Title: Ch 7: Quantum Theory and Atomic Structure
1Ch 7 Quantum Theory and Atomic Structure
7.1 The Nature of Light 7.2 Atomic Spectra 7.3
The Wave - Particle Duality of Matter and
Energy 7.4 The Quantum - Mechanical Model of the
Atom
2Electromagnetic Radiation
- WAVELENGTH - The distance between identical
points on successive waves. ( ? ) - FREQUENCY - The number of waves that pass through
a particular point per second. (?) - AMPLITUDE - The vertical distance from the
midline to a peak, or trough in the wave.
v c
???
3(No Transcript)
4Relationship between ? and ?
5Light has wave characteristics
6Figure 7.4
Different behaviors of waves and particles.
7The diffraction pattern caused by light passing
through two adjacent slits.
Figure 7.5
8Light has wave characteristics
c speed of light 3.00 x 108 m/s
Wavelength (meters)
1
Visible
Radio
TV
X-rays
Infrared
Microwaves
700 nm
400 nm
600 nm
500 nm
9Two-minute problem
- How does the wavelength of a cell phone microwave
- (3 GHz) compare to a 10 m radio wave?
- A. 100 times longer
- B. 10 times longer
- C. 10 times shorter
- D. 100 times shorter
-
10Light has particle characteristics
- Photoelectric effect
- Threshold frequency
11Light particles are called photons
- E hn
- c ln
- High energy
- frequency high
- wavelength short (small)
- Low Energy
- frequency low
- wavelength long (large)
- Sample problem The lower wavelength limit of
visible light is about 400 nm. What is the
energy of this radiation?
12Matter has particle characteristics
- Defined trajectory
- At least on macroscopic level!
13Matter has wave characteristics
- De Broglie wavelength
- ? h/mv
- Electron microscopy, neutron diffraction
- Observed only for tiny objects (why?)
14Matter has wave characteristics
The diffraction pattern caused by a beam of
electrons passing through two adjacent slits.
15Two-minute problem
- How does the wavelength of a neutron compare to a
electron of the same speed? - A. 2000 times longer
- B. 20 times longer
- C. 20 times shorter
- D. 2000 times shorter
-
16Worksheet break
17Quantization of Energy
- Max Planck (1900)
- Proposed that energy can be released or absorbed
by atoms in chunks of some minimum size - quantum smallest quantity of energy that can be
emitted or absorbed as electromagnetic radiation - Energy is quantized
- values of energy are restricted to certain
quantities - E h?
- where E Energy (J)
- h Plancks constant
- 6.63 x 10-34 Js
- ? frequency (Hz or 1/s)
18Continuous and Line Spectra
- Continuous spectrum
- a spectrum containing light of all wavelength
- examples rainbow, prism
- Line spectrum
- a spectrum showing only certain colors or
specific wavelength of light
19Bohrs Model of Hydrogen
- Niels Bohr (1913)
- Offered a theoretical explanation of line spectra
- combined classical physics and quantum theory
- proposed that only orbits of certain radii,
corresponding to certain definite energies, are
permitted - an electron in a permitted orbit has a specific
energy and is said to be in an allowed energy
state
20Bohr Model (cont.)
- Energy Level Postulate
- electrons can have only specific energy values
- where E Energy (J)
- RH Rydberg constant
- 2.18 x 10-18 J
- n energy level
- note energy is negative!
21Energy Levels
22Bohr Equation
- Used to describe the energy that is absorbed or
emitted when an electron moves from one energy
level to another - negative ?E light is emitted
- positive ?E light is absorbed
23Two-minute problem
- which of the four electron transitions shown in
the figure to the right produces the shortest
wavelength line in the hydrogen emission spectrum
24The Heisenberg Uncertainty Principle
D x m D u
25Sample Problem 7.4
Applying the Uncertainty Principle
PLAN
The uncertainty (Dx) is given as 1(0.01) of
6x106m/s. Once we calculate this, plug it into
the uncertainty equation.
SOLUTION
Du (0.01)(6x106m/s) 6x4m/s
6.626x10-34kgm2/s
Dx
10-9m
4p (9.11x10-31kg)(6x104m/s)
26Quantum Mechanics and Atomic Orbitals
- Schrodinger (1926) proposes a theory that
incorporates the wavelike and particle-like
behavior of the electron - provides information about the electrons
location in an allowed energy state - probability wavefunction ?2
- atomic orbitals describe the distribution of
electrons in space - defined by four quantum numbers
27Quantum Numbers
- Principle quantum number (n)
- Defines the size and energy of an orbital
- Positive integral values
- as n increases, the size and energy increases
- Angular momentum quantum number (l)
- Defines the shape of an orbital
- Integral values from 0 to n-1
- Value of l is designated by a letter
- Value of l 0 1 2 3
- Letter used s p d f
28Quantum Numbers (cont.)
- Magnetic quantum number (ml)
- describes the orientation of the orbital in space
- Values range from -l to l
- Spin quantum number (ms)
- describes the direction the electron is spinning
29Sample Problem
- Considering the limitations on values for the
various quantum numbers, state whether an
electron can be described by each of the
following sets. If a set is not possible, state
why. - n 2, l 1, ml -1
- n 1, l 1, ml 1
- n 3, l 1, ml -3
30Relationship between Quantum Numbers
- electron shell
- a collection of orbitals with the same value of n
- subshell
- one or more orbitals with the same set of n and l
values - Pattern
- each shell is divided into the number of
subshells equal to the principle quantum number,
n. - each subshell is divided into orbitals equal to
the number of ml values
31Electron Probability and Shape of Orbitals s
orbitals
32Electron Probability and Shape of Orbitals p
orbitals
33Orbital Diagrams
- diagram used to show how the electrons are
distributed among the orbitals of a subshell - orbital is represented by a circle or square
- electrons represented by an arrow
- Example Hydrogen
34Pauli Exclusion Principle
- An orbital can hold at most two electrons, and
then only if the electrons have opposite spin - each electron is an atom has a unique set of
quantum numbers - Example Helium
35Sample Problem
- Based on the Pauli exclusion principle, which of
the following orbital diagrams are possible?
36Magnetic Properties
37Diagonal Rule (Aufbau Principle)
1s 2s 2p 3s 3p 3d 4s 4p 4d
4f 5s 5p 5d 5f... 6s 6p 6d
6f... 7s 7p 7d 7f...
38Hunds Rule
- the lowest energy arrangement is obtained by
putting e- in separate orbital of a subshell with
parallel spin before pairing e- - Example Carbon
- Z 6 1s2 2s2 2p2
- You try Oxygen
- Z 8
39Sample Problem
- Electron Configuration of Vanadium
- Quantum Numbers
- n
- l
- ml
- ms
1s 2s 2p
3s 3p 4s
3d
40Exceptions
- Some transition metals do not follow the diagonal
rule! - Example chromium
- Z 24
- diagonal rule
- 1s2 2s2 2p6 3s2 3p6 4s2 3d4
- -filled and half-filled orbitals are more stable
than unevenly filled orbitals. - true electron configuration
- 1s2 2s2 2p6 3s2 3p6 4s1 3d5
41The Periodic Table
- Dmitri Mendeleev
- designed periodic table in which the elements
were arranged in order of increasing atomic mass - Henry Moseley
- designed periodic table in which the elements
were arranged in order of increasing atomic
number - Periodic law
- the physical and chemical properties of the
elements are periodic functions of their atomic
numbers
42Periodic Trends
- Atomic Radius
- Why?
- Ionization Energy
- Why?