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Angular node

by photon79
Tags: angular, node
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photon79
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Jan18-06, 06:07 PM
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why the angular momentum of electron in the ground state is zero?? (an s-electron) And why it has angular momentum when there is a node?? And pls give some info on what is a Radial node and what is an angular node and their contributions to the energy of electrons??
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Tom Mattson
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Jan20-06, 11:24 AM
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Quote Quote by photon79
why the angular momentum of electron in the ground state is zero?? (an s-electron)
That is what comes out of the Schrodinger equation. It is the solution with the lowest value of [itex]n[/itex], and nature happens to take advantage of that lowest energy solution.

And why it has angular momentum when there is a node??
I am not quite sure of what you are looking for here. Are you asking why a function that has at least one zero can be an eigenstate of the angular momentum operator?

And pls give some info on what is a Radial node and what is an angular node and their contributions to the energy of electrons??
A radial node occurs when the radial part of the wavefunction vanishes, and an angular node occurs when the angular part vanishes. As far as the connection of nodes to energy, how about looking at some specific wavefunctions? Note the number of each type of node, and note the energy.
Gokul43201
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Jan20-06, 12:45 PM
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Quote Quote by photon79
And why it has angular momentum when there is a node??
This goes back to Noether's Theorem. The breaking of continuous rotational symmetry is associated with the addition of angular momentum. What's easier to see is (the converse, namely) that if you have no angular nodes, you must retain spherical symmetry; in which case there would be no "special" direction along which to orient an angular momentum vector.


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