We can apply the rigid rotor approximation to the rotational energy levels of a diatomicmolecule, with E, = BJ(J + 1), where B represents a rotational constant.(a) Given the selection rules for ro-vibrational transitions, develop a formula for anabsorption in the R branch from a state with angular momentum J. Assume a harmonicoscillator vibration with frequency 785 cm¹ originating in the ground vibrational state(i.e. n = 0). You will be given a value for B and asked to compute the energy for aparticular transition on the submission quiz.(b) Suppose you measure several R-branch rotational transitions for 24Mg¹60, and you findthat the absorption lines are uniformly spaced 1.1485 cm-¹ apart. The quantity, B,represents a rotational constant related to the moment of inertia, I, of the molecule, viahB =8π² clwhen expressed in wavenumber (cm-¹) units. Based on this information, what is thevalue of the moment of inertia (in kg-m²) for MgO?(c) Using the results you have found, what is the bond length for MgO in pm?

a) we know, EJ = B~J(J+1)B~ is the rotational constantThe absorption in the R branch from the state…

Answered: We can apply the rigid rotor…

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