On transition of electrons between energy levels / potentials

Question

In an electric circuit, electron flows from the negative terminal of a voltage source to the positive terminal, which in turn, gives us the the conventional direction of electric current. So, the first question that arise in my mind is: On moving to the positive terminal, does the electron gain stability?

If it does, then we know that an electron moves from a higher energy level to a lower energy level it releases a photon of a frequency dependent upon the energy gap, to gain stability. The second question is: Why does an electron move towards a region of lower energy but in a circuit, towards higher energy (positive potential is obviously a higher energy level)

Answer 1

An electron, like any other particle, might be at a higher energy level but will only move anywhere if there is a force acting on it, as @ThePhoton pointed out. As for the electron moving from a region of lower potential to higher potential, it is not true based on the definition of electric potential.

For electric fields, we define potential at a point as the work done per unit charge to move a positive point charge from infinity to that point. So from a region of lower potential to higher potential, moving a positive charge would require energy being input into the system, which causes the total energy of the system to increase, seen by the increase in potential of the positive charge. For a negative charge, however, the work done would be flipped (imagine moving a positive charge towards a positive charge, the work done would be positive because of repulsion while if you tried to move a negative charge towards a positive charge there would be attraction). So in moving from a region of lower potential to higher potential, an electron actually converts its potential energy to other forms, and that energy can be harnessed by the load of the circuit.

The emission of a photon when an electron de-excites from a higher energy level is because the electron lost energy to do so, and this energy manifests as a quantum of electromagnetic radiation, a photon. For the circuit however, this energy has already manifested as other forms of energy in the circuit (light if there is a bulb, sound if there is a speaker and even heat due to resistance in the wire). All these ensure that there is conservation of energy, which is why a photon is not emitted.

Answer 2

In a conductive solid like the wires in a circuit, the energy levels that are available for occupancy by electrons form a continuum that does not possess discrete energy levels as would be the case for a atom sitting all by itself.

Ordinarily, no photons are released during conduction through solid wires in a circuit; to release photos during electrical conduction requires the creation of a device in which the conduction band energy levels are discontinuous- as for example in a light-emitting diode.

The other way to release photons during conduction is if the conductor is hot enough to radiate as a black body- as for example in the tungsten filament of an old-school light bulb, or in a circuit element like a resistor that has failed during operation. The failed resistor then very briefly behaves as if it were a tungsten filament, making the resistor a one-shot device known as a noise-emitting resistor.