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I can understand that the role of electrons and protons are not interchangeable for elements heavier than Hydrogen, because there is no nuclear force to keep the charged electrons together in a nucleus, but at least for the Hydrogen atom, it should be possible to exchange the proton and the electron? Is there a reason this element doesn't exist?

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    $\begingroup$ Do you also wonder whether there are solar systems with the planets on the inside and the star on the outside? $\endgroup$
    – G. Smith
    Aug 30 '20 at 21:15
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the proton is 1800 times more massive than the electron. when the two of them are in a bound state (attracting each other via the electrostatic force) the proton's inertia makes it sit almost still and it lets the lighter electron do all the orbiting.

Please note that in actuality, the electron and the proton are both orbiting the center of mass that they share, but because the proton is so much heavier, that center of mass is so close to the proton's own center of mass that the proton's orbital radius around it is very small.

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    $\begingroup$ There isn’t a “reverse” state with higher energy. $\endgroup$
    – G. Smith
    Aug 30 '20 at 21:17
  • $\begingroup$ @ G. Smith, what I meant was that if you could somehow fix the electron in position and force the proton to orbit it, the energy of that state would be higher. I will edit for clarity. $\endgroup$ Aug 30 '20 at 21:28
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And how would that element be different from "normal" Hydrogen?

The Coulomb interaction would look the same as the separation $r$ is unchanged by the particle exchange.

Plus, if I were an observer in the rest frame of the electron, I would see the proton orbiting me.

You need another interaction to "break" the "symmetry", i.e. a neutron (strong force) or another atom (molecular stuff). Otherwise these two "states" are indistinguishable.

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Why isn't there an atom with an electron at the center and a proton on the outside?

Because a proton has 1836 times more mass than an electron does. Thinking classically, this means its orbit around the center of mass is about 1836 times smaller than the electron’s. In other words, it basically stays fixed.

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  • $\begingroup$ of course, but what about a hydrogen "molecule" where a covalent bond is formed between the protons? why is that not possible? $\endgroup$
    – hyportnex
    Aug 30 '20 at 21:18
  • $\begingroup$ @hyportnex I’m not sure what you are asking. $H_2$ exists. $\endgroup$
    – G. Smith
    Aug 30 '20 at 21:19
  • $\begingroup$ @hyportnex because the binding energy of the state where electrons are shared is much lower and therefore accessible sooner. $\endgroup$
    – SuperCiocia
    Aug 30 '20 at 21:19
  • $\begingroup$ $H_2$ exists but I thought there the bond is due to the exchange forces between the electrons. $\endgroup$
    – hyportnex
    Aug 30 '20 at 21:20
  • $\begingroup$ What do hydrogen molecules have to do with the OP’s question? $\endgroup$
    – G. Smith
    Aug 30 '20 at 21:24
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When we solve the basic (i.e., non relativistic quantum mechanics) equation for the hydrogen atom, we have 2 coordinate vectors:

$$ \vec R_p,$$ $$ \vec r_e, $$

the positions of the proton and electron, respectively. Since:

$$ \vec R_{CM} =\frac{M_p\vec R_p + m_e\vec r_e}{M_p + m_e}$$

is just the center of mass, we ignore it.

We then solve for the remaining degrees-of-freedom with:

$$ \vec r = \vec r_e - \vec R_p $$

with a reduced mass:

$$ \mu = \frac{M_pm_e}{M_p+m_e} $$

If you want, you could solve for:

$$ \vec r' = \vec R_p - \vec r_e $$

and get the same results, but you would call it the proton orbiting the electron.

Once you go to reduced mass, there really is no distinction.

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There is (after some forcing of the definition). It is called anti-matter.

Otherwise, the picture of a nucleus at the center and an electron orbiting is rather simplified.

Both the electron and the nucleus are quantum particles and in bound state have a "probability cloud" with no exact boundaries. The "clouds" of the nucleus and the electrons overlap and share a common center. The probability density of the nucleus is more concentrated in the center just because the nucleus is heavier.

You can make an atom out of a proton and a tau-lepton (it is just an electron, but heavier and unstable). Tau is heavier than a proton, so you'll get an atom where at the center there is more tau than a proton.

Well, such an atom will be rather small (thousand times smaller than the hydrogen) and quite unstable. But it still will be an exotic form of hydrogen with a lot of similarities to hydrogen.

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