Current Attempt in Progress

In Chapter $3$ we saw that the electric forces acting between neighboring atoms behave very much like springs, with the spring stiffness being in the range of up to a few tens of Newtons per meter. Consider a molecule made up of two atoms of the same kind, each atom having a mass of $\backslash (6\mathrm{.}5\backslash$times $10^\{-27\}\backslash$mathrm$\{$~kg$\}\backslash ).$ Suppose that the center of the spring does not move, in which case you can model the motion of one of the atoms as that of a single atom connected to a half$-$length spring. If we should observe that a gas of these molecules emits photons whose energies are integer multiples of $\backslash (6\mathrm{.}0\backslash$times $10^\{-2\}\backslash$mathrm$\{$eV$\}\backslash ),$ what would be the stiffness of the half$-$length "spring"?

half$-$length $\backslash ($ k$\_\{$s$\}=\backslash )$

N$/$m