Why does a electron lose energy when it enters an energy level compared to the free state?

Question

I have read that when the electron is not under the influence of a nucleus, i.e. at $n = \infty$ , its energy is zero which makes sense and as comes or presents (sorry I don't know the correct word) in an energy level it loses energy and the energy is negative.

As it loses even more energy it goes to lower energy levels and since the energy is already negative the magnitude of energy increases which ultimately means its energy is reduced in comparison to the higher level which also makes perfect sense.

I understand this by referring to the atom as the solar system, if the energy of a planet is higher than the orbit requires its orbit increases or sometimes it leaves the planetary system and vice versa if its energy is less than required its orbit shrinks or it falls in the star. So if an electron wants to go in the lower shell it will lose its energy.

Why does the electron lose energy in comparison to when it is at $n=\infty$ ? Is it related to the attraction force of the nucleus? I understand this phenomenon but I want to know the "why" behind the loss of energy of electrons.

Answer 1

Think in reverse and it is more obvious

The electromagnetic force is strong. oppositely charged objects attract each other strongly (as many illustrations with simple objects show: like rubbing a rubber balloon on a wool cloth).

Consider an electron in a low energy level in the atom. It is held tightly by the electromagnetic force between it and the oppositely charged nucleus. To get the electron out of the atom we know that we have to add energy to it to overcome that attraction. Since we have to add energy to move it to a different, higher, level or to release the electron completely from the clutches of the nucleus, we define the energy it has as negative.

It is arbitrary but very convenient to define the free electron as having zero energy, but it is intuitively obvious that we ned to add energy to make a bound electron free, hence the way this works.

Answer 2

Think in terms of probabilities. Electrons don't lose energy because the nucleus exerts a force on it but because after losing some energy due to random fluctuations it's more stable closer to it. This random fluctuation becomes irreversible if something (the nucleus in this case) is exerting some sort of force on something else. Energy loss is only reversible if no work is being done which is an ideal situation (doesn't happen in the real world) just as much as $n=\infty$ never occurs but is often a good enough approximation.