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### Topic: How do you determine the electron spin quantum number  (Read 39418 times)

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#### nicoliutw

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##### How do you determine the electron spin quantum number
« on: July 01, 2011, 08:48:14 PM »
I understand spin quantum number can only be either 1/2 or -1/2. But I don't understand how do you tell whether the atom has positive 1/2 or -1/2.
Here is one of my assignment question.

n=1, l=0, m=0,

what would ms be?

#### Professor 0110

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##### Re: How do you determine the electron spin quantum number
« Reply #1 on: July 01, 2011, 11:12:24 PM »
You know that the s orbital carries two electrons right? Well, they have to spin in opposite directions. If one is spinning clockwise, the other must go anticlockwise. This helps to minimize the repulsion between them. In each orbital and sub orbital one electron has a spin of 1/2 and the other one has a spin of -1/2. In other words, one is spinning clockwise, whilst the other is spinning anti clockwise. It all comes back to magnetic quantum numbers, which describes how the various orbitals are oriented in space. And of course the magnetic quantum numbers depend on the values of the angular momentum quantum number. The angular momentum quantum number is limited by the principle quantum number (n). Thus the angular momentum number (l) can have values from 0 to n - 1. So if the value of n is 3, three values are allowed for the angular momentum quantum number: 0, 1 and 2. These correspond to the atomic sub shells. So, 0 is the s shell, 1 is the p shell, and 2 is the d shell. So therefore, the magnetic quantum number depends on the values of the angular momentum number (l). The values for the magnetic quantum number range from -l to 0 to +l. So if l = 1, that corresponds to a p shell and thus the values allowed are -1 to 0 to +1. This corresponds to the three p orbitals each carrying two electrons(p shell can hold a total of 6 electrons) arranged along the x, y and z axes.

In your case, n = 1 which is the first energy level and therefore we're talking about the s orbital. The angular momentum quantum number is 0 which again refers to the s shell. And since l = 0, the magnetic quantum number will just equal 0 too. When the orbital is full, one electron will have 1/2 spin, the other will have -1/2 spin.

Always in a full orbital, one electron will spin clockwise, the other will spin anti clockwise. There is no "overall" value.

I think I gave you an overload of information. Hopefully I didn't confuse you. The most important thing to remember is that paired electrons will spin opposite to each other to minimize repulsion.

Ben

Attempting to be a Chemistry teacher as best I can.

#### nicoliutw

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##### Re: How do you determine the electron spin quantum number
« Reply #2 on: July 02, 2011, 02:57:16 AM »
um... no you are fine. It is very detail. But are you saying that in my case, Ms will equal to positive 1/2?
If n=3, l=2, ml = -2, -1, 0, 1, 2, and ms = -1/2?

#### Borek

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##### Re: How do you determine the electron spin quantum number
« Reply #3 on: July 02, 2011, 04:32:45 AM »
If you are told to put one electron into the given EMPTY orbital, it can be either 1/2 or -1/2 - it doesn't matter what way the first one spins. However, the second must spin the other way.
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#### nicoliutw

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##### Re: How do you determine the electron spin quantum number
« Reply #4 on: July 02, 2011, 05:02:22 AM »
Thank you for everything. I think I understand it now. Thanks!!