# What gives the electron the energy to continuosly orbit

What gives the electron the apparently necessary energy to keep orbiting the nucleus for the vast time periods that this has occured for?

The electron is a moving charge, so is there a potential difference making the current flow?
Is this something to do with the field of the proton?

I hope this is question does is not to stupid to ask?

This was one of the main questions that physists in the early 20'th century struggled with. Eventually they decided that everything about classical physics was wrong at that scale and developed a completely new theory of nature that we now call quantum mechanics.

In a nutshell, The electron can only absorb or radiate energy in discrete units. If it doesn't have enough energy to radiate 1 whole unit then it must keep the energy. If it does have enough energy to radiate a unit then it is not in it's lowest possible orbital. At some point it will emit a photon and drop down to a lower orbital.

Also, it is not entirely accurate to call an electron in an orbital a "moving charge" since it's momentum and position are not well defined.

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Thanks for the speedy response mrspeedybob,
so I need to go and ask this in the quantum mechanical section.
"strictly, the calculation of atomic orbits and currents requires QM but for the sake of simplicity lets us do the calculation with classical mechanics."
It went on to define the average current along the orbit as ev/2∏r

This then got me thinking about what what causes this current.

So I am going to have to wait untill I can follow the mathematics of wavefunction for an answer it seems.

Nugatory
Mentor
What gives the electron the apparently necessary energy to keep orbiting the nucleus for the vast time periods that this has occurred for?

The electron is a moving charge, so is there a potential difference making the current flow?
Is this something to do with the field of the proton?

The earth can orbit forever about the sun without any energy input, but of course the earth doesn't carry any electrical charge. Classical physics predicts that an electron orbiting a nucleus, being a charged particle, would continuously radiate away its energy and rapidly spiral into the nucleus; as mrspeedybob says above, this was one of the great unsolved problems of late 19th-century physics.

Quantum mechanics solved the problem by showing that an electron could only shed energy in discrete chunks, not continuously. As the theory of quantum mechanics evolved, it became increasingly clear that the electron near a nucleus doesn't behave anything like a point charge in circular or elliptical orbit around a nucleus; it's more like a diffuse cloud - try doing a google image search for "electron orbitals".

Hi Nugatory I like the gravitational analogy, so the electron is interacting with the field of the proton, and cannot cascade in because only certain orbits are possible, I have got it in my head that it has something to do with standing waves and the lowest energy level is like the first harmonic on a guitar string. Is the difference with the Earth and hence the gravitational fieldthat its orbit is losing energy and it will eventually get closer and closer to the Sun?

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Nugatory
Mentor
Hi Nugatory I like the gravitational analogy, so the electron is interacting with the field of the proton, and cannot cascade in because only certain orbits are possible, I have got it in my head that it has something to do with standing waves and the lowest energy level is like the first harmonic on a guitar string. Is the difference with the Earth and hence the gravitational fieldthat its orbit is losing energy and it will eventually get closer and closer to the Sun?

The standing wave analogy is pretty good.

The electrical force between the positive-charged nucleus and the negative-charged electron goes as $\frac{1}{r^2}$ just as does the gravitational force, so a stable circular orbit is a solution for both forces.

The only difference in classical theory between a charged particle in an electrical field and a massive body in a gravitational field is that an accelerating (note: that's "accelerating", not "moving", and an object in a circular orbit is continuously accelerating even though its speed is constant) charged particle will lose energy to electromagnetic radiation; there's no equivalent mechanism for mass. Thus, the earth is not losing energy as it orbits the sun and theoretically could keep on going round and round forever - in classical mechanics a charged particle cannot.

Phew that word forever is comforting.
I also seem to have it in my head that eventually the Earth will present one side to Sun just as the Moon does to us. Lets hope were on the darkside and can have a long sleep.
Does the physics of gravitational waves carry away energy from the system?
As usual one quesion leads to many

Thanks again

Nugatory
Mentor
I also seem to have it in my head that eventually the Earth will present one side to Sun just as the Moon does to us.
yep - google "tidal locking" for an explanation of how this happens.

Do gravitational waves carry away energy from the system?

They do, so my previous answer was a bit of an oversimplification. But in practice an earth-sized mass taking a year to move from one side of the sun to the other and back again generates negligible gravitational radiation so we don't include it in our calculations.