課程名稱︰普通化學乙上
課程性質︰必修
課程教師︰林英智
開課學院：生農學院
開課系所︰森林環資系
考試日期（年月日）︰2013/12/04
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Mass of an electron me = 9.109 × 10^-31 kg.
Planck's constant h = 6.626 × 10^-34 Js.
Speed of light in vacuum c = 2.998 × 10^8 ms^-1
1.(10 points) Suppose that in an alternate universe, the possible values of l
are the integer values from 0 to n, and the possible values of m1 are the
integer values including 0 ranging from -l-1 to l+1. How many electrons
exist in each of the following levels?
a. n = 1
b. n = 2
c. n = 3
2.(15 points) An electron confined to a one-dimensional box has energy levels
given by the equation En = n^2h^2 / 8mL^2
a. Calculate the energies (in term of Joule) of the n = 1, n = 2 and n = 3
levels for an electron in a box with a length of 155 pm.
b. Calculate the wavelength (in terms of nanometer) of light required to
make a transition from n = 1 → n = 2 and from n = 2 → n = 3.
3.(5 points) The heat of fusion of ice is 6.00 KJmol^-1. Find the number of
photons of wavelength 6.42 × 10^-6 m that must be absorbed to melt 1.00 g
of ice.
4.(5 points) Determine the number of unpaired electrons and magnetic
properties of vanadium and its 3+ ion. Use electron configurations to
explain your statement.
5.(5 points) The electron affinity of each group 5A element is more positive
than that of each corresponding group 4A element. Use the outer electron
configurations for these columns to suggest a reason for this behavior.
6.(10 points) A carbon atom can absorb radiation of various wavelengths with
resulting changes in its electronic configuration. Write orbital diagrams
for the electronic configuration of carbon that would result from absorption
of the three longest wavelengths of radiation it can absorb.
7.(5 points) Even though adding two electrons to oxygen atom or sulfur atom
forms an ion with a noble gas electron configuration, the second electron
affinity of both of these elements is positive. Explain.
8.(10 points) The cyanate ion OCN- and the fulminate ion CNO- share the same
three atoms but have vastly different properties. The cyanate ion is stable,
while the fulminate ion is unstable and forms explosive compounds, Draw
Lewis structures for these two anions including possible resonance forms,
and use formal charge to explain why the fulminate ion is less stable than
the cyanate ion.
9.(10 points) The standard heat of formation of calcium bromide is -675
kJmol^-1. The first ionization energy of calcium is 590 kJmol^-1 and its
second ionization energy is 1145 kJmol^-1. The heat of sublimation of
calcium is 178 kJmol^-1. The bond energy of diatomic bromide molecule is 193
kJmol^-1, the heat of vaporization of bromine molecule is 31 kJmol^-1, and
the electron affinity of bromine is -325 kJmol^-1. Calculate the lattice
energy of calcium bromide.
10.(5 points) Adamantane has the formula C10H16 and does not contain any
double or triple bonds. There are only two kinds of carbons out of four
possible C, CH, CH2 or CH3 groups in the structure, and any two carbons of
the same type do not bond to each other. Draw the Lewis structure for this
molecule.
11.(10 points) For a particle in a one-dimensional box, the general solution
to the Schrödinger equation HΨ(x) = EΨ(x) is Ψ(x) = A coskx + B sinkx
a. On the basis of wave properties, derive the exact wave function for all
states in the region 0≦x≦L with appropriate values of A, B and k.
b. What is the probability that the particle in the ground state is in the
first quarter of the box (0≦x≦L/4)?
12.(10 points) Specify the following hydrogen-like wave functions to the
corresponding atomic orbitals. Only very simple calculation is required.
a. Ψa = (1/(81sqrt(3π)))((z/a0)^(3/2))(27 - 18σ + 2σ^2)e^(-σ/3), where
σ = (z/a0)r
b. Ψb = (1/(4sqrt(2)pi))((z/a0)^(3/2))σe^(-σ/2)sinθsinφ
c. Ψc = (1/(81sqrt(2)pi))((z/a0)^(3/2))(σ^2)e^(-σ/3)sin^2θcos2φ
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