Exclusion Principle application to very large systems

In summary, the exclusion principle applies not only to a single atom but also to larger systems. It states that fermionic particles with half-integer spin cannot have the same quantum numbers, which applies to the electrons in atoms. When forming a molecule, the electrons in the atomic orbitals mix and occupy bonding and anti-bonding levels according to their spin. This principle has many consequences, including the stability of materials and celestial objects.
  • #1
Xcellerator
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Hi,
I've had something that's been bothering me for a while and I've been researching it, but I just want to clear something up.
I understand that the exclusion principle dictates that fermionic particles with half-integer spin have an anti-symmetrical wavefunction under exchange, and therefore implies that no two fermions can have have the exact same quantum numbers.
I understand how this can apply to a single atom, in that each electron must be in a different quantum state (of n,l,m & s), but I do not understand how it can still apply to anything larger than a single atom.
If I had two hydrogen atoms, then the two innermost electron shells of one of them would have the same set of quantum numbers as the other one. Does the exclusion principle not apply to larger systems?
Also, if a wavefunction was computed of two hydrogen atoms then how can the two innermost electrons of each atoms NOT have the same quantum number.

I get the feeling I've either missed something tiny or something massive, so any response is greatly appreciated...
 
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  • #2
The exclusion principle is not applicable just to a single atom. Let us say, you have 2 Hydrogen atoms with electrons in each of them in the 1s orbital. When you bring them together to form a bond, the 2 1s orbitals mix/hybridize into two energy levels named as bonding (sigma) and anti-bonding levels (sigma*). The bonding level has a lower energy state than 1s (thus favorable to bond) and anti-bonding has an higher energy than 1s. As per Pauli's exclusion principle, the bonding level can contain only 2 electrons with opposite spins.

So for H2 molecule, the bonding level is occupied with 2 electrons and the energy is less than the energy of 2 separate Hydrogen atoms. Hence bonding is favorable.

But now consider the scenario for Helium molecule. Having two electrons from each atom, and because of the exclusion principle, both the bonding and anti-bonding levels are occupied with electrons. The net result is that there is no energy gain by forming a molecule. Hence Helium doesn't form a molecule like Hydrogen.

Apart from this exclusion principle can be used to explain many things - band structure of materials, stability of neutron star etc...

You may refer this for more consequences
http://en.wikipedia.org/wiki/Pauli_exclusion_principle#Consequences
 

1. What is the Exclusion Principle?

The Exclusion Principle, also known as the Pauli Exclusion Principle, states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously in a given system. This principle is a fundamental law of quantum mechanics and was first proposed by physicist Wolfgang Pauli in 1925.

2. How does the Exclusion Principle apply to very large systems?

In very large systems, such as atoms or molecules, the Exclusion Principle ensures that the electrons occupying the same energy level have different quantum states. This means that electrons cannot have the same set of quantum numbers, including energy, spin, and angular momentum, within a given system. This leads to distinct energy levels and stable, well-defined structures for these systems.

3. What are the implications of the Exclusion Principle for atomic and molecular structures?

The Exclusion Principle plays a crucial role in determining the stability and properties of atoms and molecules. It explains why atoms have discrete energy levels, which in turn determine their chemical and physical properties. It also explains the stability of atoms and prevents them from collapsing into a single point.

4. Does the Exclusion Principle have any exceptions?

While the Exclusion Principle applies to most particles, there are some exceptions. One example is in the case of superconductors, where electrons can form pairs and behave as bosons (particles with integer spin), thus not being subject to the Exclusion Principle. Another exception is in the case of quarks, the building blocks of protons and neutrons, which can also form pairs and behave as bosons.

5. How does the Exclusion Principle relate to the stability of matter?

The Exclusion Principle is crucial for the stability of matter. Without it, atoms and molecules would not have well-defined energy levels and would be highly unstable. In large systems, such as stars, the Exclusion Principle also plays a role in determining the maximum mass that can be supported by a given pressure and temperature, thus influencing the stability of these systems as well.

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