The vibrational properties of a diatomic molecule can often be described by Mie's pair potential: U(r)...

   

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The vibrational properties of a diatomic molecule can often be described by Mie's pair potential: U(r) = C c[9-9]. 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 X > 6 is a constant. The case with X = 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. TLTR: (a) Find a combination of C, m, o that has the units of frequency. (10 pts) (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. (40 pts) The vibrational properties of a diatomic molecule can often be described by Mie's pair potential: U(r) = C c[9-9]. 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 X > 6 is a constant. The case with X = 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. TLTR: (a) Find a combination of C, m, o that has the units of frequency. (10 pts) (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. (40 pts)

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