The nuclei of the 02 molecule are separated by a dis- tance 1.20 x m. the mass of each oxygen atom in the molecule is 2.66 > < 10-26 kg.

(a) determine the rotational energies of an oxygen molecule in electron volts for the levels corresponding to j = 0, 1, and 2.
(b) the effective force constant k between the atoms in the oxygen molecule is 1 177 n/ m. determine the vibrational energies (in electron volts) corresponding to v = 0, 1, and 2.

Answer

given,

distance between the nuclei of an O₂ molecule = 1.20 x 10⁻¹⁰ m

mass of oxygen atom = 2.66 x 10⁻²⁶ Kg

the reduced mass of O₂ molecule =

moment of inertia of O₂ molecule

            I = 1.9152 x 10⁻⁴⁶ kg.m²

a) Rotational energy  of oxygen molecule

       J = 0

       J = 1

            E₁ = 3.63 x 10⁻⁴ eV

    J = 2

            E₂ = 1.089 x 10⁻³ eV

b) Effective force constant between the molecule

for v = 0

         E = 1.569 x 10⁻²¹ J

         E₀ = 9.8 x 10⁻³ eV

for v = 1

       E₁ = 3 E₀

       E₁ = 3 x 9.8 x 10⁻³

       E₁ = 29.4 x 10⁻³ eV

For v = 2

       E₂ = 5 E₀

       E₂ = 5 x 9.8 x 10⁻³

       E₂ = 49 x 10⁻³ eV