Determine the expected diffraction angle for the first$-$order reflection from the $(113)$ set of planes for FCC platinum when monochromatic radiation of wavelength $0\mathrm{.}1542$ nm is used.

For which set of crystallographic planes will a first$-$order diffraction peak occur at a diffraction angle of $46\mathrm{.}21$ for $BCC$ iron when monochromatic radiation having a wavelength of $0\mathrm{.}0711$ nm is used?

Chromium has four naturally$-$occurring isotopes: $4\mathrm{.}34\%$ of ${?}^{50}Cr,$ with an atomic weight of

$49\mathrm{.}9460a,83\mathrm{.}79\%$ of ${?}^{52}Cr,$ with an atomic weight of $51\mathrm{.}9405a,9\mathrm{.}50\%$ of ${?}^{53}Cr,$ with an

atomic weight of $52\mathrm{.}9407$ amu $,$ and $2\mathrm{.}37\%$ of ${?}^{54}Cr,$ with an atomic weight of $53\mathrm{.}9389$ amu $.$ On

the basis of these data, confirm that the average atomic weight of Cr is $51\mathrm{.}9963$ amu $.$

Relative to electrons and electron states, what does each of the four quantum numbers specify?

Give the electron configurations for the following ions: $F{e}^{2+},A{l}^{3+},C{u}^{+},B{a}^{2+},B{r}^{-},$ and $O^{2-}.$

Calculate the force of attraction between $a{K}^{+}$and an $O^{2-}$ ion the centers of which are

separated by a distance of $1\mathrm{.}5$ nm $.$

The force of attraction between a divalent cation and a monovalent anion is $8\mathrm{.}02{10}^{-9}N.$ If

the ionic radius of the cation is $0\mathrm{.}060$ nm $,$ what is the anion radius?

For a $K^{+}-Cl-$ ion pair, attractive and repulsive energies $E_A$ and $E_R,$ respectively, depend on

the distance between the ions $r,$ according to

$E_A=-\frac{1\mathrm{.}436}{r}$

$E_R=\frac{5\mathrm{.}8{10}^{-6}}{r^9}$

For these expressions, energies are expressed in electron volts per $K^{+}-$Cl$-$ pair, and $r$ is the

distance in nanometers. The net energy $E_N$ is just the sum of the two expressions above.

$($a$)$ Superimpose on a single plot $E_N,E_R,$ and $E_A$ versus $r$ up to $1\mathrm{.}0$ nm $.$

$($b$)$ On the basis of this plot, determine $($j$)$ the equilibrium spacing ro between the $K^{+}$and

Cl$-$ions, and $($ii$)$ the magnitude of the bonding energy $E_0$ between the two ions.

$($c$)$ Mathematically determine the ro and Eo values using the solutions to Problem $2\mathrm{.}18$ and

compare these with the graphical results from part $($b$).$

Compute the percents ionic character of the interatomic bonds for each of the following

compounds: $Ti{O}_2,$ZnTe,$CsC{l}_s.$ InSb and $MgC{l}_2.$