Why do electrons jump back after absorbing energy and moving to a higher energy level?
This is a very fundamental question and for really understanding the &quot;why&quot; some advanced physics is involved. I will describe the process rather superficially.
As you might know, the level energies of atoms and molecules can be calculated (in principle) using quantum mechanics. The simplest system is the hydrogen atom as it consists of a single proton and a single electron. Ignoring higher order effects (such as interactions of electron and nuclear spins and QED effects), the quantum mechanical calculation gives the same result as the Bohr model, that is, the level energies of hydrogen are given by the Balmer formula, which you probably know.
The calculation does not predict that the excited levels fall back to the ground state. An electron in an excited orbital will, according to this calculation, always stay in this orbital if nothing happens to the system.
Because we know that excited states decay, something must happen to the system to induce the decay. It turns out that in our calculation we have ignored the interaction of the atom with the photon field. Atoms can absorb light and emit light and we have completely neglected this. If you do take this coupling into account, you will find that excited states have a limited lifetime and that an excited electron will fall back to a lower level eventually.