Consider the isoelectronic ions F^-and Na^+. (a) Which ion is smaller? (b) Using Equation 7.1 an

Consider the isoelectronic ions F^-and Na^+. (a) Which ion...

Consider the isoelectronic ions $\mathrm{F}^{-}$and $\mathrm{Na}^{+}$. (a) Which ion is smaller? (b) Using Equation 7.1 and assuming that core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant, $S$, calculate $Z_{\text {eff }}$ for the $2 p$ electrons in both ions. (c) Repeat this calculation using Slater's rules to estimate the screening constant, $S$. (d) For isoelectronic ions, how are effective nuclear charge and ionic radius related?

Key Concepts

Effective Nuclear Charge

Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in an atom or ion after accounting for the shielding or screening effect exerted by other electrons. It is calculated by subtracting a screening constant from the total nuclear charge (Z), and it is a crucial concept in understanding how electrons are held and the relative attraction they experience from the nucleus.

Screening Constant

The screening constant (S) quantifies the extent to which inner-shell electrons or electrons in the same shell reduce the full nuclear charge felt by an outer electron. In simplified models, core electrons are often assigned a screening contribution of 1.00 while valence electrons may contribute less, or effectively 0.00, which helps in estimating Z_eff when precise electron-electron repulsions are not fully calculated.

Slater's Rules

Slater's rules provide a systematic method for estimating the screening constant by assigning different weightings to electrons depending on their principal quantum number and subshell relative to the electron of interest. These empirical rules help refine the estimation of effective nuclear charge beyond the simplistic view of full screening by all inner electrons.

Ionic Radius

Ionic radius refers to the size of an ion, which is influenced by the effective nuclear charge; as Z_eff increases, electrons are drawn closer to the nucleus, resulting in a smaller ionic radius. This concept is crucial for comparing isoelectronic ions, where the relative charge and electron configurations determine the overall size of the ion.

Isoelectronic Ions

Isoelectronic ions are species that have the same number of electrons but different numbers of protons. The differences in their ionic radii and other physical properties arise from variations in the effective nuclear charge, as a higher nuclear charge leads to a smaller size due to stronger attraction of the electrons to the nucleus.

Transcript

00:01 This question asks us to consider the isoelectronic ions, fluorine minus, and sodium plus.

00:07 First, it asks us which ion is smaller? since they're isoelectronic, they have the same number of electrons, therefore the same screening constant.

00:14 So the only thing that's going to change here is the nuclear charge, and that's determined by the number of protons.

00:21 Since sodium is further along on the periodic table than fluorine, it would have a greater number of protons, greater nuclear charge.

00:28 That means the electrons are held more tightly.

00:31 Smaller atom.

00:32 So sodium plus is the smaller of those two ions.

00:36 Then it says using equation 7 .1 and assuming that core electrons contribute 1 .0 and valence electrons contribute 0 .0 to the screening constant s, calculate z effective for the 2 p electrons in both ions.

00:50 So here's equation 7 .1.

00:52 Z effective equals z minus s or the effective nuclear charge equals the nuclear charge which minus the screening constant.

01:00 And so for f, the nuclear charge or the number of protons is nine.

01:05 And for sodium, there are 11 protons.

01:08 And then we're going to subtract the screening constant, which is the number of valence electrons, or the number of core electrons times one in f minus.

01:18 There are only two core electrons in the 1s orbital.

01:22 So 2 times 1 .0.

01:26 This gives us an effective nuclear charge of 7.

01:31 And for sodium, it has the same screening constant because they're isoelectronic...

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