Supplementary Problems.

In the the hypothetical linear tetra-sodium (Na₄) molecule, which valence electrons from each sodium will be involved in bond formation?

What does each such valence atomic orbital look like?

Following the same procedure that had been used in class on 1,3 butadiene (H₂C=CH-CH=CH₂), construct a picture of the four delocalized molecular orbitals in the hypothetical linear tetra-sodium (Na₄) molecule.

Consider the ion formed by removing an electron from the above molecule to form Na₄⁺. After constructing a molecular orbital energy diagram, determine what are the bond orders for each of the three bonds in this ion? (Use the same partial bond orders per electron as in 1,3 butadiene.)

What are those bond orders in the excited state of Na₄⁺ formed by promoting the highest valence electron in the molecule to the next available state?

Use the particle-in-a-box model (E_n = n²h²/8mL²) to estimate the wavelength of light needed to promote the electron mentioned in the previous question. Assume the box dimension to be 300 pm.