Periodic Table of Elements Constants R = 8.314 J / mol K = 0.0821 L atm / K mol = 8.314 L kPa / K mol h = 6.6310‐34 Js  = 1.0510‐34 Js Mass of e , me = 9.10939  10 -31 kg 1 1. (10%) In 1925, De Broglie proposed that all particles should be regarded as
having wavelike properties, so-called the “matter wave” with the
relationship = h/p. Using this relationship and the quantization of the
matter wave in a box to derive the expression for the energy level of a
particle with mass m in a one-dimensional box of length L.
2. (8%) Atomic orbitals may be combined to form molecular orbitals. In such
orbitals, there is a non-zero probability of finding an electron on any of the
atoms that contribute to that molecular orbital. Consider an electron that is
confined in a molecular orbital that extends over two adjacent carbon
atoms with the C-C distance of 150 pm. Using the particle-in-the-box model,
calculate the wavelength of the photon required to promote an electron
from the n = 1 to the n = 2 level, assuming that the length of the box is
determined by the distance between the two carbon atoms.
3. (10%) Treat the -system of a dye molecule composed of a conjugated
carbon chain of N carbon atoms as a box of length NR, where R is the
average C-C bond length. Given that each carbon atom contributes one
electron and that each state of the box can accumulate two electrons,
derive an expression for the wavelength of the light absorbed by the
lowest-energy transition (from HOMO to LUMO).
4. (5%) An astronomer discovers a new red star and finds that the maximum
intensity is at = 715 nm. Predict the temperature of the surface of the star
according to Wien’s law, the maximum intensity is inversely proportional to
the temperature with a proportional constant 2.88×10-3 K·m.
5. Write the Lewis structure (including lone pairs) of (a) SCl2; (b) XeOF2. (6 %)
6. For each pair, determine which member is more energetically stable: (a)
NaBr or NaBr2 ; (b) F3- or I3-. Justify your choice. (8 %)
7. (a) Are Mg2+(g) and O2-(g), respectively, more stable than Mg+(g) and O-(g)?
2 Justify your answer. (b) Why does solid magnesium oxide contain Mg2+ and
O2- ions rather than Mg+ and O-? (8 %)
8. Which of the compounds below has bonds with the most covalent character:
(a) CaO, (b) Li2O, (c) MgO, (d) MgS, or (e) CaS? (3 %)
9. Draw three resonance structures that follow the octet rule (including the
most important structure) for NCO-, with carbon as the central atom. Using
formal charge arguments, predict which of the three Lewis structures is
probably the most important. (8 %)
10. Consider the diatomic species N22+, N2 and N22
(1) Draw molecular orbitals 2s*, 2p for a N2 molecule. (6 pts)
(2) Determine the bond order and relative bond lengths for N22+, N2 and
N22 species. (6 pts)
(3) How many unpaired electrons are present in each species? (3 pts)
(4) Predict the magnetic property of N22 (paramagnetic or diamagnetic)
and describe your reasoning. (5 pts)
11. For each of the following molecules, draw and name the molecular
structure, give the expected hybrid orbitals on the central atoms, and
predict the overall polarity. The central atom for each molecule is in the first
place with bold face. (20 pts)
(1) SeCl4
(2) BrIF
(3) TeF42
(4) PCl3
3 Answers
1. Soln：
1 2 p2
h 1
h2
mv 
 ( )2

2
2m  2m 2m 2
(2) For particle in the box, the quantization condition is
1
3
n
L =  ,  ,  , 2 ,  =  , where n = 1, 2, 3, 
2
2
2
2L
with n = 1, 2, 3, 
 
n
h2 n 2 n2h2
(3) Therefore, En 
( ) 
with n = 1, 2, 3, 
2m 2 L
8mL2
(1) Ek 
2. Soln：
3. Soln:
4 4. Soln:
T·(715×10-9)= 2.88×10-3
T = 4030 K
5.
(b)
..
..
F
.. ..Xe F..
..
..
6.
O
..
..
..
.. .. ..
Cl
..
.. S.. Cl
..
..
(a)
a) NaBr, sodium does not form stable Na2+ ion.
(b) I3-, because I3- contains empty d orbitals and is able to expand its
valence shell to accommodate more electrons than the octet rule.
Or,
because
7.
(a) Mg2+(g) and O2-(g), respectively, are less stable than Mg+(g) and O-(g),
because the formation of Mg2+(g) and O2-(g) from Mg+(g) and O-(g),
respectively, requires a lot of energies.
(b) Lattice energy of Mg2+O2- is much greater than that of Mg+O-.
8.
MgS.
9.
The Lewis structures are:
0
0
0
C
..0
O
..
..-2
N
..
0
+1
C O
..
..-1
N
..
..
..
..
N C
..-1
O
..
The Lewis structure in the left is probably the most important as it is the
structure with the formal charges of the individual atoms closest to zero
and the negative formal charge on the most electronegative atom.
5 I0.
6 11.
7