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Name: Jeff
Status: educator
Grade: 9-12
Location: TX
Country: N/A
Date: February 2007

Question:
When measuring the orbit of a electron is the measurement taken from the nucleus to the electron or is it the circumference of the orbital? For instance: the orbit of electrons in helium is about 0.03 nanometers. Is that measurement the circumference of the orbit or the distance from the nucleus to the orbit?



Replies:
That is the average distance between the electrons and the nucleus. It is not a set, single position like a planetary orbit; instead it is a distribution.

Richard Barrans
Department of Physics and Astronomy
University of Wyoming


Jeff,

First of all, let us make a clear distinction between "orbit" and "orbital". Orbit (as in the Bohr planetary model of the atom) relates (in a false imagery) the energy of an electron to a distance from the nucleus. The Schrodinger Model of the atom corrected that idea by stating that electrons have a set energy that may be described by a set of variables which are only marginally related to distance. In the Schrodinger model, there is a "most probable" distance, often called a "shell" and we, unfortunately, imagine this as a sphere around the nucleus. But truly, these are just ways for us to visualize the mathematical description of an electron's energy and are NOT truly physical manifestations of the electron's properties.

So what do scientists mean when they say a distance of so-and-so nanometers? There are two relevant issues: (1) we can measure the light coming out of atoms when electrons decay from high orbital states to lower orbital states, and (2) we can measure the distances of nuclei in bonded atoms (by measuring the bond energy) and relate this to the overall dimensions of each of the bonded atoms. Note that in both these cases, there is no mention of an actual measurement of the distance of the electron to the nucleus, this distance is inferred. In case 1, we only know the energy difference between two orbital states - not the energy of each of the individual orbitals. In case 2, we measure the *average* distance of two nuclei, and infer on average the dimension of a single atom. From this, is built the *erroneous* idea that electrons are at a particular distance from the nucleus.

What the Schrodinger model emphasizes is that an electron has a particular quantum of energy that is described by 4 different variables - none of which state that the electron is at a particular distance from the nucleus. The principal quantum number, n, (one of the 4 variables) alludes to distance because it describes the idea that as n increase, the most probable distance of the electron to the nucleus also increases. However, this is not to be taken to mean that the electron is at this particular distance (or shell, or circumference). So what we really are saying is that electrons have energy and this energy establishes distances of nuclei in bonded atoms and most probable distances in individual atoms.

Greg (Roberto Gregorius)



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