Chapter 10, Problem 128FP

In this problem, we examine the basis of three different electronegativity scales and work through the same types of calculations as those performed by the people who initially suggested these scales. The scale developed by Robert Mulliken employs ionization energies (E) and electron amenities $E_{ea}$ whereas the scale developed by Linus Pauling is based on bond dissociation energies (D). The scale developed by A. Louis Aired and Eugene G. Rochow employs effective nuclear charges $\left(Z_{ea}\right)$ and covalent radii The key equations for each scale are given below.

In devising his scale, Pauling observed that the bond energy, $D_{a-z}$ for the $A-B$ bond is greater than the average of $A-A$ the and $B-B$ bond energies, $\frac{1}{2}\left(D_{A-A}+D_{B-B}\right)$ , and he attributed the increase in bond strength to the partial ionic character of the $A-B$ bond.
Mulliken argued that the ionization energy $\left(E_1\right)$ and electron affinity $\left(E_{ea}\right)$ are of equal importance for the electronegativity Of an atom. Therefore, he suggested that the average of these two quantities, $\left(E_1+E_{ea}\right)/2$ be used to define the electronegativity of an atom.
Alred and Rochow focused on the attractive Coulombic force between an electron near the surface of an atom and the nucleus of that atom.

They argued that the magnitude of this force is proportional to where $(e)(Z_{ar}e)/r^2{}_{eav}\}=e^2{Z}_{am}/r^2{}_{eav}$ where $e=1.602\times {10}^{12}C$ is the magnitude of the charge of an electron, $Z_{ea}e$ is the nuclear charge experienced by an electron near the atom's surface, and r is the covalent radius and a realistic measure of the size of an atom.
The values of $D,Z_{ea}$ and r given below are the actual values used by Pauling and by Alfred and Rochow in their original papers. use the data below and the equations above to calculate the electronegativities of F, CI, Br, and l. Summarize your results in a table having four columns:
Atom, EN(Pauling), EN(MuIliken), (Hint: The Pauling values you calculate will not be exactly equal to those in Figure 10-6. The values in Figure 10-6 are based on bond dissociation energies from a wider range of molecules than we are considering in this problem.