Download Chem 150 Problem Set Introductory Quantum Chemistry 1

Chem 150
Problem Set Introductory Quantum Chemistry
1. Determine which of the following statements are false and correct them.
a) Electromagnetic radiation is incapable of passing through water.
b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of the
wavelength.
c) Infrared light has higher frequency than visible light.
d) The glow from a fire place, the energy within a microwave oven and a for horn blast are all
forms of electromagnetic radiation.
2.
a) What is the frequency of radiation that has wavelength of 955 μm?
b) What is the wavelength of radiation that has a frequency of 5.50 x 1014 s-1?
c) Would the radiation in part a) or part b) be visible to the human eye?
3.
Energy from radiation can be used to cause rupture in chemical bonds (wanted e.g. as in
photosynthesis or in degradable plastics that decompose in sunlight or unwanted as in a
sunburn). A minimum energy of 941 kJ/mol is required to break the nitrogen-nitrogen bond in
N2. What is the longest wavelength of radiation that possesses the necessary energy to break
the bond? What type of radiation is that?
4.
It requires a photon with a minimum energy of 4.41 x 10 -19 J to emit electrons from sodium
metal.
a) What is the minimum frequency of radiation necessary to emit electrons from sodium metal?
b) What is the wavelength of this light?
5.
Calculate the de Broglie wavelength of a muon, a subatomic particle that decays within a few
nanoseconds after formation traveling with a velocity of 8.85 x 10 5 cm s-1. The resting mass of a
muon is 206.8 electron masses.
6.
a) According to the Bohr model an electron in the ground state of a hydrogen atom orbits the
nucleus at a specific radius of 0.53 x 10-10 m. In the quantum mechanical description of the
hydrogen atom, the most probable distance of the electron from the nucleus is 0.53 x 10 -10 m.
Why are these two statements different?
b) Why is Schrődinger’s wave equation to describe the location of a particle very different from
the description obtained from classical physics?
c) In the quantum mechanical description of an electron what is the physical significance of the
square of the wave function Ψ2?
7.
Give the values for n, l, and ml for a) each orbital of the 2p subshell, b) each orbital in the 5 d
subshell.
8.
What is the maximum number of electrons in an atom that can have the following quantum
numbers: a) n = 2, ms = -1/2; b) n = 5, l = 3; c) n = 4, l = 3, ml = -3; d) n = 4, l = 1, ml = 1.
9.
a) What are valence electrons? b) What are unpaired electrons? c) How many valence electrons
does a P atom possess and how many of them are unpaired?
10.
Represent the electronic configuration of the following elements with an orbital diagram: F, S,
Ar, Ti, and Ni.
11.
Draw a 2pz orbital. Make sure to include a labelled axis or coordinate system on your drawing
and show phasing either as + and – or shaded and not shaded.
12.
What is the uncertainty in the position of an electron whose speed is known with an uncertainty
of 1 m/s.
13.
How does Valence bond theory describe the bonding in a) HCN and b) C2H4 (ethylene)? Sketch
and label the atomic and/or hybrid orbitals that overlap. Clearly show phasing and occupancy of
each orbital. How many σ-bonds and how many π-bonds (if any) have you formed in each
molecule?
14.
Given below is the molecular orbital diagram for diatomic species of the first period. Assume the
species H2- was postulated to exist, a dihydrogen anion.
a) How many electrons does this species possess?
b) Show how the electrons occupy the molecular orbital diagram below.
c) What is the bond order in H2- ?
d) Would you expect a bond length longer or shorter as that in dihydrogen?
e) Is the species dia- or paramagnetic?
f)
Should H2- exist?
15. Given below is an empty an unlabeled molecular orbital diagram of homonuclear diatomic species
of the second period in the periodic table for atomic number Z equal or greater 8.
a) Label the atomic as well as the molecular orbitals.
b) How many of the molecular orbitals are bonding and how many are anti bonding?
c) How does MO theory describe the bonding in fluorine gas? Fill the MO diagram with the
appropriate number of electrons. What is the bond order in F2?
d) Is F2 diamagnetic or paramagnetic?
16. Why does the conductivity of a semiconductor such as silicon increase with temperature?
Formulas and constants
pV = nRT
piVi(Ti)-1 = pfVf(Tf)-1
Ptotal = p1 + p2 + p3 + .... + pn
[p + n2a/V2][V – nb] = nRT
Vmol = 22.4 L mol-1 at STP (1 atm = 101.325 kPa and 273.15 K)
R = 8.3145 L kpa mol-1 K-1
Fundamental wave equation
c = λν
Plank’s equation
E = hν
Heisenberg’s uncertainty principle
ΔxΔp ≥ h/4π
De Broglie’s wave-particle dualism
λ = h/p
Impulse
p = mv
Kinetic energy
Ekin = 0.5mv2
Planks constant
h = 6.626 10-34 Js
Avogadro’s number
Na = 6.022 x 1023 mol-1
Unified atomic mass unit
1 u = 1.660 x 10-27 kg
Mass of electron
me = 9.109 x 10-31 kg
Mass of proton
mp = 1.673 x 10-27 kg
Mass of neutron
mn = 1.675 x 10-27 kg
Speed of light
c = 3 x 108 ms-1
End of formula sheet. The orbital pictures on the next page will not be on the formula sheet!