We can apply the rigid rotor approximation to the rotational energy levels of a diatomic molecule, with E, = BJJ + 1), where B represents a rotational constant. (a) Given the selection rules for ro-vibrational transitions, develop a formula for an absorption in the R branch from a state with angular momentum J. Assume a harmonic oscillator 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 a particular transition on the submission quiz. -1 (b) Suppose you measure several R-branch rotational transitions for 24Mg¹60, and you find that the absorption lines are uniformly spaced 1.1485 cm-¹ apart. The quantity, B, represents a rotational constant related to the moment of inertia, /, of the molecule, via h

We can apply the rigid rotor approximation to the rotational energy levels of a diatomic molecule, with E, = BJJ + 1), where B represents a rotational constant. (a) Given the selection rules for ro-vibrational transitions, develop a formula for an absorption in the R branch from a state with angular momentum J. Assume a harmonic oscillator 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 a particular transition on the submission quiz. -1 (b) Suppose you measure several R-branch rotational transitions for 24Mg¹60, and you find that the absorption lines are uniformly spaced 1.1485 cm-¹ apart. The quantity, B, represents a rotational constant related to the moment of inertia, /, of the molecule, via h