Photoelectric Effect and Temperature.

[Jules18]

If a substance is warmer, is it easier for it to emit photoelectrons?

I was thinking that maybe light of lower frequency would be required.

 

[Gan_HOPE326]

If a substance is warmer, is it easier for it to emit photoelectrons?

I was thinking that maybe light of lower frequency would be required.

Hmm... I'm just guessing based on my knowledge, but I'd say the answer is YES.

We're talking about metals, right? So, at any temperature above absolute zero, following Fermi's distribution there will be a few electrons with greater energy than Fermi level - some of them could even have enough energy to escape the crystal. That's what happens when you really heat up the metal: thermoionic emission, without help of light, just based on thermal energy. So, it's a statistical matter, I think. At high temperatures, there will be electrons which still lack only a few tenths eV to escape the metal, and even a low-energy photon will be enough for them to leave the surface. Actually, I think at temperatures aboze absolute zero the photoelectric effect can't really begin just above a certain frequency - maybe it'll grow very fast, but it won't just pop out of nothingness. For semiconductors it's a different story, of course.

 

[Vanadium 50]

So, at any temperature above absolute zero, following Fermi's distribution there will be a few electrons with greater energy than Fermi level - some of them could even have enough energy to escape the crystal.

That's called thermionic emission; it's a separate process entirely.

 

[Dadface]

That's called thermionic emission; it's a separate process entirely.

But since the work function depends on the nature/structure of the substance one might expect that it changes with temperature.

 

[ZapperZ]

But since the work function depends on the nature/structure of the substance one might expect that it changes with temperature.

It does, but I don't think Vanadium is disputing that.

In a typical metal, the higher the temperature, the lower the effective work function since, as has been mentioned, there's a larger Fermi broadening of the electron energy distribution around the Fermi energy.

Zz.

 

[Gan_HOPE326]

I'd say the thing works more or less like this. Let's call E_F the Fermi level, and E_G the energy an electron must possesses to escape the metal. Then:

1) At 0 K, the electrons possesses at most E_F energy. Then, to stimulate photoelectric emission, photons with E_G - E_F will be needed. With the usual formula, we can calculate the frequency of such photons;

2) At T > 0 K, there will be a certain amount (even little) of electrons with energy greater than E_F. Then even photons with less energy than E_G - E_F will be able to extract them: although, they are few, so this current will have low intensity;

3) At T >> 0 K, there will even be electrons possessing an energy of E_G. These electrons will be able to escape themselves the metal, without relying on photons. And that would be the thermionic emission.

I found here and there on the net some articles about experiments demonstrating how, with the same intensity of yellow light, magnesium's photoelectric emission increases with temperature, while this effect was less noticeable with light of higher frequency. I'd say this must be due to the fact that increasing the temperature, the number of electrons possessing an energy, say, E_F2, greater than E_F, so that E_G - E_F2 is equal to the energy of a yellow light photon, increases.