Molecular Pair Potential The vibrational properties of a diatomic molecule can often be described by Mie's pair potential 3 U (r) = ¤ [(;)* - (;)*] . C (4) where U(r) is the potential energy between the two atoms, r is the distance between the two atoms, C, o are positive constants, and λ > 6 is a constant. The case with λ 12 is the Lennard-Jones potential and was covered in Lecture #2. For the purposes of this problem, assume there is a mass ‘m' that represents the dynamical mass of the molecule. 4 = TLTR: (a) Find a combination of C, m, o that has the units of frequency. (b) Derive the ratio of the equilibrium positions and of the frequencies of small oscillations for X = 10, 14. Show that the units for the equilibrium position and for the frequency of the oscillations are consistent.

Molecular Pair Potential The vibrational properties of a diatomic molecule can often be described by Mie's pair potential 3 U (r) = ¤ [(;)* - (;)*] . C (4) where U(r) is the potential energy between the two atoms, r is the distance between the two atoms, C, o are positive constants, and λ > 6 is a constant. The case with λ 12 is the Lennard-Jones potential and was covered in Lecture #2. For the purposes of this problem, assume there is a mass ‘m' that represents the dynamical mass of the molecule. 4 = TLTR: (a) Find a combination of C, m, o that has the units of frequency. (b) Derive the ratio of the equilibrium positions and of the frequencies of small oscillations for X = 10, 14. Show that the units for the equilibrium position and for the frequency of the oscillations are consistent.