Angular Node: Exploring Electron Angular Momentum

In summary, the angular momentum of an electron in the ground state is zero because it is the solution with the lowest energy value according to the Schrodinger equation. However, it can still have angular momentum when there is a node present. A radial node occurs when the radial part of the wavefunction vanishes, while an angular node occurs when the angular part vanishes. The presence of these nodes can affect the energy of the electron. Additionally, the breaking of continuous rotational symmetry is associated with the addition of angular momentum. If there are no angular nodes, then spherical symmetry is retained and there is no preferred direction for an angular momentum vector.
  • #1
photon79
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angular node!

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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  • #2
photon79 said:
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.
 
  • #3
photon79 said:
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.
 

1. What is Angular Node?

Angular Node is a concept in quantum mechanics that refers to the region around a nucleus where an electron is most likely to be found. It is also known as an orbital or energy level.

2. How is Angular Node related to Electron Angular Momentum?

Angular Node is related to Electron Angular Momentum because it determines the shape and orientation of the electron's orbital, which in turn affects its angular momentum. The number of Angular Nodes also determines the value of the electron's orbital angular momentum quantum number.

3. What is the significance of exploring Electron Angular Momentum?

Exploring Electron Angular Momentum allows scientists to better understand the behavior and properties of electrons in atoms and molecules. It also has practical applications in fields such as material science, chemistry, and electronics.

4. What is the difference between Angular Node and Angular Momentum?

Angular Node refers to the spatial distribution of the electron's probability density, while Angular Momentum is a physical quantity that describes the rotational motion of the electron around the nucleus. Angular Momentum is dependent on Angular Node, but they are not the same concept.

5. How does Electron Angular Momentum affect an atom's properties?

The value of Electron Angular Momentum affects an atom's properties such as its energy levels, ionization energy, and chemical reactivity. It also determines the shape of an atom's electron orbitals, which in turn affects its chemical bonding and molecular structure.

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