Electronic Structure (magnetic quantum number)

In summary, the 44th electron in mercury has a principle quantum number of 4, an azimuthal quantum number of 2, a magnetic spin number of -1/2, and a magnetic quantum number of 2 in the 4d orbital. This is determined by Hund's rules and the fact that there are 6 other electrons in the 4d orbital, making it more than half filled. The magnetic quantum number with the lowest energy level in this case is 2.
  • #1
Attraction
28
0

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.
 
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  • #2
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 [tex]^4\mathrm{P}[/tex] 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?
 
  • #3
Fenn said:
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 [tex]^4\mathrm{P}[/tex] 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.
 
  • #4
Attraction said:
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!
 
  • #5
Fenn said:
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.
 
  • #6
Attraction said:
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?
 
  • #7
I figured it out Fenn, thank you!
 

FAQ: Electronic Structure (magnetic quantum number)

What is the magnetic quantum number and how does it relate to electronic structure?

The magnetic quantum number, denoted by ml, is one of the four quantum numbers that describes the state of an electron in an atom. It specifies the orientation of the orbital in which the electron is located. This number ranges from -l to +l, where l is the orbital angular momentum quantum number. The value of ml determines the shape of the orbital and the direction of its angular momentum.

How is the magnetic quantum number determined?

The value of the magnetic quantum number is determined by the orbital angular momentum quantum number, l, and can range from -l to +l. The value of l is determined by the principal quantum number, n, and can range from 0 to n-1. Therefore, the possible values of ml for a given value of n are -l, -l+1, ..., 0, ..., l-1, l.

How does the magnetic quantum number affect the orbital shape?

The value of the magnetic quantum number, ml, determines the shape of the orbital. For example, when ml = 0, the orbital is spherically symmetrical and is called an s orbital. When ml = 1, the orbital is divided into two lobes along the x-axis and is called a p orbital. The number of lobes increases as the value of ml increases, resulting in d orbitals with four lobes and f orbitals with eight lobes.

How does the magnetic quantum number affect the energy of an electron?

The energy of an electron in an atom is determined by its principal quantum number, n, and its orbital angular momentum quantum number, l. However, the magnetic quantum number, ml, does not directly affect the energy of an electron. It only determines the orientation of the orbital, which indirectly affects the energy due to the electron's interaction with the atom's magnetic field.

How does the magnetic quantum number affect the electron's spin?

The magnetic quantum number, ml, does not directly affect the electron's spin. The spin quantum number, ms, is responsible for determining the direction of an electron's spin. However, the value of ml indirectly affects the spin by determining the energy of the electron, which can influence the electron's spin state. For example, electrons with the same value of n and l, but different values of ml, will have different energies and therefore different spin states.

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