Consider the Morse Potential, 2 ·ax V(x) = D (1 - D₂(1 - e-ªx) ² е where x is the displacement of the bond from its equilibrium position and De is the value of V(x) at large separations. (Note that De in the above equation is in units of J.) (a) Expand V(x) in a Taylor Series about x = 0, through the x² term. (b) Notice that the quadratic term looks like a harmonic oscillator. Write the force constant k as a function of De and a. (c) Given that De constant. = = 7.31 x 10-¹⁹ J/molecule and a = 1.82 x 10¹⁰ m³¹ for HCl, calculate the force (d) Plot the Morse Potential (before the expansion) and plot the corresponding harmonic oscillator potential on the same graph. How do these two curves compare near the well minimum?

Consider the Morse Potential, 2 ·ax V(x) = D (1 - D₂(1 - e-ªx) ² е where x is the displacement of the bond from its equilibrium position and De is the value of V(x) at large separations. (Note that De in the above equation is in units of J.) (a) Expand V(x) in a Taylor Series about x = 0, through the x² term. (b) Notice that the quadratic term looks like a harmonic oscillator. Write the force constant k as a function of De and a. (c) Given that De constant. = = 7.31 x 10-¹⁹ J/molecule and a = 1.82 x 10¹⁰ m³¹ for HCl, calculate the force (d) Plot the Morse Potential (before the expansion) and plot the corresponding harmonic oscillator potential on the same graph. How do these two curves compare near the well minimum?