MadSci Network: Physics

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

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

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 Bohr radius.

I hope I could help you
greetings, Michael.

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