Electronic Structure (magnetic quantum number)

[Attraction]

Homework Statement

Describe a possible set of quantum numbers for the 44th electron in mercury.

The Attempt at a Solution

I can't help but feel a bit embarrassed by some of the questions I ask on this forum.

Nevertheless, I am having problems with figuring out what the magnetic quantum # for this 44th electron it. I know the principle quantum number is 4 (4p orbital) and the azimutal quantum number is 2, the magnetic spin number is -1/2. But I'm not sure what the magnetic number is or how to get it. I know it's range, but not sure how exactly to figure it out. It is related to the orientation of the orbital.

 

[Fenn]

Do you know what orbital this should reside in? You stated "4p orbital", and you have identified the principal quantum number as 4. You identify the orbital (or azimuthal) quantum number as 2, but that contradicts the orbital you named. Check http://en.wikipedia.org/wiki/Azimuthal_quantum_number to be sure on that. Also, if you are thinking this electron belongs in the ^4\mathrm{P} orbital, how did you arrive at that conclusion?

Regarding your question, how about you start with http://en.wikipedia.org/wiki/Magnetic_quantum_number and see if that clears things up a little?

 

[Attraction]

Do you know what orbital this should reside in? You stated "4p orbital", and you have identified the principal quantum number as 4. You identify the orbital (or azimuthal) quantum number as 2, but that contradicts the orbital you named. Check http://en.wikipedia.org/wiki/Azimuthal_quantum_number to be sure on that. Also, if you are thinking this electron belongs in the ^4\mathrm{P} orbital, how did you arrive at that conclusion?

Regarding your question, how about you start with http://en.wikipedia.org/wiki/Magnetic_quantum_number and see if that clears things up a little?

OK, let me start again.

The 44th electron is in the 4d orbital. Principle quantum number = 4.
d orbital = 2, therefore the azimuthal quantum number is 2.
Magnetic spin number is -1/2.

Because the azimuthal number is 2, the possible numbers for the magnetic spin quantum number are -2/-1/0/1/2. I am having trouble narrowing that range down and cannot find anything online that helps.

 

[Fenn]

OK, let me start again.

The 44th electron is in the 4d orbital. Principle quantum number = 4.
d orbital = 2, therefore the azimuthal quantum number is 2.
Magnetic spin number is -1/2.

Because the azimuthal number is 2, the possible numbers for the magnetic spin quantum number are -2/-1/0/1/2. I am having trouble narrowing that range down and cannot find anything online that helps.

Ok, the 4D sounds more reasonable to me. Next, check how many other electrons occupy the 4D orbital. By the Pauli exclusion principle, they must all have a unique set of magnetic quantum number and spin quantum number values.

The 44th electron must be placed in such a way that it is in the lowest energy configuration when added to the other 43 electrons. For this, I suggest checking out Hund's rules, at http://en.wikipedia.org/wiki/List_of_Hund's_rules.

Good luck!

 

[Attraction]

Ok, the 4D sounds more reasonable to me. Next, check how many other electrons occupy the 4D orbital. By the Pauli exclusion principle, they must all have a unique set of magnetic quantum number and spin quantum number values.

The 44th electron must be placed in such a way that it is in the lowest energy configuration when added to the other 43 electrons. For this, I suggest checking out Hund's rules, at http://en.wikipedia.org/wiki/List_of_Hund's_rules.

Good luck!

There are 6 other electrons in the 4d orbital, which can hold 10 electrons (2 in each orbital).

Would I be right in saying that each orbital has a respective value of 2/1/0/-1/-2? I think so.

I know about hunds rule and the magnetic spin number so my question is, how do I know which value is correct for the magnetic quantum number. Is the first orbital just given the positive 2, second orbital given the positive 1, third orbital given 0 and so on?

If so, the magnetic quantum number would have to be 2 in this case.

 

[Fenn]

There are 6 other electrons in the 4d orbital, which can hold 10 electrons (2 in each orbital).

Would I be right in saying that each orbital has a respective value of 2/1/0/-1/-2? I think so.

I know about hunds rule and the magnetic spin number so my question is, how do I know which value is correct for the magnetic quantum number. Is the first orbital just given the positive 2, second orbital given the positive 1, third orbital given 0 and so on?

If so, the magnetic quantum number would have to be 2 in this case.

From my count, there would be five other electrons in the 4d orbital. This orbital can hold a total of 10 electrons, which means that all the other electrons before the 44'th electron will half-fill the orbital. What does Hund's rules say about how these 5 electrons are arranged? When you add one more to this arrangement, the orbital will now be more than half filled. Which magnetic quantum number will give the lowest energy level? Is it different than an orbital that is less than half filled?

 

[Attraction]

I figured it out Fenn, thank you!