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We all know (or maybe know) that to move, we need to spend energy. If you want to drive a car, you gotta spend gasoline.

We also know that energy can't be created (first law of thermodynamics, and perpetual motion).

Also, we know that in energy transformation, in real-world almost some part of it is converted into heat produced because of the friction between motion bodies. (for example, part of the gasoline of the car in burned to overcome car's friction with air, and thus would be converted into heat, and won't serve any movement at all).

Now a question has obsessed my mind. How electrons circulate around nucleus for ever? Where does electron get its energy from?

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    $\begingroup$ "If you want to drive a car, you gotta spend gasoline." Expresses a fact about the motion of cars, not a fundamental principle. Cars are subject to two dissipative forces (rolling friction and areodynamic drag), that would bleed their kinetic energy into thermal channels if the system were left to itself; and the engine burns gasoline to replenish the kinetic energy. Atomic electrons are not subject to dissipative forces. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Nov 15, 2016 at 17:19

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There is a basic misunderstanding of elementary classical physics in your question.

We all know (or maybe know) that to move, we need to spend energy

The first law of Newtonian mechanics says"

The velocity of a body remains constant unless the body is acted upon by an external force.

So there is no need to spend energy to keep on moving, unless external forces are acting on the body.

Electrons around a nucleus are not a classical problem, but conservation of energy holds also in the quantum states. The electron around the nucleus is in a quantized energy level and can change it only if an external interaction intervenes. It is quantization that guarantees this, since in the classical problem of a charge circulating around an opposite charge there would be continuous radiation which would have made the electron fall into the nucleus. Quantized energy states for the electrons are necessary for atoms to exist and were first proposed by Bohr.

Subsequently quantum mechanics became a full blown theory and needs years of study to assimilate it.

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  • $\begingroup$ So, does this mean that if hypothetically, we consume energy of electron little by little, its speed will slow down? $\endgroup$
    – Saeed Neamati
    Commented Dec 19, 2011 at 9:30
  • $\begingroup$ Also, does this mean that there is no energy-wasting (like friction) in the level of an electron? Does electron rotate in an absolute empty space? $\endgroup$
    – Saeed Neamati
    Commented Dec 19, 2011 at 9:33
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    $\begingroup$ We cannot change the energy of the electron, hypothetically or really, except by the allowed transitions from one energy level to another. That is what quantization means in the microcosm. There is no energy incoming or outgoing in the sysem "nucleus-electron" unless there is external interaction. That is the whole point of quantum mechanics. We only know what the electron is doing if we interact with it. Otherwise we only have probability distributions of where it may be if we interact with it. It is not rotating in the sense of classical physics, like the moon around the earth. $\endgroup$
    – anna v
    Commented Dec 19, 2011 at 10:19
  • $\begingroup$ continued: It is a distribution that describes the electrons probable path at the given energy level. One needs the mathematical tools to get an understanding of the situation, words are inadequate. $\endgroup$
    – anna v
    Commented Dec 19, 2011 at 10:22
  • $\begingroup$ @annav your explanations were fantastic. Thank you! $\endgroup$
    – Dexters
    Commented Jan 16, 2015 at 4:17
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With no friction the angular momentum of the electrons is preserved, just like planets orbits their stars with very very little (general-relativistic) losses.

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    $\begingroup$ To describe elementary particles, classical mechanics is not enough. One needs quantum mechanics, and a lot of study to get what is really going on in the microcosm of the atom. en.wikipedia.org/wiki/Atom – $\endgroup$
    – anna v
    Commented Jan 8, 2013 at 7:35
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    $\begingroup$ No. The difference to planets is that the electron has charge. If it was orbiting around the nucleus in the classical sense, it would be an accelerated charge and as such would radiate energy in the form of electromagnetic waves. Losing energy like that it would very quickly fall into the nucleus. In fact that is one of the reasons physicists came up with quantum mechanics. $\endgroup$
    – user1583209
    Commented Dec 9, 2016 at 0:54
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Before I give you my answer, here are a few other answers that will give you some insight:

Why do electrons occupy the space around nuclei, and not collide with them?

What prevents an atom's electrons from "collapsing" onto its protons?

Why don't electrons crash into the nuclei they "orbit"?

How does quantum mechanics explain stability of electron orbitals?

Where did Schrödinger solve the radiating problem of Bohr's model?

Quantum mechanics,and how the law $ΔxΔp≥ℏ/2$ explains the paradox regarding atoms

How does an electron move around in an orbital? Is it "wave-like" or random?

These answers all have some pieces of answers to your question, but they do not explicitly give you a very understandable simple answer.

I am going to try to explain this to you with my own words, but pieces of these ideas also might appear in the other answers.

I am NOT trying to copy or cite anything pretending it would be my own discovery (I had been warned in the past). All of these ideas have already been addressed on this site, but only pieces of it are together. But I believe that the specific answer to your question needs to be addressed fully in one simple understandable answer.

OK I will try to give you a very easy to understand way with my very simplistic words:

  1. Anna V is of course right that

"conservation of energy holds also in the quantum states. The electron around the nucleus is in a quantized energy level and can change it only if an external interaction intervenes."

I believe that you are asking whether what is it (what effect or what force) that holds the electron in this "quantized energy level".

  1. "the electron is constantly interacting with the nucleus via "virtual particles/photons" and the opposite electric charge of the nucleus creates a force that attracts the electron towards the nucleus."

  2. the position of the electron is described by it's wavefunction, and that gives you a 'cloud' around the nucleus with the probability distribution of where you will find the electron.

  3. This cloud will then 'limit' the electron's position into a somewhat spherical 3D location around the nucleus.

  4. Heisenberg's uncertainty principle states that

"we cannot know the position and the momentum of the electron better then to a certain limit at the same time."

  1. If the electron would 'move' to a lower orbit, so then it's 'cloud' would limit it into a smaller space around the nucleus. But because of 4. this is only possible if it's momentum will be known with lesser certainty, that is, it's momentum will have higher probabilities at bigger momenta, and that will increase the momentum of the electron at the same time as it's position 'shrinks'.

  2. So this increasing momentum will keep the electron away from the nucleus. It is (or it can be thought of as one very simplistic way to understand) the balance of the two effects that will create this "quantized energy level".

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As mentioned by anna v, Newton's first law implies a force is only needed if the object is accelerating. The amount of work done is the integral of the force along the direction of motion. In a circle the force is perpendicular to the direction of motion and so no energy is needed. However, as pointed out by anna v, electrodynamics will cause the electron to radiate in classical physics, but quantum physics stops that happening.

I think the main point of your question would be clearer if it was where do planets get their energy to keep going round the Sun. Even then they don't strictly circulate but rather travel in ellipses. The slight change in kinetic energy is compensated by an opposite change in the gravitational potential energy of the system.

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Solar system is wrong, Bohr model is wrong. Solar system doesn't dismantle and rebuild, it always maintains running. Atom gets dismantled and rebuilt at any time, all the time. Hydrogen atom ionization does so. According to solar model, electron will crash onto proton, just same as that Earth and Mars crash into sun if being rebuilt.

In terms of the electrons in quantum model, increased momentum doesn't necessarily mean it will appear in a far away position from nuclear. The direction of moving (quantum neglects this) is a key factor. If moving towards nuclear with big momentum, the electrons will crash onto nuclear, more quickly and more intensely.

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