Chemistry
Midterm Test
Nov 13, 2009
Periodic Table of Elements
1. The energy and the wavefunction of a particle in a box can be expressed as
n2h2
and Ψ ( x) = 2 sin nπx (n=1, 2, 3, … ) where L is the width of the
2
8mL
L
L
box, m is the mass of the particle, h is the Planck’s constant, and n is the quantum
number.
(a) What is the energy of the ground state? (4%)
(b) What is the wavefunction of the first excited state? (4%)
(c) What is the energy released for a transition from n = 4 to n = 1? (4%)
(d) If the energy is released as light emission, what is the frequency of the light
emitted for a transition from n = 2 to n = 1? (4%)
(e) Find a general formula to express the energy required to induce a transition
from n = i to n = j (j > i). Based on the formula, discuss whether the energy
would becomes larger or smaller as the width of the box becomes larger.
Correct or Wrong? (4%)
Note: You do not need to obtain numerical results. You only need to show your
result in terms of the variables defined above.
En =
1
2. (4%) In an experiment of the photoelectric effect, increase the intensity of the
light will (Multiple choices. No credit unless you have all correct answers.)
(a) cause more electrons to be emitted from the metal if the frequency is
sufficiently high;
(b) cause the electrons to be emitted with higher kinetic energy if the frequency is
sufficiently high;
(c) ensure that electrons will be emitted from all metals.
(d) have no effect on the kinetic energy of the emitted electrons.
3. (a) How many orbitals does the n =3 shell have? (3%)
(b) How many electrons can this shell host at most? (3%)
4. Which ion of each of the following pairs has the larger radius?
(a) Ca2+, Ba2+ (1%)
(b) As3-, Se2- (1%).
5. Give the ground-state electron configuration expected for each of following ions:
(a) S2- (5%);
(b) Cd2+ (5%).
6. Write the Lewis structure and state the number of lone pair on xenon, the central
atom of each of the following compounds:
(a) XeOF2 (5%);
(b) XeF4. (5%)
7. Show how resonance can occur in the following organic ions, and indicate the
location of the formal charge of -1 with “-“ (minus sign):
(a) acetate ion, CH3CO2- (5%);
(b) amidate ion, CH3CONH- (5%).
8. Write the Lewis structures, give the VSEPR formula for each of the following
species and predict its molecular shape:
(a) PCl5 (5%);
(b) IF5 (5%).
2
9. Among the three molecular orbital energy-level diagrams shown below, please
select the correct one for the following diatomic molecules and answer questions:
(1) O2-, (2) CO, (3) N2+.
(a) Draw the correct MO energy-level diagrams and fill the appropriate electrons
for each molecule. (3% for each molecule, total 9%)
(b) Determine their bond order. (1% for each molecule, total 3%)
(c) Determine whether the molecule is paramagnetic. (1% for each molecule, total
3%)
10. The six π-orbitals of benzene C6H6 are drawn below.
π1
π2
π3
π4
π5
π6
The icons of π-orbitals are represented as
(a) How many nodal planes are there vertical to the benzene ring (6 carbon ring)
for each of π1…π6. (6%)
(b) Which orbitals are degenerate? (4%)
(c) Draw the π molecular orbital energy level diagram and fill the appropriate π
electrons. (3%)
3
標準解答：
1.
(a)
E = h 2 8mL2
(4 pts)
(b) Ψ ( x) = 2 sin 2πx
(4 pts)
(c) E = 15h 2 (8mL2 )
(d) ν = 3h (8mL2 )
(4 pts)
(4 pts)
L
(e)
L
( j 2 − i 2 )h 2
8mL2
Because L is in the denominator of the expression, the energy required to
induce a transition would become smaller as the width of the box
becomes larger.
(4 pts)
ΔE i − j =
2.
(a) and (d)
(4 pts)
3.
(a) 9
(b) 18
(3 pts)
(3 pts)
4.
(a) Ba2+
(b) As3-
(1 pts)
(1 pts)
5
(a) [Ar] or [Ne] 3s2 3p6
(b) [Kr] 4d10
(5 pts)
(5 pts)
F
6.
F
Xe
O
(a)
(3 pts)
2 lone pairs
F
(b)
F
Xe
(2 pts)
F
F
(3 pts)
2 lone pairs
(2 pts)
4
7. 基本上必須共振的兩個結構都必須正確，每小題即可得3分。負號位置正確，
才可得另外2分；也就是說，每一個正確負號位置可得一分。
(a)
(b)
8.
(a)
(3 pts)
AX5
(1 pt)
trigonal bipyramidal
雙三角錐 (可寫中文)
(1 pt)
(b)
(3 pts)
AX5 E
(1 pt)
square pyramidal 方形角錐或四角錐(可寫中文)
5
(1 pt)
9.
(a)
(3 pts)
Bond Order = 1.5
(1 pt)
-
O2 is paramagnetic.
(1 pt)
(b)
(3 pts)
Bond Order =3
(1 pt)
CO is not paramagnetic. (or CO is diamagnetic.)
6
(1 pt)
(c)
(3 pts)
Bond Order = 2.5
(1 pt)
N2+ is paramagnetic.
(1 pt)
10 (a)
π1
π2
π3
π4
π5
π6
1 nodal
plane
2 nodal
planes
2 nodal
planes
0 nodal
plane
3 nodal
planes
1 nodal
plane
(1 pt)
(1 pt)
(1 pt)
(1 pt)
(1 pt)
(1 pt)
(b) π1 and π6 are degenerate.
π2 and π3 are also degenerate.
(c)
(2 pts)
(2 pts)
(3 pts)
7