Are any electrons ejected below the threshold frequency?

[lawlieto]

I've been reading about the photoelectric effect, and something got me thinking. If the frequency of light shone onto the metal is below the threshold frequency, no electrons are liberated from the surface of the metal, since electrons absorb quanta of energy, so if that light is shone for a long time, energy wouldn't be absorbed on a continuous basis etc.. but, what if 2 or 3 consecutive photons hit the same electron? Wouldn't the energies absorbed from those 2-3 photons accumulate so that an electron is liberated?

Or is there a very little probability for that to happen? (but then we could increase the intensity of light ie more photons emitted so that gives a higher probability)
Or does the energy for liberation has to be absorbed all at once? If that is the case, what happens to the photons? Are photons still absorbed if they're not energetic enough? (In that case I don't see why the energy from consecutive photons accumulated wouldn't liberate an electron)

 

[NFuller]

Or is there a very little probability for that to happen?

I think so. Here's a bit from a wiki article which seems related to your question. https://en.wikipedia.org/wiki/Photoionization#Multi-photon_ionization

 

[DrChinese]

...what if 2 or 3 consecutive photons hit the same electron? Wouldn't the energies absorbed from those 2-3 photons accumulate so that an electron is liberated?... Or is there a very little probability for that to happen? (but then we could increase the intensity of light ie more photons emitted so that gives a higher probability)

There is essentially no chance for that to happen.

There is a theoretical process called spontaneous parametric up conversion, which merges 2 photons together into a more energetic one. But the requirements for that could not be met in the situation you describe for a variety of reasons. (For example, there needs to be phase matching.)

 

[NFuller]

There is essentially no chance for that to happen.

It is done quite often using pulsed CO2 lasers.
http://www.springer.com/cda/content/document/cda_downloaddocument/9781441994905-c1.pdf?SGWID=0-0-45-1163443-p174103292
http://iopscience.iop.org/article/10.1088/1742-6596/194/3/032031/pdf
http://aip.scitation.org/doi/10.1063/1.439604

 

[DrChinese]

It is done quite often using pulsed CO2 lasers.
http://www.springer.com/cda/content/document/cda_downloaddocument/9781441994905-c1.pdf?SGWID=0-0-45-1163443-p174103292
http://iopscience.iop.org/article/10.1088/1742-6596/194/3/032031/pdf
http://aip.scitation.org/doi/10.1063/1.439604

Nice! I didn't see your earlier post until I did mine. The below quote is from the first reference, not really that different from the OP:

As our first example, Fig. 1 shows the response of the Ne atom to pulses with central photon energies of 11.6 and 7:3 eV, respectively. In these cases, at least two or three photons, respectively, need to be absorbed in order to ionize the system."