# Solving Hund's Rule Q: Gd [Xe] 6s^2,4f^7,5d^1

• Old Guy
In summary, the problem at hand is to find the ground state L and S for Gd with the electron configuration [Xe]6s^2,4f^7,5d^1. The maximum spin value, Smax, is calculated to be 4, with 1/2 coming from the 5d^1 electron and 7/2 from the 7 electrons in the f level. To determine the maximum orbital angular momentum, Lmax, it is necessary to consider the magnetic quantum numbers, with the s^2 having a value of 0 and the p^7 having all possible values filled. This leaves the d^1 electron with a maximum value of 2, resulting in a total of
Old Guy
I'm certainly missing something here. The problem is to find the ground state L and S for Gd, with a configuration given as [Xe]6s^2,4f^7,5d^1.

I start by calculating Smax. I'm figuring you get 1/2 for the 5d^1 electron, plus (since the f level has room for 14 electrons, all 7 can have +1/2 spin) 7/2 give Smax = 4.

How do I get L? It would seem that Lmax would be 4 for the 5d^1 electron and 3 for the others, making a total of 7. The book says it should be 2, and I can't see how, for example, the Pauli exclusion principle should get me there. Any help would be appreciated - I really want to understand the concept as much as deal with this problem. Thanks.

Old Guy said:
I'm certainly missing something here. The problem is to find the ground state L and S for Gd, with a configuration given as [Xe]6s^2,4f^7,5d^1.

I start by calculating Smax. I'm figuring you get 1/2 for the 5d^1 electron, plus (since the f level has room for 14 electrons, all 7 can have +1/2 spin) 7/2 give Smax = 4.

How do I get L? It would seem that Lmax would be 4 for the 5d^1 electron and 3 for the others, making a total of 7. The book says it should be 2, and I can't see how, for example, the Pauli exclusion principle should get me there. Any help would be appreciated - I really want to understand the concept as much as deal with this problem. Thanks.
The magnetic quantum numbers m_l have 2l+1 possible values ranging from -l to +l in integer steps. The s^2 has only 0, the p^7 has one of every m filled, so the net contribution from these is zero. The one remaining electron in the d^1 has a maximum value of 2, so it looks like 2 is it.

## What is Hund's Rule?

Hund's Rule is a principle in quantum mechanics that states that for a given set of orbitals with the same energy, electrons will occupy separate orbitals with parallel spins before pairing up in the same orbital.

## How does Hund's Rule apply to the electron configuration of Gd [Xe] 6s^2,4f^7,5d^1?

In the electron configuration of Gd, there are 7 electrons in the 4f orbital and 1 electron in the 5d orbital. According to Hund's Rule, these electrons will first occupy separate orbitals with parallel spins (4f^7) before pairing up in the 5d orbital (5d^1).

## Why is Hund's Rule important in understanding the electron configuration of elements?

Hund's Rule helps to explain the stability and reactivity of elements by determining the most energetically favorable arrangement of electrons in orbitals. It also helps to predict the magnetic properties of elements.

## Can Hund's Rule be violated?

Yes, Hund's Rule can be violated in certain cases, such as when the energy difference between orbitals is small or when there is a repulsion between electrons in the same orbital. However, these violations are rare and Hund's Rule generally holds true.

## How does Hund's Rule differ from the Aufbau principle and Pauli exclusion principle?

The Aufbau principle states that electrons will occupy the lowest energy orbitals first, while the Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers. Hund's Rule, on the other hand, specifically deals with the arrangement of electrons in orbitals with the same energy. Together, these three principles help to determine the electron configuration of elements.

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