Why electrons in orbitals have negative energy?

Question

The potential energy of electron is negative so;

kinetic $+$ potential $= \ \ -$energy ;

but the kinetic energy gets lower as an electron is farther from nucleus; needs less acceleration to orbit

I understand that you need energy to get the electron out of the orbit ;(the kinetic energy keeps it from going towards the proton)

But it was derived from :

Total Energy $=$ kinetic energy $+$ potential energy

How people understood that before the negative conventions? i.e ; how did they think about energy levels , intuitively?

Negative (potential) energy is like the particle is jailed. You have to do something (like pay bail) to make it free. — George Menoutis, Feb 28 '22 at 14:44
This may help. Potential energy curve for intermolecular distance — mmesser314, Feb 28 '22 at 15:42
Isn't the potential energy ,; a hypothetical case where an object would gain energy ; f*d = energy — user11531643, Feb 28 '22 at 16:37
How can we include this hypothetical energy , for me it's just that higher electrons have lower kinetic energy,but higher potential energy , — user11531643, Feb 28 '22 at 16:39

score 1 · Answer 1 · answered Feb 28 '22 at 16:19

The potential energy of electron is negative

The potential energy is only defined to an arbitrary additive constant. That means we can add some constant $C$ to all the energy levels in a system, and the physics of how the system behaves doesn't change.

Normally we do this by defining a reference potential energy.

For example, if we define the energy of a free, but stationary, electron as zero, then the energy of bound electrons will be negative. This is a very common convention, and its the one you were probably thinking of as you wrote your question.

But we could just as well define the energy of the ground state bound electron to be zero. Then all the other states would have positive potential energy. This wouldn't change the physics of the system. But it would get inconvenient if you want to compare this first atom with an atom of some other element, for example.

score 1 · Accepted Answer · answered Mar 01 '22 at 17:56

When an electron returns to a smaller distance from the nucleus, it emits electromagnetic radiation. It loses energy, so its energy content is lower than in the free state. To gain that, (EM) energy must be absorbed by the electron. So the electron in the free state has a higher energy content than in the bound state.

An electron in the ground state has a negative energy difference to an electron in a higher state or in the unbound state. Kinetic energy plays no role whatsoever. An electron is not a satellite orbiting around the nucleus.

but from a classical point of view how ?like i understand that it's got lower energy etc... But classically , — user11531643, Mar 04 '22 at 16:23

Why electrons in orbitals have negative energy?

2 Answers2