kelvin490 said:
Electrons absorbed from a photon can only be in discrete amount and match the energy difference between different energy level. However, in photoelectric effect a photon can ionize an electron and give K.E. to the electrons. As K.E. can be any arbitrary amount instead of discrete, does it mean that any photon with energy greater than the ionizing energy can be absorbed by an electron in any arbitrary amount (all the excess energy becomes K.E. of electron)?
A few misunderstandings here:
1. The "discrete" energy levels of a system (not JUST for the electrons) is due to the nature of the system itself. In an atom, this is the energy level
OF THE ATOM, which is manifested by the state the occupation of the electrons within that atom. So it has to do with, mathematically, the "boundary conditions" of the system.
2. In a metal, this discreteness is practically gone. That is why, instead of discrete energy levels, we talk about energy BANDS in solids such as metals, semiconductors, insulators, etc. There are no more discrete energy levels.
3. The vacuum state is one such continuous level. So in a photoelectric effect (as in metals) and in photoionization (which is the atomic/molecular equivalent of the photoelectric effect), if the energy source (such as photons) has energy greater than some threshold, then yes, there will be a continuous spectrum of kinetic energy of the emitted electrons. This is what we study in photoemission spectroscopy, the kinetic energy and momentum spectrum of the photoemitted electrons.
Zz.