A simple picture of an H₂ molecule sharing two electrons is shown in Fig. 40–56. We assume the electrons are symmetrically located between the two protons, which are separated by r₀ = 0.074 nm. Determine analytically the value of d that gives minimum U (greatest stability).

One possible form for the potential energy (U) of a diatomic molecule (Fig. 40–8) is called the Morse Potential:

$U=U_0{[1-e^{-a(r-r_0)}]}^2$

(a) Show that r₀ represents the equilibrium distance and U₀ the dissociation energy.

One possible form for the potential energy (U) of a diatomic molecule (Fig. 40–8) is called the Morse Potential: $U=U_0[1-e^{-a(r-r_0{)}^2}]$. Graph U from r = 0 t o r = 4r₀, assuming a = 18nm^-1, U₀ = 4.6 eV, and r₀ = 0.13 nm.

A simple picture of an H₂ molecule sharing two electrons is shown in Fig. 40–56. We assume the electrons are symmetrically located between the two protons, which are separated by r₀ = 0.074 nm. When the electrons are separated by a distance d, write the total potential energy U in terms of d and r₀.

A simple picture of an H₂ molecule sharing two electrons is shown in Fig. 40–56. We assume the electrons are symmetrically located between the two protons, which are separated by r₀ = 0.074 nm. Make a graph of U in eV as a function of d in nm.