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Unformatted text preview: Chem 210 Chapter 6B / WANG
Chapter 6.4 through 6.5
Electronic Structure of Atoms Diffraction patterns of x-rays (“waves” of “light”)
and electrons (“particles” of “matter”).
(“particles” 6.1 Wave Nature of Light
6.2 Quantized Energy & Photons
6.3 Bohr’s Atomic Model 6.4 Wave Behavior of Matter
6.5 Quantum Mechanics and Atomic Orbital
Online practice goal: achieve >90% in Chap 6.
homework 5 and Quiz 5
http://wps.prenhall.com/esm_brown_chemistry_8e/51/13242/3390185.cw/index.html EOC (end-of-chapter problems)
(end-of6.14, 6.16, 6.36, 6.44, 6.54, 6.64, 6.68, 6.74
(textbook page 253-255)
due date – Wed. Sept. 23rd Matter Waves
The idea of particle-wave duality of light was
boldly extended to matter, such as electrons,
by de Broglie, who proposed the existence of
“matter waves”, for which he received the
1929 Nobel Prize in physics. de Broglie’s equation: λ = h
mv • mv (momentum): particle property
• λ: w ave property
• h: Planck’s constant Experimental proof of Matter Waves
Diffraction pattern of electron beams.
As visible light allows
our eyes to detect
objects by diffraction
patterns at the edges,
reveal objects on the
cellular and atomic
levels, as the λ values of
electron beams are 100 100
5000 times smaller than
visible light. Fall 2009 UM-SJTU JI Electron micrograph
of cotton fibers. x-ray diffraction of
aluminum foil electron diffraction of
aluminum foil Electrons behave as if they are “waves”! Matter Waves
Wavelength (λ) of a particle depends on
its mass (m) and velocity (v).
Question: Calculate the wavelength of an electron
with mass of 9.0×10-31 kg traveling at a velocity of
6.7×106 m/s. Question: Calculate the wavelength of a ball with
mass of 0.20 kg traveling at a velocity of 25 m/s. Matter Waves
Why is it that we do not notice the wave
characteristics of matter in general? • wavelength is too small (~10-34 m)
• frequency is too high (~ 1042 Hz)
• Similar reason why we can’t “see” x-ray
wavelength ~10-10 m
Frequency ~ 1018 Hz Page 1 Chem 210 Chapter 6B / WANG
Heisenberg’s Uncertainty Principle
λ = h /mu
The de Broglie Wavelengths of Several Objects
Substance Mass (g) slow electron Speed (m/s) 9x10-28 λ (m)
7x10-4 1.0 fast electron 9x10-28 5.9x106 1x10-10 alpha particle 6.6x10-24 1.5x107 7x10-15 1.0 0.01 7x10-29 142 25.0 2x10-34 one-gram mass
Earth 6.0x1027 3.0x104 4x10-63 Heisenberg’s Uncertainty Principle
• On the mass scale of atomic particles,
we cannot determine exactly the
position, direction of motion, and speed
• The product of the uncertainty in the
position (∆ x) and that of the momentum
(∆p) are greater or equal to h/2π.
h/2 ∆x ⋅∆p ≥ h
incorporated the idea of
particleparticle-wave duality of an
electron in the H atom by
proposing a differential
equation for which he
received the Nobel Prize in
1933. Fall 2009 UM-SJTU JI Based on the dual nature of matter,
Heisenberg formulated his
uncertainty principle. At age 32, he
received the 1933 Nobel Prize in
physics for this work.
Heisenberg’s principle states that
particle - wave duality
fundamentally limits how precisely
we can know both the location and
the momentum of any matter.
The uncertainty becomes
proportionally important only when
we study matters at the subatomic
level. Quantum Mechanical Model of the Atom
Heisenberg’s and de Broglie’s work led to
the replacement of Bohr’s planetary atomic
model by the Quantum Mechanical (QM)
• in which the precise location of an
electron is uncertain when its
momentum (or kinetic energy) is known
• And, it is impossible for an electron to
move in well-defined orbits about the
wellnucleus. Schrödinger’s wave equation • Each particle is represented by a wave function,
Ψ , with precisely determined momentum, but
totally uncertain position. The momentum
corresponds to the allowed energy level of
• Ψ 2 represents the probability of finding the
electron at a certain location.
– a specific distribution of electron density in
space with characteristic shape and volume. Page 2 Chem 210 Chapter 6B / WANG Ψ2 of an s orbital
Ψ2 = region in space
where an electron is
most likely found.
S orbital shows
occurs in a spherical
the nucleus. Ψ2 of Atomic Orbitals in the QM Model
Ψ 2 of p orbitals Ψ2 = region in
space where an
electron is most
likely found. Ψ 2 of d orbitals Higher density occurs
closer to the nucleus Size of Atomic Orbitals
• Orbitals vary in size or the
volume occupied in space.
• QM uses the principal quantum
number, n, to indicate this size.
• Smallest orbital size has n = 1.
• Orbital becomes larger as n
increases to 2, 3, 4, etc.
• All orbitals w ith the same n
value is called an electron
shell. Shape of Atomic Orbitals
• Designated by the angular momentum
quantum number, l.
• Each value of l corresponds to a letter:
all designate certain shapes.
– s (l = 0), spherical shape
– p (l = 1), dumbbell shape
– d (l = 2), two shapes, one is like a
– f (l = 3),
– g (l = 4),
– h (l = 5), etc. Fall 2009 UM-SJTU JI 1s 2s 3s All are spherical, though size increases with
quantum number, n. p sub-shells are dumbbell shaped; they
orient differently in the 3-D space. Ways to represent one of
the 2p orbitals.
Three 2p orbitals
shown together. Page 3 Chem 210 Chapter 6B / WANG
One of the seven
orbitals. 3d orbitals.
orbitals. five 3d orbitals
shown together. Shape of Atomic Orbitals:
(continued) • Orbitals of the same l are called a sub-shell.
• Each electron shell has different number of
– Shell n = 1: one sub-shell
– Shell n = 2: two sub-shells 2s & 2p
sub– Shell n = 3: three sub-shells 3s, 3p, 3d
sub– Shell n = 4: four sub-shells 4s, 4p, 4d, 4f
sub– Etc. Possible sub-shells from shell n = 1 to n = 7
Each higher shell has one more variety of
5s 7p 7d 7f 7g 7h 6p 6d 6f 6g 6h 5p 5d 5f 5g 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s Orientation of Atomic Orbitals
•Orbital has specific orientations in space,
each designated by the magnetic quantum
number, m. Possible m values depend on the l
value (shape). For example,
•p orbitals (l = 1) has
3 possible m values = (-1, 0, +1)
2px, 2py 2pz each is perpendicular to others.
others. Fall 2009 UM-SJTU JI 7i shape variations Orientation of Atomic Orbitals (continued)
d orbitals (l = 2) has 5 possible m values
(-2, -1, 0, +1, +2)
dxy, dyz and dzx each sits
on a plane perpendicular
dx2-y2 sits on the x & y
dz2 is on the z axis & has
a ring on the xy plane.
–Depending on how x, y, z
axes are defined, the above
d orbital designations are
each linked to a specific m
value: (-2, -1, 0, +1, +2). Page 4 Chem 210 Chapter 6B / WANG
Question: How many orientations are possible
for the s orbital based on its quantum
numbers, l and m? Explain. The f Orbitals Question: Tell how many orientations are possible
for f orbitals. Explain your answer. ml: -3, -2, -1, The Hierarchy of Quantum Numbers for Atomic
(size, energy) integer
(1, 2, 3, ...)
momentum, l 0 to n-1
(shape) Magnetic, ml
(orientation) Quantum Numbers 1 2 0 0 0 3 1 0 0 1 2 0
-1 0 +1 -1 0 +1
-2 -1 0 +1 +2 Since each atomic orbital can be
occupied by 2 electrons ….
A 4th quantum number is needed to label
each electron: Spin quantum number.
ms = -½ or +½
Denoting the direction of
(1,0,0, +½) and (1,0,0, -½)
identify the two electrons
in the Helium atom at
ground state. Fall 2009 UM-SJTU JI 0, +1, +2, +3 Capacity of Atomic Orbitals
Each orbital has 2e capacity.
total capacity of 6e from 2px, 2py, 2pz
• 3 orbitals, each can hold 2 electrons.
total capacity of 10 e from 5 orbitals.
How many electrons can occupy 4f?
• 4f has 7 possible orientations (orbitals),
each can hold 2e
total of 14 electrons! Summary
Summary of Quantum Numbers
Principal quantum number: n = 1, 2, 3, …
Value denotes an electron shell
azimuthal quantum number: l = 0 to n-1
nValue denotes an electron subshell
Magnetic quantum number: ml = -l to +l
Value denotes the orientation of an electron
Spin quantum number: ms = -½ or +½
Each value denotes the direction of electron
spin Page 5 Chem 210 Chapter 6B / WANG QM model of the atom
Question: Compare and contrast these terms
used to describe electronic structure: orbit
versus orbital. Quantum Numbers and Atom Orbitals
Question: Give the set of 3 quantum
numbers for the:
(a)3s orbital: Similarities:
Electrons are located outside nucleus
quantized energy level
Larger size, greater energy
Orbital - QM model
a wave function Ψ
Ψ2 ~ electron density
Ψ2 has different shapes & orientations Fall 2009 UM-SJTU JI (b) 4px orbital:
orbit – Bohr’s model
a circular path.
all circular Page 6 ...
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