Electron Configuration and energy levels

[Nusc]

--------------------------------------------------------------------------------

1. Homework Statement
The electrons of a nelectronically-excited neutral magnesium atom have the coniguration 1s^2 2s^2 2p^6 3p 3d. Provide spec notation for the possible quant states of the atom as a whole


2. Homework Equations



3. The Attempt at a Solution

We neglect 1s^2 2s^2 2p^6 and only focus on 3p and 3d. I don't know what to do because we have two high energy levels to consider. If there was just one the then problem would be trivial.

 

[Astronuc]

OK - the three is the principal quantum number n.

But what about the s, p, d, f, . . . designators?

See if this helps - http://hyperphysics.phy-astr.gsu.edu/hbase/qunoh.html

 

[Nusc]

Okay so n = 3 therefore l = n-1 = 2.

Thus, when l = 2 we have d.

So d is our designator of choice.

 

[Nusc]

Was the above correct? Because if I apply the same reasoning to this following problem:

an excited e-state of aluminimum atom is labelled by the config: 1s2 2s2 2p6 3s 3p2. What are the possible e-states for a atom with this config?

Here we have a choice between 3s and 3p2. n = 3 in this case therefore l = n-1 = 2 which would correspond with a d.

What the heck am I doing?

 

[Kushal]

i don't know if i understood your problem correctly;

Mg is 1s2 2s2 2p6 3s2

when it is excited, one electron from 3s will be promoted to an empty 3p orbital.

hence:

*Mg 1s2 2s2 2p6 3s1 3p1

 

[Astronuc]

This is a good discussion of electron configuration
http://en.wikipedia.org/wiki/Electron_configuration

http://www.chemicalelements.com/show/electronconfig.html - chart

http://www.webelements.com/


Anyway, I was wondering if one has an example of what is meant by "Provide spec notation for the possible quant states of the atom as a whole"

Mg has the ground state electron configuration of 1s² 2s² 2p⁶ 3s², and Al has the g.s. e-config of 1s² 2s² 2p⁶ 3s² 3p¹ as indicated by Kushal.

The problem statement for an excited Mg atom states 1s² 2s² 2p⁶ 3p 3d, so it appears one 3s electron is excited to 3p and one to 3d.


Is the problem asking for the possible quantum states described by n, l, m (or m_l), m_s? Does one need to provide descriptions for the n=1 and n=2 electrons, or just the outermost (valence electrons)?

See - http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html#c3

For n, what are the possible values for l, and then for l, what are the possible values for m. Then m_s has two possibilities.

l is constrained such that l = 0, 1, . . . n-1,
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydcol.html#c2

then m = -l, -l+1, . . . , 0, 1, . . . , l-1, l (there are 2l+1 values)
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydazi.html#c2
http://en.wikipedia.org/wiki/Magnetic_quantum_number

 

[Nusc]

The problem wants the configuration based on the 2S+1{L}_J labelling.

 

[Nusc]

Here's an example: What are the poss gs of Cl+.

1s2 2s2 2p6 3s2 3p4

We need only consider the 3p4.

S = 1/2 + 1/2 + 1/2 + 1/2 : + indicates direct sum notation

So S = {0,1,2}

Since we only consider the four p electron, l =1

Therefore ml = -1,0,1

=> At least one of the spin particles must have opposite spin to the others so at least 2o f hte elctrons pair cancellin their psins. THus S= 1/2 + 1/2 = {0,1}
So the spin degeneracies are 2S+1 = {1,3}

Then L = 1 + 1 + 1 + 1 = {0,1,2,3,4}


|L-S| <= J <= L+S

Gives us a whole number of values using the 2S+1 {L}_J

Does that help?

 

[Nusc]

I think the problem is asking for the possible quantum states described by n, l, m (or ml), ms

 

[Astronuc]

I think the problem is asking for the possible quantum states described by n, l, m (or m_l), m_s

That is what I'm thinking.

OK, so in the example of the excited Mg, there is 1 p and 1 d electron. Then, what are the possible states for the p and for the d electron?

 

[Nusc]

You mean with a given p state and d state you want the orbital ang mom states?


FOr p, l =1
so ml = -1 , 0, 1

and for d, l = 2.
so ml = -2,-1 , 0, 1,2
N =3 in this case
IS that what you want?

 

[Astronuc]

Focus on p, l =1 and d, l = 2.

J runs from |L+S| to |L-S|.

See this discussion of optical spectra.

 

[nrqed]

The problem wants the configuration based on the 2S+1{L}_J labelling.

From that statement I will assume that we are doing L-S coupling (as opposed to j-j coupling).

Each electron has s=1/2. So what are the possible values of the total spin S?

One electron has l=1 (a p state) and the other electron has l=2 (a d state). What are the possible values of the total orbital angular momentum L?

Now, for each combination (S,L) you have (there will be a total of 6 combinations), figure out the possible values of J. Then, in each case, give the result in the notation $$\,^{2S+1} L_J$$. For example, if the total spin is 1, L is 2 and J is 2, you have a$$\,^3 D_2$$ state.

I hope this helps