Hund's rule and angular momentum coupling

In summary, the conversation discusses the calculation of the value of L in Hund's second rule and the confusion surrounding its relationship to the eigenvalue of L^2. It is clarified that L is the maximum eigenvalue of L_z, while L(L+1) is the eigenvalue of a different operator. The question of why L=L_z is also raised.
  • #1
daudaudaudau
302
0
Hi.

In Hund's second rule, it seems that we calculate the value of L simply by summing the [itex]L_z[/itex] components of the individual electrons. But L has to do with the eigenvalue of the L^2 operator, i.e. the eigenvalue is L(L+1). So how can this be correct?
 
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  • #2
L is the maximum eigenvalue of L_z.
L(L+1) is the eigenvalue of a different operator, L^2.
 
  • #3
Meir Achuz said:
L is the maximum eigenvalue of L_z.
L(L+1) is the eigenvalue of a different operator, L^2.

Yeah that is exactly my point. We know that that L_z has some particular value. Now why is L=L_z ?
 

1. What is Hund's rule and why is it important in chemistry?

Hund's rule is a principle in quantum mechanics that states that in a multi-electron atom, the electrons will occupy orbitals of the same energy level with parallel spins before pairing up. It is important in chemistry because it helps to explain the observed electron configurations of atoms, which in turn affects their chemical and physical properties.

2. How does Hund's rule relate to angular momentum coupling?

Hund's rule is closely related to angular momentum coupling, which is the phenomenon of the total angular momentum of a system being the sum of the individual angular momenta of its components. In the case of electrons in an atom, Hund's rule dictates that the electrons will occupy orbitals with parallel spins, which results in a larger overall angular momentum for the atom.

3. What is the difference between Hund's rule and the Pauli exclusion principle?

Hund's rule and the Pauli exclusion principle are both principles in quantum mechanics that govern the behavior of electrons in an atom. However, Hund's rule is concerned with the filling of orbitals with parallel spins, while the Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers, including spin.

4. Can you give an example of how Hund's rule and angular momentum coupling affect the properties of an atom?

One example is the element manganese, which has a half-filled d-orbital due to the influence of Hund's rule and angular momentum coupling. This results in unique magnetic properties, making it useful in the production of steel and other alloys.

5. How does the Aufbau principle relate to Hund's rule and angular momentum coupling?

The Aufbau principle, which states that electrons will fill lower energy orbitals before higher energy ones, is closely related to Hund's rule and angular momentum coupling. This is because the order in which electrons fill orbitals is influenced by the overall energy and stability of the electron configuration, which is affected by the principles of Hund's rule and angular momentum coupling.

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