Is there any way to find the distance between a nucleus and its electrons?

[durkadurka282]

Is there any way to find the distance between a nucleus and its electrons?

If possible, how can you figure out the distance between the nucleus and the electrons of an atom?

Specifically, a carbon atom?

 

[malawi_glenn]

There is no such things as "distances" in atoms, in the way you think. The classical picture of a nucleus having electrons around it as planets is wrong.

What you do is that ou solve the so called Shrodinger eq for the system, which gives you the probability to find an electron of a certain state at a certain radial distance from the nucleus. For example hydrogen, which you can solve with pen and paper:
http://panda.unm.edu/Courses/Finley/P262/Hydrogen/WaveFcns.html

So an electron can be INSIDE the nucleus with a non-zero probability, and also interact with a proton with a certain probability, then you get a thing called inverse beta decay:
http://en.wikipedia.org/wiki/Electron_capture

If you want to find out how to get radial wave functions for carbon, then wait til this thread is beeing moved to atomic physics forums, since this is nuclei and particle physics forum ;-)

 

[arivero]

What you do is that ou solve the so called Shrodinger eq for the system, which gives you the probability to find an electron of a certain state at a certain radial distance from the nucleus. For example hydrogen, which you can solve with pen and paper:
http://panda.unm.edu/Courses/Finley/P262/Hydrogen/WaveFcns.html

Note that the answer is given under the label "Figure 4" in this link. You want the maximum of $r^2 e^{-r/a_0}$. If you work it out, please tell in the thread.

Also you can calculate the probability for the electron of the Hidrogen to be inside the nucleus. And instead Carbon, you can try to discuss Berilium first. Actually I find surprising its ability to decay via EC.

 

[durkadurka282]

allright, thanks for the help!

 

[Zymandia]

May I also point out that every fermion has an anti-symmetric wave-function which by definition means that it has zero chance of being at the origin, ie. the nucleus.
The nucleus does have structure, albeit a lot less than the atom's dimensions. Thus the reaction cross-section between a nucleus and an associated fermion will be miniscule. If a nucleus could hold on to a boson (impossible AFAIK) then its wave-function would have to be non-zero at the origin.

 

[Enthalpy]

Somehow the deduction through anti-symmetric wave-functions is flawed, because 1S, 2S etc orbitals have the maximum probability density right at the centre.

P, D and all orbitals with a momentum have zero probability density a the centre. This is why electron capture always swallows S electrons (and almost always 1S electrons, whose orbital is denser at the centre). Observed in subsequent emission spectra, as electrons rearrange around the nucleus.

Nice pictures at http://www.webelements.com/ - useful site anyway, which sends to http://winter.group.shef.ac.uk/orbitron/
(Carbon's) 2P is there http://winter.group.shef.ac.uk/orbitron/AOs/2p/index.html
2S there http://winter.group.shef.ac.uk/orbitron/AOs/2s/index.html
and 1S there http://winter.group.shef.ac.uk/orbitron/AOs/1s/index.html

This may not be obvious from Orbiton's pictures, but a radius is a fuzzy notion for an orbital, and you'll have to decide some kind of subjective definition to get a figure.

 

[Zymandia]

Just because it is a spherical wave-function it doesn't mean that there is a maximum at zero. The s orbital is zero at the origin or it isn't a fermion.

 

[ZapperZ]

Just because it is a spherical wave-function it doesn't mean that there is a maximum at zero. The s orbital is zero at the origin or it isn't a fermion.

Plot the radial solution $R_{nl}$ function for l=0 from the Schrödinger equation for a hydrogenic atom, and then come back and tell us that it is zero at the origin.

Zz.

 

[malawi_glenn]

Just because it is a spherical wave-function it doesn't mean that there is a maximum at zero. The s orbital is zero at the origin or it isn't a fermion.

fermions have antisymmetric wave function w.r.t particle exchange, you should not mix this concept into wavefunctions of single fermionic wavefunctions.

Solve the Shrödinger eq för the hydrogen atom, and you'll get the wavefunctions and the radial parts are non zero at origin for S orbitals. (the angular part are alos nonzero since spherical harmonics is a constant for L = 0)

 

[Zymandia]

"w.r.t particle exchange,"
Yup, sorry, wrong end of the stick.