About energy quantization and conservation of energy It is my understanding that in quantum mechanics energy comes in discrete pieces - quanta, and in order for these quanta to be absorbed by some process it must match the energy required for it.
Now imagine, for example, that I hit an isolated table and transmitted to it 10 units of energy. That energy will make the table giggle by activating some phonons. So what happened to those 10 units of energy? Imagine that 5.5 units of energy were used to activate phonons of frequency A, and that 4 untis of energy were used to activate phonons of frequency B. Now imagine that that remaining 0.5 units of energy are so small that they cannot be used to activate any other process, what happens to it? 
Is that energy lost?
Is it transformed in to a photon? If yes, by which mechanism?
Or is it something wrong with my reasoning?
 A: If you hit a table, part of the work you do goes into total momentum of the table (the table as a whole starts moving) and the other part goes into phonons. I guess, the split is done such that only allowed phonon modes are excited.
A: It's not really true that energy always comes in discrete pieces in quantum mechanics. There are many situations in quantum mechanics where energy can take on any continuous value. For example, the momentum of a free particle can have any energy whether it be 5.5 units or 3.58918 units, regardless of what units you are measuring it in.
In the case of phonons (sound vibrations within a rigid object) energy quantization does happen.  So there are only certain discrete amounts of energy that can be transferred into phonon modes.  So for example... it would be impossible for 5.5 units of energy to activate phonons of frequency A if the each phonon is 1 unit of energy.  You could activate 5 units or 6 units, but not 5.5.
There are situations where the energy being supplied is too small to activate any mode.  For example, in the photo-electric effect if you supply 0.5 units of energy and 1 unit is required to stimulate 1 photon, then nothing will happen--no energy is transferred because that's not enough to activate a single mode.  In that case, the 0.5 units of energy would have to stay in whatever original form it was in.
