A large normal atom, but with a muon in its outer shell?

[bbbl67]

So let's say we have a large neutral atom, e.g. gold with 79 electrons around it. Let's say we replace its outermost electron with a muon. Muons orbit closer to the nucleus than electrons, much closer. Will the outermost muon be closer into the nucleus than even its innermost ground-state electron?

Secondly, when muons replace electrons in an atom, do the muon orbital shapes look similar to the original electron orbital shapes, except scaled much smaller and closer to the nucleus?

 

[Baluncore]

Muons orbit closer to the nucleus than electrons, much closer. Will the outermost muon be closer into the nucleus than even its innermost ground-state electron?

https://en.wikipedia.org/wiki/Muon#Negative_muon_atoms
"In multi-electron atoms, when only one of the electrons is replaced by a muon, the size of the atom continues to be determined by the other electrons, and the atomic size is nearly unchanged. However, in such cases the orbital of the muon continues to be smaller and far closer to the nucleus than the atomic orbitals of the electrons".

 

[Vanadium 50]

. Will the outermost muon be closer into the nucleus than even its innermost ground-state electron?

Yes.

Furthermore, that muon will quickly fall to the n=1 level. Since it's not an electron, there is no Pauli blocking.

 

[bbbl67]

Yes.

Furthermore, that muon will quickly fall to the n=1 level. Since it's not an electron, there is no Pauli blocking.

Will it push the ground electron to a higher energy level, and thus push all of the other electrons too?

 

[Vanadium 50]

Will it push the ground electron to a higher energy level

Why should it?

 

[bbbl67]

Why should it?

Because it's at a lower energy level than the ground electron? So shouldn't the ground electron get pushed out a bit?

 

[bbbl67]

Yes.

Furthermore, that muon will quickly fall to the n=1 level. Since it's not an electron, there is no Pauli blocking.

Isn't the Pauli exclusion due to the electronegativity of the electrons pushing against each other? So if a muon is as equally electronegative as an electron, shouldn't there be as much push out from the muon against the electrons?

 

[Vanadium 50]

No, Pauli blocking means that two electrons can't be in the same state, Once the n=1 level is full, for example, the electrons need to go in the n=2 level, and so on.

Muons aren't electrons so they can share an n=1 level with both electrons.

 

[bbbl67]

No, Pauli blocking means that two electrons can't be in the same state, Once the n=1 level is full, for example, the electrons need to go in the n=2 level, and so on.

Muons aren't electrons so they can share an n=1 level with both electrons.

So basically, I guess even if you think the muon is going into replace the outermost layer of electrons, in actual fact it's always going into become its very own first muon level, no matter what? It couldn't care less what the electrons are doing?

 

[PeroK]

So basically, I guess even if you think the muon is going into replace the outermost layer of electrons, in actual fact it's always going into become its very own first muon level, no matter what? It couldn't care less what the electrons are doing?

The Pauli exclusion principle applies to all fermions, but separately. It applies to electrons in orbitals and muons in orbitals separately. A muon in its ground state and an electron in its ground state are not two identical fermions in the same state.

The presence of a muon will, however, affect the value of the electron energy levels, as their is an electromagnetic interaction between muons and electrons.

 

[snorkack]

So basically, I guess even if you think the muon is going into replace the outermost layer of electrons, in actual fact it's always going into become its very own first muon level, no matter what? It couldn't care less what the electrons are doing?

It cares, especially if it is outermost. Because it is NOT required to be on its first muon level.
Consider the excited states of a hydrogen/-like atom. The one electron is not bound to be on first electron level - that is the ground state. In excited states the electron is on second, third, thirtieth et cetera electron level, and the first level is simply unoccupied.
Short of relativistic and reduced mass effects, a muon on first level is 207 times closer to nucleus than electron would be. Whereas in hydrogen-like atoms, the radius of the 2nd level is 4 times that of 1st level, the radius of 3rd level is 9 times that of first level, and the radius of 15th level is 225 times that of 1st level. Thus a muon on its 15th level is slightly further than an electron on its first.
Consider a He atom with 1 electron on its first level, and 1 muon on its 15th.
In the absence of any muon, the electron in He⁺ ion would orbit at 1/2 the distance it has in H, with 4 times the energy.
For the muon orbiting well outside He⁺ ion on muon´ s 15th orbital, the He+ ion looks much like H+. With one difference, though - the electron has some polarizability.
The muon on its distant orbit is 15 times slower than the electron in H would be. The electron in He+ is further 2 times faster in linear, 4 times faster in angular speed - total 60 times faster in angular speed than the muon. Over the timescale of muon orbital movement, the electron is orbiting in slowly varying field.

Now, the muo on its 15th orbital is unstable and can eventually fall to its first.
He-μ^- is 200 times smaller than He⁺, thus 400 times smaller than H. The muon has the same linear speed as electron in He⁺, 400 times the angular speed of electron in H. Thus an electron will simply barely feel the difference between He-μ^- and H⁺, while the muon will barely feel the presence of electron.

In between, you are going to have excited states where te electron and muon orbit on the same timescale, which cannot be simplified in either above described direction.

 

[hutchphd]

This is interesting about muonic atoms:

https://link.springer.com/article/10.1140/epjp/s13360-020-00777-y