Why can't an electron emit more than 1 photon when moving down from an excited state Why is the following statement false?
When an electron loses energy in making a transition from one state to another, energy is conserved by several photons being emitted.
I don't see which conservation law this violates.
 A: This process is perfectly possible; it's just very unlikely, because of the details of how atoms couple to the electromagnetic field. 
If you want a concrete example, the simplest case is the 2s-1s transition in hydrogen, for which single-photon mechanisms are forbidden by symmetry, but which will still decay via a two-photon route. The decay rate is about nine orders of magnitude slower than normal radiative decay in hydrogen, but it's nevertheless nonzero. 
A: The electron isnt traveling from one energy state to another, he literally cant be between energy levels , which means the diffrence of energy between those two levels have to be somewhere , when you calculate the diffrence you basiclly see its an energy of one photon with a specific frequency , and only this frequency match the diffrence. This is aprroved by the spectrum emmiting from this atom
If an electron is falling few levels ,one by one , its gonna emmit a photon for every level - which the photon frequency is gonna match the diffrence of energy between each level
A: It's because all possible states which quantum systems (for example atom with electron/s)  could be are allways discrete sets. (It's one of quantum mechanics principles) 
This means - if you want change energy state of something, you can make it only in "steps".
Knowing this, emission of more than 2 photons means - system has to make two "steps" - emission more than one photon from atom indicates exisiting of 2 states. 
2s-1s transition in hydrogen isn't emission of 2 photons from one state, it's just states beeing extremly close to each other and one of them (first) has very little time of life.
Summarizing - it's isnt violating any conservation law, but quantum mechanics principles - which means that maybe it is possible, but you can't use Schrodinger equation (and generally any quantum equation/theory) to observe or predict that phenomena. 
