### Re: Why are electron orbitals so huge rel. to the size of a nucleus?

Date: Wed Nov 7 14:58:16 2001
Posted By: Michael Wohlgenannt, Grad student, Department of Theoretical Physics , University of Munich, Germany
Area of science: Physics
ID: 1003973239.Ph
Message:
```
Hi Matt,
thank you for your question. You are asking for the "size" of bound states
considering various interactions. You are right, the size of bound states
such as protons (bound state of quarks), nucleus (bound state of protons
and neutrons) and atoms (bound state of nuclei and electrons) depends above
all on the strength of the force involved. The strong nuclear force binds
the quarks, they are bound in protons and neutrons (and all other hadrons).
This force is the strongest of them all. Some residual force of the strong
force between the quarks keeps protons and neutrons together. This force is
much weaker than the strong force and can be compared to the van der Waals
force concerning electromagnetic interaction. But it is still rather
strong. The electromagnetic interaction is responsible for the electron
orbitals. Compared to the strong force between quarks and hadrons this
force is very weak, therefore the orbits are comparatively large.

Let us stick to the electromagnetic interaction for a second. The socalled
Bohr radius is a measure for the size of electron orbits. In fact, it is
the radius of the ground state in a hydrogen atom. It is given by the
formula
h^2
r = -----------------,
4(pi)^2 m e^2

where h is Planck's constant, m is the mass of the electron, e is the
electron charge. We see (in case of electromagnetism) that increasing the
mass of the electron m decreases the size of the orbit (Bohr radius) r.
Further is the magnitude of the electron charge e a measure for the
strength of the electromagnetic interaction. So increasing the strength of
the electromagnetic force (i.e., increasing the charge) again decreases the

greetings, Michael.

```

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