In a simple model of a potassium iodide (KI) molecule, we assume the K and I atoms bond ionically by the transfer of one electron from K to I. (a) The ionization energy of K is 4.34 eV, and the electron affinity of I is 3.06 eV. What is the activation energy Ez? That is, what is the energy (in eV) needed to transfer an electron from K to I, forming K+ and I ions from neutral atoms in the process?
eV
(b) In our simple model, the potential energy of the KI molecule is given by the Lennard-Jones potential: u(r) = 48 4e [C)"?- 9)%] +E where r is the distance between the nuclei of the K and I ions, & and o are adjustable parameters, and is the activation energy (added to give the correct asymptotic behavior at large r). At the equilibrium separation distance, r=ro = 0.305 nm, U(r) is a minimum, du and = 0. In addition, uro) is the negative of the dissociation energy: U(ro) = -3.37 eV. Find o (in nm) and & (in eV).
d = nm
r = eV
(c) What force magnitude (in nN) is needed to break up a KI molecule?
nN s
(d) Calculate the force constant (that is, the "spring" constant, in N/m) for small oscillations about r = ro. Suggestion: Set r = ro + s, where s < 1, and expand U(r) in powers of ro up to second-order terms.
N/m