2. The Lennard-Jones potential is a popular interatomic potential energy surface (PES) for diatomic molecules given...

2. The Lennard-Jones potential is a popular interatomic potential energy surface (PES) for diatomic molecules given by the following formula

VLJ(R)=4ε[(σ/R)^12 - (σ/R)^6]

with R the distance between the two nuclei in the molecule, and σ and ε molecule-dependent parameters.

(c) Consider the diatomic molecule O2, for which the Lennard-Jones parameters are given by ε = 5.164eV and σ = 1.075 ̊A. The atomic mass of oxygen is m(O) =15.999. Find a value for the force constant k and the vibrational zero-point energy E0 = 1 ̄hω. What is the2 wavenumber 1 (in cm−1) of the incident light needed to excite O2 from the vibrational λ ground state to the first vibrational excited state?

(d) Consider again the diatomic molecule O2. What is the moment of inertia I if the molecule can be approximated as a rigid rotor fixed at the equilibrium distance? What is the wavenumber 1 (in cm−1) of the incident light needed to excite O2 from the rotational λ ground state to the first rotational excited state?

The value of R was not given, so I'm not sure how to solve or where to find R.

Expert Solution

genius_generous answered 2 years ago

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