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

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.

• Well you could say as a result of it losing energy it becomes attracted to the nucleus. With enough energy it cannot be held back by the nucleus. Energy tends towards an irreversible state so probabilistically it will be favoured for the electron to lose its energy if this loss is irreversible. Commented Aug 12 at 18:48
• An electron has to emit a photon to fit into a shell. Emitting a photon should cost energy. Vice versa, a same photon is necessary to free this electron Commented Aug 14 at 5:19
• Fully generally, how can an object moving from upper to lower energy state NOT to lose energy? One cannot both eat the cake and have the cake. Commented Aug 14 at 7:21
• An alternative energy source or sink - depending on the energy change sign - are collisions with other molecular entities. Commented Aug 14 at 10:27

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.