except the atomic orbital shapes would be circles overlapping along the
bond axis. The partial bond orders per electron could be carried over to the
sodium picture.
Answers to Supplementary Problems.
In the the hypothetical linear tetra-sodium (Na4)
molecule, which valence electrons from each sodium will be
involved in bond formation? The
4s.
What does each such valence atomic orbital look like? Like the 4s (spherical pictured as a
circle)
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.
|
This is what the butadiene looked like. The
tetrasodium would look the same except the atomic orbital shapes would be circles overlapping along the bond axis. The partial bond orders per electron could be carried over to the sodium picture. |
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?
The first sigma would have
bond orders 2(.166) = 0.333 for each Na-Na link. The second
sigma, with only one electron remaining would contribute 0.25 to
both outer bonds and nothing to the central Na-Na link. There is
no underlying framework. The total bond
orders would thus be 0.583 for the outer Na-Na bonds and 0.333
for the central Na-Na bond.
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? Sigma #1 has the overall effect of its two electron's
altered by placing the third electron in the tetrasodium ion into
sigma #3. The contribution of that highest electron is now -0.25
to the outer bond order, counteracting the +0.333 from sigma #1's
pair
leaving a net (very weak) 0.083 bond order for the outer Na-Na
bonds. The central bond increases by 0.50 from sigma #3 to a
total of 0.833 bond order.
Use the particle-in-a-box model (En = 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.
E3-E2=
(32-22)h2/8mL2 =
5(6.63 X 10-34)2/8(9.11 X 10-31)(300
X 10-12)2 = 3.35 X 10-18 joules
= hc/wavelength
wavelength = 5.94 X 10-8 m = 59 nm