Approximating the inter atomic potential as a harmonic oscillator with angular frequency vib , the vibrational

Approximating the inter atomic potential as a harmonic oscillator with angular frequency ω_vib, the vibrational - rotational energy levels of a diatomic molecule are given by  E(n, J) = ℏω_vib(n+1/2)+ℏ² J(J+1)/(2μr²_e ). Here r_e is the equilibrium inter atomic separation,μ is the reduced mass, and J = 0, 1, 2, . . . is the rotational quantum number. The CO bond in carbon monoxide has r_e ≅ 1.13 × 10⁻¹⁰ m and ℏω_vib =0.2657 eV. Ignoring rotations, what is the wavelength λ_vib (in microns) of the radiation absorbed when the CO molecule makes a transition from vibrational level n to n + 1? Vibrational transitions are always accompanied by a transition from rotational level J to J ±1. There sult is a sequence of equally spaced absorption lines centered at λ_vib. What is the spacing between these vibrational-rotational absorption lines?