Pauli exclusion principle question

In summary, the conversation discusses the placement of five electrons in an infinite square well and the calculation of the lowest energies. One person suggests placing the first two electrons in n=1 and the remaining electrons in n=2, while the other suggests placing two in n=1, two in n=2, and one in n=3 due to Pauli exclusion. The question of why one electron should be placed in n=3 is raised, with the response being that the well is not spherical symmetric and therefore the quantum number L is not relevant. The conversation ends with the clarification that L only plays a role in potentials with spherical symmetry, such as the atom.
  • #1
drullanorull
4
0
I have a question in my book where five electrons are placed in a infinite square well and I am supposed to calculate the lowest energies. My problem is with the electron configuration. I think that the first two shall be placed in n=1 and then the rest shall be placed in n=2. This since l=0,1 and m=-1,0,1 (plus the spin). However my book gives me a different solution. Two in n=1, two in n=2 and one in n=3, due to Pauli exclusion. But three electrons can have different quantum numbers in n=2. So why shall one of the electroons be placed in n=3?
 
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  • #2
Is the well spherical symmetric? No.

In the infinite square well, your quantum numbers are only n and m_s, you don't have L since it isn't spherical symmetric - hence angular momentum is not a good quantun number here.

So for each n, you can put 2 number of electrons due to 2 different m_s values.

So L only plays a role if your potential has spherical symmetry - in the atom for example - the nuclei is generating a spherical symmetric potential - and here L quantum number becomes important.
 
  • #3
of course! thanks a lot
 

FAQ: Pauli exclusion principle question

What is the Pauli Exclusion Principle?

The Pauli Exclusion Principle is a fundamental principle in quantum mechanics that states that no two identical fermions can occupy the same quantum state simultaneously. This means that two electrons cannot have the same set of quantum numbers (such as energy level, spin, and orbital angular momentum) in an atom or molecule.

Why is the Pauli Exclusion Principle important?

The Pauli Exclusion Principle is important because it explains many of the properties and behaviors of matter at the atomic and subatomic level. It helps us understand why atoms and molecules have specific electronic configurations, and why certain elements are more stable than others. It also plays a crucial role in determining the properties of materials and their behavior in various environments.

Who discovered the Pauli Exclusion Principle?

The Pauli Exclusion Principle was first proposed by Austrian physicist Wolfgang Pauli in 1925. He was studying the properties of atoms and noticed that certain patterns emerged in their electronic configurations that could not be explained by existing theories. Pauli then proposed the exclusion principle to explain these patterns, and it has since been supported by numerous experiments and observations.

What happens when the Pauli Exclusion Principle is violated?

If the Pauli Exclusion Principle is violated, it would mean that two identical fermions can occupy the same quantum state at the same time. This would have significant consequences for our understanding of the behavior of matter and could potentially lead to a breakdown of fundamental laws of physics. However, no experimental evidence has been found to suggest that the Pauli Exclusion Principle is violated.

How does the Pauli Exclusion Principle relate to the periodic table?

The Pauli Exclusion Principle plays a crucial role in determining the electronic configurations of atoms and the ordering of elements in the periodic table. It explains why each element has a unique number of electrons in its outermost energy level and why certain elements have similar properties. It also helps us understand the trend of increasing ionization energy and electron affinity across the periodic table.

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