrier: