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Chemistry 1B Fall 2013
Lectures 3-4
Chemistry 1B
Fall 2013
What to do ??
lectures 3-4
(pp. 536-541, *(541-547), 548-556 )6th
[537-542, *(543-549), 549-557]7th
October 2 Atomic spectrum of Hydrogen. The Bohr Atom
4 Quantum Mechanical model of the Hydrogen atom. Atomic orbitals
7 Atomic orbitals (continued). Many electron atoms, orbital energies
invent quantum mechanics !!!
chap 12 p531-537
chap 12 p537-542, 549-553 1st HW due 10/6
chap 12 p553-560
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quantization of energy
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Solvay Conference 1927
Ephoton= h
absorption and emission spectra of hydrogen atom
The mid-1920's saw the development of the quantum theory, which had a profound effect on chemistry. Many theories in science are first
presented at i nternational meetings. This photograph of well-known scientists was taken at the international Solvay Conference in 1927. Among
those present are many whose names are still known today. Front row, left to right: I. Langmuir, M. Planck, M. Curie, H. A. Lorentz, A.
Einstein, P. Langevin, C. E. Guye, C. T. R. Wilson, O. W. Richardson. Second row, left to right: P. Debye, M. Knudsen, W. L. Bragg, H. A.
Kramers, P. A. M. Dirac, A. H. Compton, L. V. de Broglie, M. Born, N. Bohr. Standing, left to right: A. Piccard, E. Henriot, P.
Ehrenfest, E. Herzen, T. De Donder, E. Schroedinger, E. Verschaffelt, W. Pauli, W. Heisenberg, R. H. Fowler, L. Brillouin.
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wave-particle duality
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‘fuel’ for quantum mechanicians
• diffraction of electrons(Davisson-Germer Experiment; p. 530)
• De Broglie relationship (p. 528) (HW#1 12.30,12.33)
• What is “meaning” of electron wave??
(http://phys.educ.ksu.edu/vqm/html/doubleslit/index.html)
• Wavelengths of “ordinary” objects
(p. 528, example 12.2) Silberberg Table 7.1 (HW#1 prob S2)
• Compton Experiment
• Heisenberg uncertainty principle (p. 539)
boing!! (HW#1 12.45)
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Chemistry 1B Fall 2013
Lectures 3-4
quantum mechanics: WEIRD
goals of lectures 3-4
the quantum mechanics of the hydrogen atom
(nucleus + electron)
• what is the quantum mechanical equation that determines the
properties of electrons in atoms and molecules?
• what are the “allowed” (stationary) states in which the electron in
an hydrogen atom can exist ?
• what will be the energy of an electron in a given state ?
• what are the “probability waves” (orbitals) that describe the
where an electron in a given state will be “found”?
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Quantum Jujitsu π Quantum Mechanics
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Bohr model vs Quantum
• Bohr model got the energies of allowed levels correctly
• However Bohr model assumed electrons traveling around
nucleus in orbits of fixed radius (different radii for different n’s)
and with specific En
• This is inconsistent with the wave properties of electron and
Heisenberg Uncertainty Principle
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what quantum mechanics must “include”
electron orbits: no, no
electron orbitals : si, si
(probability waves)
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Schrödinger equation (see pp 540 and 549)
SCHRÖDINGER EQUATION
• particles have wave-like properties
• some properties, like energy, can only have
certain values (energy is quantized)
• basic equation of quantum mechanics
• the emission or absorption of photons result
in the system going from one state to another
• what does it involve ??
• what does it tell you ??
• where can you learn ALL about it in
upper division chemistry?
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not responsible for pp. (543-549)*, Table 12.1
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Chemistry 1B Fall 2013
Lectures 3-4
hydrogen’s electron waves: the three quantum numbers (pp. 550-551)
segue/review from LECTURE #3
1. Yn,,m possible allowed states ñ waves fo an electron in H atom
2. Allowed values of n, , m
3.
states of given n but various , m have same
energy (are degenerate)
n the principal quantum number
4. Shapes of orbitals, Y, Y2, 4pr2Y2
n- -1 radial (spherical) nodes
 the angular momentum quantum number
m the magnetic quantum number
 angular (planar) nodes
5.
Table 12.1****
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quantum mechanics of the hydrogen atom
(the electron waves in H atom and their physical meaning)
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shapes of orbitals nodal surfaces (identifying orbitals)
radial and angular “nodes” of atomic orbitals
• quantum numbers of “allowed” orbitals
radial node: a spherical shell (of radius r) where Y=0 (and Y2=0) ;
Y has different sign on opposite sides of radial node
table 12.2 and 12.3
angular node: a surface (plane) where Y=0 (and Y2=0);
Y has different sign on opposite sides of angular node
• orbitals and the electron density diagram
• orbital (wavefunction, ) [ can have relative sign, ± values]
d’ rules !!
• electron density (probability, 2) [ 2≥ 0]
an orbital with quantum numbers n, , m  will have
n--1 radial nodes
 angular nodes
n-1 total nodes
and 2+1 components in different orientations
• radial probability distribution (4r2 2)
Fig 12-16 & 12-17 handout figures
(from the different possible m values)
“hold your horses”
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energies of hydrogen orbitals
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shapes of orbitals
•
•
radial and angular “nodes”
• s-orbitals
Fig. 12.18
• p-orbitals
Fig. 12.19 & 12.20
• d-orbitals
Fig. 12.21
for H atom, Z=1
• in hydrogen atom, energy only
depends on n quantum number
Fig. 12.23
• orbital pics in handouts
• the ‘size’ of the orbital is approximated by
WWW orbital viewers
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Chemistry 1B Fall 2013
Lectures 3-4
properties associated with n, , m (HW#2 Prob x)
Zuo, Kim, O’Keeffe and Spence, Nature, 1999.
• n
– energy
– radial and total nodes
– average distance from the nucleus
• 
– angular velocity (angular momentum)
– shape (angular nodal planes )
• m
– orientation of orbital
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a sighting !!!!!!
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Larsen
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no not aliens !!!
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just d-orbital electrons
WHEW !!!
end of lectures 3-4
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Chemistry 1B Fall 2013
Lectures 3-4
Silberberg: figure 7.16
Zumdahl: figure 12.23
R2ºY2
R2ºY2
Zumdahl: figure 12.16-17
Y2
radial probability 4pr2Y2
contour
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Silberberg: figure 7.16
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Zumdahl Tables 12.2 and 12.3
Y2 = probability density in small volume at (x,y,z) [(r,q,f)]
probability of finding electron at position (r,q,f)
4pr2Y2= radial probability
add up density in ALL small volumes at distance r
total probability density in small spherical shell at distance r from nucleus
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probability of finding electron at r (irrespective of its q and f)
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Zumdahl: figure 12.18 and Silberberg: figure 7.17
representations of orbitals
90 % contour
with sign
+
Y
Y vs r
contour with sign
-
+
density of dots
Y
Y vs r
probability
3-D shading
pr2Y
radial
probability
density of dots
prY
vs r
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Chemistry 1B Fall 2013
Lectures 3-4
0
Radial probability distribution
(sum of all 2)
0 2 4
r (10–10 m)
Radial probability distribution
(sum of all 2)
n=2
l=0
n=1
l=0
2
4 6 8
r (10–10 m)
n=2
l=0
0 2 4
r (10–10 m)
0
A 1s orbital
B 2s orbital
n--1=3-2-1=0 radial nodes
2
4
6 8 10 12 14
r (10–10 m)
n=3
l=0
0
2 4 6 8
r (10–10 m)
Zumdahl Figs 12-19, 12-20
n=3
l=0
0
Radial probability distribution
(sum of all 2)
n=1
l=0
Probability density
(2)
Probability density
(2)
Probability density
(2)
Silberberg: figure 7.19
2
4
6 8 10 12 14
r (10–10 m)
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C 3s orbital
Silberberg: figure 7.18
Silberberg Table 7.1
note mass in g, need to use kg for mvl=h
(l correct in table)
1 angular
x
3px
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Zumdahl figure 12.21
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Uncertainty and measurement
y
z
x
x
3dxy
3dx2-y2
3dz2
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