What is the relationship between angular momentum and energy in electrons?

The total energy of the electron is the sum of these two components, and the individual components of angular momentum (spin and orbital) contribute to the total energy in different ways.In summary, the angular momenta of an electron, including its orbital angular momentum and intrinsic spin, can have integer values of h-bar and both can be positive or negative. These values relate to the energy of the electron in a multi-electron atom, along with the energy from its linear motion. The total angular momentum is composed of both spin and orbital components, which contribute to the electron's energy in different ways.
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I'm a little fuzzy on the meaning of the angular momenta in electrons. From my understanding, the orbital angular momentum of an electron can have integer values of h-bar and the intrinsic "spin" can be 1/2 (and both can be positive or negative). How does this relate to the energy of the electron? It doesn't mean that the electron can only have energies of 3/2, 5/2, 7/2 h-bar, etc., does it? I mean a photon can have a much bigger energy than that. But it tells us something about the energy of the electron. What exactly is this total angular momentum telling us, and what are the individual components telling us?
 
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In a multi-electron atom, the energy of an electron does indeed depend on its total angular momentum ##l##, so it does follow the quantization rule.

However, angular momentum is not the only source of energy. There is also energy related to linear (orbital) motion of the electron.
 

1. What are quantum numbers?

Quantum numbers are a set of numerical values that describe the energy, position, and other properties of an electron in an atom. They are used to explain the behavior and arrangement of electrons within an atom.

2. What is the purpose of quantum numbers?

The purpose of quantum numbers is to provide a way to identify and differentiate between electrons in an atom. They also help to explain the unique properties and behaviors of different elements.

3. How many quantum numbers are there?

There are four quantum numbers: the principal quantum number, the angular momentum quantum number, the magnetic quantum number, and the spin quantum number. Each number corresponds to a specific property or characteristic of an electron.

4. What is the relationship between quantum numbers and electron orbitals?

Quantum numbers are used to describe the energy levels and sublevels of an electron within an atom. These levels and sublevels correspond to different electron orbitals, which are regions around the nucleus where an electron is most likely to be found.

5. How does confusion in quantum numbers occur?

Confusion in quantum numbers can occur when there is a lack of understanding of their meaning and how they relate to the behavior of electrons in an atom. It can also arise when trying to determine the quantum numbers for more complex atoms or molecules.

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