Discuss the evidence from the periodic table

[awat]

Homework Statement

Discuss the evidence from the periodic table of the need for a fourth quantum number. How would the properties of He differ if there were only three quantum numbers, n, l, and m?

Homework Equations

The Attempt at a Solution

The Pauli Exclusion Principle dictates that no two electrons can occupy exactly the same orbital configuration. If there was no fourth quantum number, atoms with the same n,l, and m, would be smaller.

 

[BruceW]

The Pauli Exclusion Principle dictates that no two electrons can occupy exactly the same orbital configuration. If there was no fourth quantum number, atoms with the same n,l, and m, would be smaller.

I agree with the first sentence. But I don't understand what you mean by the second sentence.

 

[awat]

It was a hint someone else gave me, but it doesn't make sense to me either.

 

[Dickfore]

could you enumerate the possible (n, l, m) combinations in terms of rising energy?

 

[BruceW]

It was a hint someone else gave me, but it doesn't make sense to me either.

hmm. I think we should move on from that then. Your first sentence is the key to the answer.

To answer how the properties of the helium atom changes, first think how many electrons are in a helium atom. Then from here, how would you determine the properties of the atom?

 

[dextercioby]

If there was no spin, there wouldn't be a periodic table...

 

[Dickfore]

for what particles does the Pauli Exclusion Principle hold?

 

[awat]

Fermions, which include electrons, the relevant particles here.

 

[Dickfore]

Fermions, which include electrons, the relevant particles here.

yes, but saying something is a fermion is merely a tautology, because the Fermi-Dirac statistics is a consequence of the Pauli Exclusion Principle. There is another intrinsic characteristic of a particle which determines what kind of statistic it obeys.

 

[awat]

...particles that can only have antisymmetric total wave functions?

 

[Dickfore]

you are saying the same thing over and over. There is one crucial piece of evidence.

 

[awat]

particles that are identical to each other?

 

[Dickfore]

particles that are identical to each other?

photons are identical to each other as well. Do they obey the Pauli Exclusion Principle?

 

[awat]

Does it have something to do with the electrons' bound state and their overlapping wavefunctions?

A appreciate your patience and won't be offended if you decide to abandon the thread.

 

[Dickfore]

Actually, I don't want to guide you in a wrong direction. I think your professor wants you to pursue a line of reasoning that I started with my first reply in this thread. However, while looking at reply #6, it occurred to me that the division of particles in fermions and bosons has to do with one fundamental property that they posses. If you are a chemist, or in lower undergraduate course, you might not be aware of this connection, so I appologize for derailing this thread.

 

[BruceW]

Dickfore - I agree with your last post. You got a bit carried away :)

awat - start with how many electrons are in a helium atom.