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CHEMISTRY 214
QUESTIONS
1. a) Calculate the rotational constant B(cm-1) for the 12C16O molecule. (req = 1.124Å)
(3)
b) There are equal populations of the initial (ground) atates that give rise to the third
and fourth lines in the rotational absorption spectrum of 12C16O. Determine the
temperature (K) at which the spectrum was obtained.
(5)
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CHEMISTRY 214
2. a) For a particle in a cubic box (a = b = c) determine the degeneracy of the 75h2/8ma2
energy level.
(3)
b) The dimension of the box above is altered in the z-direction: c → a/2. Determine
the energy, degeneracy and the quantum numbers of the state(s) that derive from the
original 27h2/8ma2 energy level.
(5)
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CHEMISTRY 214
3. The virial theorem in a form in which: ET = -EK would apply to which of the
following systems. Justify briefly.
a) a particle in a 3D cubic box
b) a Bohr atom
c) a rotating diatomic molecule
d) a hydrogen-like atom from the S-equation
e) a harmonic oscillator
f) planetary e.g. Earth/Sun systems
(6)
4. A photoactive metal is irradiated with light at 440 nm and photoelectrons with a
velocity of 6.11 x 105 ms-1 are produced. Wha is the longest radiation wavelength
(nm) that would result in the production of photoelectrons?
(4)
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CHEMISTRY 214
5. For an electron in a 2p-orbital in carbon a Zeff = +3.14 is derived from energy
minimization. If the electron were out at the van der Waals distance from the nucleus
(1.7Å, i.e. e.g. one-half the distance between 2 stacked base pairs in DNA), then:
a)
b)
c)
d)
e)
6 > Zeff > 3.14
Zeff = 3.14.
3.14 > Zeff ≥ 1.0
Zeff ≥ 6
Zeff = 6
Justify briefly.
(4)
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CHEMISTRY 214
6. From the radial wavefunction R(r) for an electron in a 2pZ orbital:
R(r) =
1
r r 2ao
e
2 6 ao a o
find the most probable distance from the nucleus of finding the electron (assuming
spherical symmetry).
(5)
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CHEMISTRY 214
7. For a rotor with masses m1 and m2 located at distances r1 and r2 from the center of
mass show that I (moment of inertia) can be represented as a reduced mass rotating at
a distance r about a fixed point. (r = the distance between m1 and m2 ).
(6)
8. Calculate the change in potential energy resulting from an electronic transition in a
Bohr atom from: n = 3 → 2. (Rydberg constant = 109,700 cm-1)
(4)
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CHEMISTRY 214
9. Write spectroscopic term symbols for:
a) Na (Z = 11) KL3s1
b) Co (Z = 27) KL3s23p63d74s2
(5)
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McGILL UNIVERSITY
FACULTY OF SCIENCE
CHEMISTRY 214
MIDTERM EXAM 2 HOURS
Examiner: Dr. W.C. Galley
March 3, 2006
6:30-8:30 PM
________________________________________
SURNAME (Print)
INITIALS
_______________________
STUDENT NUMBER
CONSTANTS + CONVERSIONS
R (gas constant)………….…...8.314 J mol-1K-1, 8.314x107 erg mol-1K-1
0.083l4 atm mol-1K-1
k (Boltzmann constant…..…...1.381 x 10-23 JK-1
0.695 cm-1K-1
h (Planck’s constant)………...6.626 x 10-34 Js
e (electronic charge)……..…..1.6027 x 10-19 C
No (Avogadro’s #)…………...6.022 x 1023 mol-1
Me (electron rest mass)…...….9.1094 x 10-31 kg
Mp (proton rest mass)……..…1.673 x 10-27 kg
c(speed of light)……………...2.997 x 108 ms-1, 2.997 x 1010 cm s-1
Å(angstrom)………………….1.0 x 10-10m, 1.0 x 10-8 cm
o…………………………….8.758 x 10-12 C2N-1m-2
(permittivity of empty space)
4o = 1.11 x 10-10 C2N-1m-2
INSTRUCTIONS
1. There are 9 questions on the exam.
2. Answer all questions on the exam paper.
3. The total value is 50 marks with the marks
for each question in the margin.
5. All work must be carried out on the exam.
6. No extraneous material, e.g. formula sheet,
allowed.
7. Calculators with alphanumeric memory are
not permitted.
8. RETURN THE EXAMINATION PAPER
WITH YOUR NAME & ID NUMBER ON
IT.
8
QUESTION
VALUE
1
2
3
4
8
8
6
4
5
6
7
8
9
TOTAL
4
5
6
4
5
50
MARK