Answer to Question #229579 in Mechanical Engineering for john luvis

Question

 This problem illustrates both the structure of a diatomic molecule and the large disparity between changes in rotational, vibrational, and electronic energy levels. It also illustrates the formation of a band head, the abrupt end of a spectroscopic band. The following data for I2 are available from the NIST website:

(a) Construct an energy-level diagram for the ground electronic state. Consider only the first 10 rotational levels within the first two vibrational levels. Label the ordinate in cm−1 and indicate the total degeneracy of each individual rotational energy level on the diagram. 242

(b) Determine the energies (in cm−1 ) of the 10 purely rotational transitions for the v = 0 energy level within the ground electronic state and plot them on a second energy-level diagram. Draw a vertical line representing v = 0, J = 10 → 9 on the diagram from part (a).

Answer 1

Part a

Energy-level diagram

Part b

The eigenstate-to-eigenstate transitions (e.g., 1→2) possible are numerous and have absorption lines at

$ν_{obs}=E_2−E_1\\$

and for simplification, we refer to constants associated with these states as | ′⟩|′⟩ and ||″⟩, respectively.

$ν_{obs}=E′′(v′′)−E′(v′)\\$

Also important to note that typically vibronic transitions are usually the result of the vibrational v

′=0  vibrational state. Within this assumption and excluding the rotational contributions (due to their low energies)

$ν~obs=T~el+(12ν~′e−14χ~′eν~′e)−(12ν~′′e−14χ~′′eν~′′e)+ν~′ev′′−χ~′eν~′ev′′(v′′+1)$