A method for estimating electron affinities is to extrapolate \(Z_{\text {eff }}\) values for atoms and ions that contain the same number of electrons as the negative ion of interest. Use the data in the table on the next page to answer the questions that follow. $$\begin{array}{lll} \hline \begin{array}{l} \text { Atom or lon: } \\ \text { I(kJmol }^{-1} \text {) } \end{array} & \begin{array}{l} \text { Atom or lon: } \\ \text { I(kJmol }^{-1} \text {) } \end{array} & \begin{array}{l} \text { Atom or lon: } \\ \text { I(kJmol }^{-1} \text {) } \end{array} \\ \hline \text { Ne: 2080 } & \text { F: 1681 } & \text { O: } 1314 \\ \text { Na }^{+}: 4565 & \text { Ne }^{+}: 3963 & \text { F }^{+}: 3375 \\ \text { Mg }^{2+} \text { : 7732 } & \text { Na }^{2+}: 6912 & \text { Ne }^{2+}: 6276 \\ \text { A1 }^{\text {3 }^{+}: 11,577} & \text { Mg }^{3+}: 10,548 & \text { Na }^{3+}: 9540 \\ \hline \end{array}$$ (a) Estimate the electron affinity of \(F\), and compare it with the experimental value. (b) Estimate the electron affinities of \(\mathrm{O}\) and \(\mathrm{N}\) (c) Examine your results in terms of penetration and screening.

Step by step solution

01

Calculate Zeff value for each atom/ion

First, you need to calculate the effective atomic number (Zeff) for each atom and ion in the table. The first ionization energies are used to calculate Zeff values. Zeff values for given atoms and ions are calculated using the formula Zeff=n^2*I/(13.6) where n is the number of electrons and I is the ionization energy in eV.

02

Estimate the electron affinity for Fluorine

The next step is to estimate the electron affinity for Fluorine. This is done by extrapolating the values of Zeff for atoms and ions that contain the same number of electrons as the F- ion. Meaning, we look at the Zeff values of Ne, Na+, Mg2+ and Al3+ as they all have 10 electrons (same as F-). We plot Ionization energy against Zeff for these ions, and draw the best fit line. The point where this line intersects the Zeff value for Fluorine gives us the estimated electron affinity of Fluorine.

03

Compare with the Experimental Value

The estimated electron affinity of Fluorine can then be compared with the experimental value to assess how close the estimation is.

04

Estimate the Electron Affinity for Oxygen and Nitrogen

To estimate the electron affinities of Oxygen and Nitrogen, we follow the same procedure of extrapolating Zeff values as was done for Fluorine.

05

Examine the Results in terms of Penetration and Screening

Finally, the results are analyzed in terms of penetration and screening. If the estimated affinities are significantly higher than the experimental ones, it indicates good penetration (high probability of finding electron near the nucleus) and less effective screening by inner shell electrons. If the estimated affinities are lower, it indicates less penetration and more effective screening.

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