Consider the elementary reaction $A{r}^{+}+H_{2}Ar{H}^{+}+H.$ The compound $Ar{H}^{+},$ also

known as argonium, is isoelectronic with $HCl$ and is observed in astrochemical

measurements.

a$.$ The reaction is exoergic, with the products being are $1\mathrm{.}34eV$ lower in energy than

the reactants. The bond energy of $H_2$ is $4\mathrm{.}52eV,$ so placing the $H_2+A{r}^{+}$minimum

potential energy at $-4\mathrm{.}52eV$ is a reasonable way to set "zero energy" for the system.

Essentially this sets the energy of $A{r}^{+}$as the reference point for the energy scale.

The vibrational energy spacing of $H_2$ is $4401c{m}^{-1}$ and the vibrational energy

spacing of argonium is $2625c{m}^{-1}.$ Using this information, create a sketch of this

reaction using similar format to Fig. $1\mathrm{.}1$ of the Levine text. Make an effort to

establish rough quantitative accuracy as you place states along the energy axis.

b$.$ The argon atom can be considered as a spectator in this reaction. Why?

c$.$ What vibrational states of the $Ar{H}^{+}$project are accessible?