Question 57db5

Apr 7, 2017

The effective nuclear charge is the net positive charge experienced by an electron in an atom.

Explanation:

Electrons that are further from the nucleus are somewhat shielded from the full attraction of the nucleus by the electrons that are closer in.

The effective charge ${Z}_{\textrm{e f f}}$ is

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} {Z}_{\textrm{e f f}} = Z - S \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

where $Z$ is the atomic number and $S$ is the screening constant.

Slater's Rules

Slater's rules enable us to estimate the value of $S$. Here are the rules as they apply to a magnesium atom.

1) Write the electron configuration for the atom using the pattern: $\text{(1s)(2s,2p)(3s)}$

3) All other electrons in the same group as the electron of interest shield to an extent of 0.35 nuclear charges.

4) All electrons with one less value of the principal quantum number shield to an extent of 0.85 charges. All electrons with two less values of the principal quantum number shield to an extent of 1.00 unit.

${Z}_{\textrm{e f f}}$ for a $\text{3s}$ electron in $\text{Mg}$

The electron configuration for $\text{Mg}$ is ${\text{1s"^2 "2s"^2 "2p"^6 "3s}}^{2}$.

We group the orbitals in the order

$\textcolor{w h i t e}{m m l l} \left(\text{1s")color(white)(mml)("2s,2p")color(white)(mmll)("3s}\right)$
S = 2×1 + 8×0.85 +1×0.35 = 9.15#

Thus, the 11 other electrons in a magnesium atom shield the 12th electron from 9.15 nuclear charges.

Then, for a $\text{3s}$ electron in $\text{Mg}$,

${Z}_{\textrm{e f f}} = \text{12 - 9.15} = 2.85$