# Why the orbitals can contain maximum of 2 electrons?

why orbitals like s, px, py, pz etc can hold maximum of 2 electrons?
Why not some other number?

mfb
Mentor
Electrons have spin 1/2, so they just have two different states (called "up" and "down"). The Pauli exclusion principle does not allow multiple electrons in the same state.

The link is assuming that we are aware that the orbital can hold maximum of two electrons and then assigning 1/2 and -1/2 spins to two electrons.
Electrons have spin 1/2, so they just have two different states (called "up" and "down"). The Pauli exclusion principle does not allow multiple electrons in the same state.
Why in Pauli exclusion principle the electrons have 1/2 and -1/2 spin accounting for 2 electrons?
For example if we have 1/4 spin, then we can have 4 electrons in an orbital, with 2 electrons having 1/4 spin and other 2 -1/4 spin.

bhobba
Mentor
For example if we have 1/4 spin, then we can have 4 electrons in an orbital, with 2 electrons having 1/4 spin and other 2 -1/4 spin.

Spin 1/4 is impossible - its a basic property of spin as just about any book on QM will derive eg see page 144 of Dirac - Principles Of QM which is the book the came to hand. It can only be values +-n/2 where n is an integer. It turns out for electrons, as explained by Quantum Field Theory, they have only values +-1/2.

Thanks
Bill

vanhees71
Not read that book. I think it is taught in university. Is that true?
Well I was reading a high school level stuff.

bhobba
Mentor
Not read that book. I think it is taught in university. Is that true? Well I was reading a high school level stuff.

Yes.

That being the case you just have to take our word for it.

Thanks
Bill

That being the case you just have to take our word for it.

Thanks
Bill
Okay and thanks, but why are you thanking Bill. I nowhere find Bill in the discussion.

bhobba
Mentor
Okay and thanks, but why are you thanking Bill. I nowhere find Bill in the discussion.

I am Bill - that's what the b in bhobba is.

Its just acknowledging the reader going to the trouble to read and consider what I wrote.

Many moons ago when I was a team leader doing programming work my director always signed her communications like that and I, being on the receiving end of it, thought it nice enough that I should reciprocate.

As a young person starting out its something to think about as well. Over the years I have unfortunately found, and I am far from immune to this, that those involved in highly technical pursuits sometimes forget we are dealing with human beings and this type of thing keeps you grounded.

Thanks
Bill

Raghav Gupta
Yeah understood

Thanks for the explanation
Raghav

Okay and thanks, but why are you thanking Bill. I nowhere find Bill in the discussion.

OFF-TOPIC:

Omg. I just have to say that I laughed for like 2mins after reading this. So funny mate!

Raghav Gupta and TESL@
mfb
Mentor
Spin 1/4 is impossible - its a basic property of spin as just about any book on QM will derive eg see page 144 of Dirac - Principles Of QM which is the book the came to hand. It can only be values +-n/2 where n is an integer. It turns out for electrons, as explained by Quantum Field Theory, they have only values +-1/2.
To extend that: particles with spin 1 can have +1, 0 and -1, particles with spin 3/2 can have +3/2, +1/2, -1/2, -3/2 and so on. Particles with spin 0 have no choice.
The exclusion principle applies to fermions only, those are particles with non-integer spin values (1/2, 3/2, ...).

To extend that: particles with spin 1 can have +1, 0 and -1, particles with spin 3/2 can have +3/2, +1/2, -1/2, -3/2 and so on. Particles with spin 0 have no choice.
The exclusion principle applies to fermions only, those are particles with non-integer spin values (1/2, 3/2, ...).