No they cannot.
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The (theoretical) limits are about from 10um to 250nm
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No, as they are impossible
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Leds emit light via an optical recombination in a direct gap semiconductor.
The gap energy is normally in the 0.5-3 eV range, for resons that would be very hard to explain (in short, the "energy gap" happens if you have an odd number of charge carriers in the brillouin zone of the material lattice. The pauli principle inhibits electrical conductivity, because all occupieable spots are already taken.
Thus there is a filled valence band, and the next higher energies (in the n+1 brillouin zone) will form the conductance band, with a small energy gap inbetween.
Small simply because this only affect the "outermost" electrons, as the inner ones already form compete multiplets and are inert. So the biggest possible energy _at all_ would be about 20ev for helium.
But the other requirement is that it actually has to be solid _and_ be able to be doted (as, like explained before, there is no conductance in the valence band, so the electricity has to find some way to actually _get_ in the recombination zone).
The highest energy gap material thats actually dotable should be diamond, at the moment, with energies in the 4-5ev range. Of couse diamond is, IIRC, an non-direct gap semiconductor, so it wouldne be possible to build lights ...
The whole thing is a very complicated matter (if you want to know it exactly, take a look at ashcrofts solid state phyics textbook), or it wouldnt have the taken the brightest (pun intended) people in the field decades to get good blue/near UV leds
