Iron(II) oxide, FeO, makes up 9% of the earth's mantle and is used as a black pigment in cosmetics and inks (Figure 2). Spectroscopic measurements for a single Fe-O molecule in the gas phase have shown that the interatomic equilibrium distance between the Fe atom and the O atom is 190pm with an interaction energy of 50kJ/mol. The two atoms in an Fe-O molecule in the gas phase carry atomic charges of +/0.8 e, i.e., an Fe charge of +0.8e and an O charge of 0.8e(e= elementary charge 1.60210 19C). a) Write down the total energy as a function of distance for a single iron(II) oxide molecule, utilizing the expression of the energy, EN=rA+rnB, and the Coulomb law for the attractive portion of this energy, assuming only nonbonded forces consisting of Coulomb attraction and exponential repulsion. b) Using the data given and an exponent n=12, compute the value of the pre-factor B in the unit (pm12J). c) An iron (II) oxide crystal consists of closely packed solid structures with more extensive charge transfer and larger bond length (Figure 2). Assuming charges of +/1.2e and a new bond length of 214 pm, compute the interaction energy between a pair of nearest Fe and O atoms in the crystalline environment using the potential function derived in a). The interaction energy is also called cohesive energy, especially in solids. We neglect the presence of the 3D crystal lattice for this calculation. d) Would you expect the energy to increase or decrease in an extended 3D crystal lattice compared to a single Fe-O molecule in the gas phase, when both are normalized to one FeO unit? Do the calculation results from b) and c) qualitatively follow this trend? List a few assumptions that are made in these calculations and expected uncertainties