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PostPosted: Tue, 6 Dec 2011 02:28:30 UTC 
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I would like it (if you can) keep the answer appropriate for a General Chemistry course. Thank you.

Earlier in the textbook, we estimated the effective nuclear charge on Beryllium's valence electrons to be slightly greater than +2. What would a similar treatment predict for the effective nuclear charge on boron's valence electrons? Would you expect the effective nuclear charge to be different for boron's 2s electrons compared to its 2p electron? In what way?

Attempt:
http://i1084.photobucket.com/albums/j40 ... MG-002.png
We assume that the valence electrons feel an effective nuclear charge of about 2+, but not 4+ because of the inner electrons shielding them. So using this, how would it work when a 2p-orbital.

Thank you for reading.
ARQ


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PostPosted: Tue, 6 Dec 2011 05:45:21 UTC 
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A-R-Q wrote:
I would like it (if you can) keep the answer appropriate for a General Chemistry course. Thank you.

Earlier in the textbook, we estimated the effective nuclear charge on Beryllium's valence electrons to be slightly greater than +2. What would a similar treatment predict for the effective nuclear charge on boron's valence electrons? Would you expect the effective nuclear charge to be different for boron's 2s electrons compared to its 2p electron? In what way?

Attempt:
http://i1084.photobucket.com/albums/j40 ... MG-002.png
We assume that the valence electrons feel an effective nuclear charge of about 2+, but not 4+ because of the inner electrons shielding them. So using this, how would it work when a 2p-orbital.

Thank you for reading.
ARQ


I'm not sure what method the textbook used for estimating the effective nuclear charge, but here is one: compare the (mean) radius of 2p-orbital for boron with that of hydrogen or hydrogen-like (i.e. single electron, nucleus has charge +Z_{eff}e). Since 2s-orbital (in addition to 1s) also shields the 2p-orbital (as 2s is much closer than 2p to the nucleus), we expect the effective nuclear charge experienced by the 2p-orbital be less than that of 2s-orbital.

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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