1 Chapter 7 QUANTUM THEORY & ATOMIC...
Transcript of 1 Chapter 7 QUANTUM THEORY & ATOMIC...
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Chapter 7 QUANTUM THEORY & ATOMIC
STRUCTURE
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7.1 The Nature of Light
• Most subatomic particles behave as PARTICLES and obey the physics of waves.
• Light is a type of electromagnetic radiation
• Light consists of energy particles called photons that travel as waves.
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Wavelength (λ) The distance a wave travels in one cycle The distance between two corresponding points
on a wave Units are meters (m) or commonly nanometers
(nm = 10-9 m)
The Wave Nature of Light
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Frequency (ν) The number of wave cycles that move through a
point in space in 1 sescond Units are hertz (Hz) which are the same as
inverse seconds (1/s)
The Wave Nature of Light
Long wavelength --> low
frequency
Short wavelength --> high
frequency
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The Wave Nature of Light
Amplitude - The height of the crest (or depth of a trough) - Indication of the light intensity or brightness
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Long wavelength --> low freq.
Short wavelength --> high freq.
The Wave Nature of Light
wavelength
wavelength Node
Speed The distance the wave moves per unit time (m/s) The product of its frequency (cycles per second)
and wavelength (m/s)
• = c
In a vacuum, speed of light: c = 3.00 x 108 m/sec
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Electromagnetic Spectrum arranges wavelength from shortest to longest
arranges frequency from highest to lowest
shows visible light with wavelengths from 400–700 nm
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Wavelength (), Frequency () & Energy (Ephoton)
= C C = 3.00 x 108 m/s (speed of light)
h = 6.626 × 10-34 J.s (Planck’s constant)
Photons are packets of light energy
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Red light has = 700. nm; calculate the frequency and energy of a photon.
Freq = 3.00 x 108 m/s
7.00 x 10-7 m 4.29 x 1014 sec-1
700 nm • 1 x 10 -9 m
1 nm = 7.00 x 10 -7 m
Ephoton = h•
= (6.63 x 10-34 J•s)(4.29 x 1014 s-1)
= 2.85 x 10-19 J per photon
Problem
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Figure 7.6 Familiar examples of light emission related to
blackbody radiation.
Lightbulb filament Smoldering coal Electric heating element
The Particle Nature of Light Black body radiation
A solid object emits visible light when it is heated to
about 1000 K. The intensity ) of the light changes as
the temperature changes.
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The Particle Nature of Light Black body radiation &
the Quantum Theory of Energy
- Any object (including atoms) can emit or absorb
only certain quantities of energy.
- Energy is quantized; it occurs in fixed quantities,
rather than being continuous. Each fixed quantity of
energy is called a quantum.
- An atom changes its energy state by emitting or
absorbing one or more quanta of energy.
DE = n • h • n can only be a whole number
h = 6.6262 x 10-34 J•s (the Planck’s constant) Max Planck
(1858-1947)
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Problem
Ephoton = h•
= (6.63 x 10-34 J•s)(4.29 x 1014 s-1)
= 2.85 x 10-19 J per photon
E per mol =
(2.85 x 10-19 J/ph)(6.02 x 1023 photons/mol)
E = 171.6 kJ/mol
Calculate the energy of 1.00 mol of photons of red
light (wavelength 700. nm, frequency 4.29 x 1014
sec-1).
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7.2 Atomic Spectra
•Excited atoms can emit light characteristic of that element.
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Spectrum of White Light
White light (sunlight, or light from regular light
bulbs) that passes through a prism
is separated into all colors that together are
called a continuous spectrum gives the colors of a rainbow
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Line Spectra of Excited Atoms & the Rhydberg Equation
• Excited atoms emit light of only certain wavelengths
Line Spectrum of Excited Hydrogen Gas
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Line Spectra of Other Elements in the Gas Phase
Line Spectra of Excited Atoms & the Rhydberg Equation
The wavelengths of emitted light are specific for
the element.
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Three series of spectral lines of atomic hydrogen.
The Rydberg Equation
is wavelength of the line
R is Rydberg’s constant: 1.0967776 x 107 m-1
n1 and n2 are positive integers with n2 > n1
for the visible series, n1 = 2 and n2 = 3, 4, 5, ...
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The Bohr Model of Hydrogen Atom
The H atom has only certain energy
levels, which Bohr called stationary states.
- Each state is associated with a fixed circular orbit of the electron around the nucleus.
- The higher the energy level, the farther the orbit is from the nucleus.
- When the H electron is in the first orbit, the atom is in its lowest energy state, called the ground state.
Bohr’s atomic model postulated the following:
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The atom does not radiate energy while in one of its stationary states.
The atom changes to another stationary state only by absorbing or emitting a photon.
ΔE = Efinal Einitial
- The energy of the photon (h) equals the difference between the energies of the two energy states.
Ephoton = ΔE = h
When the E electron is in any orbit higher than n = 1, the atom is in an
excited state.
The Bohr Model of Hydrogen Atom
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Features of the Bohr Model Quantum numbers are integers: n = 1, 2, 3, …
Radius of electron orbit directly relates to the
electron’s energy: the lower the n value, the
smaller the electron orbit, and the lower the
energy level.
If electrons are in quantized
energy states, then ∆E of
states can have only
certain values. This
explains sharp line spectra.
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Features of the Bohr Model
Ground state: when the electron is in the lowest
possible orbit, which is closest to the
nucleus.
Excited state: when the electron is any orblt
farther from the nucleus.
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Absorption when H atom absorbs a photon whose energy equals the difference between the lower and higher energy levels, then the electron moves to the higher orbit. Emission when H atom in a higher energy level returns to a lower energy level, then the atom emits a photon whose energy equals the difference between the two levels.
Features of the Bohr Model
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The Bohr explanation of three series of
spectral lines emitted by the H atom
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The Energy Levels of the Hydrogen Atom
For an energy level n:
For a transition between two energy levels
The Bohr Equation:
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Problem
Solution:
Energy of transition:
∆E = Efinal - Einitial = -2.18 x 10 -18 J [(1/12) - (1/2)2]
= -1.635 x 10-18 J ==> EMISSION PROCESS
Energy of emitted light
Ephoton = hC/ = 1.635 x 10-18 J
Wavelength of this light: = 121.6 nm
This is exactly in agreement with experiment!
What is the wavelength corresponding to the
transition of electron from n =2 to n = 1?
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7.3 The Wave-Particle Duality of
Matter and Energy Matter and Energy are alternate forms of the same entity.
E = mc2
All matter exhibits properties of both particles and waves.
Electrons have wave-like motion and therefore have only
certain allowable frequencies and energies.
Matter behaves as though it moves in a wave, and the
de Broglie wavelength for any particle is given by:
m = mass in kg
u = speed in m/s muhλ
L. de Broglie
(1892-1987)
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Problem Determine the de Broglie wavelength of
(a) an electron with a speed of 1.00 x 106 m/s.
[electron mass = 9.11 x 10-11 kg].
(b) a lithium atom moving at 2.5 x 105 m/s
Solution:
(a)
(b)
mxJ
smkg
smxkgx
sJx
mv
h 1022
631
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1027.71
/.1
)/1000.1)(1011.9(
.10626.6
mass of a lithium atom:
gxatomsLix
mol
molLi
g 23
2310152.1
10023.6
1
1
941.6
mxJ
smkg
smxkgx
sJx
mv
h 1322
526
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103.21
/.1
)/105.2)(10152.1(
.10626.6
This wavelength is within the range of g-rays (10-12 – 10-17 m)
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7.4 The Quantum-Mechanical Model
of the Atom - Electron behaves simultaneously as a wave and a
particle. The matter-wave of the electron occupies the space
near the nucleus and is continuously influenced by it.
- The Schrödinger wave equation allows us to solve for the
energy states associated with a particular atomic orbital. The
wave function (or atomic orbital) is a mathematical
description of the electron’s matter-wave in 3-D — the region of
3D-space within which an electron is most likely to be found,
and NOT the path the electron follows.
- The square of the wave function 2 gives the probability
density, a measure of the probability of finding an electron of
a particular energy in a particular region of the atom. It
describes the shape of an orbital.
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Figure 7.16
Electron probability density in
the ground-state H atom.
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Quantum Numbers of an Atomic Orbital
An atomic orbital is specified by three quantum numbers:
n (principal): 1, 2, 3, ….
l (angular momentum): 0 to n-1
ml (magnetic): -l to 0 to +l
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Quantum Numbers
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Quantum Numbers & Energy Levels The energy states and orbital of an atom are
associated with one or more quantum numbers:
Level (or shell) given by the n values. Each designates
the energy (size) of the electron. The lower the n value means the greater probability that the electron is closer to the nucleus.
Sublevel (or subshell) given by the l values. Each
designates the orbital shape with a letter:
l = 0 is an s sublevel l = 1 is a p sublevel
l = 2 is a d sublevel l = 3 is an f sublevel
Name a subshell by its n value with the designated subshell letter.
Orbital given by the ml values. Each designates the orbital orientation.
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Problems
a) What are the n, l, ml values for the 3d and 5f sublevels?
b) Identify the incorrect quantum numbers:
n l ml Sublevel
name
a) 2 1 +1 2p
b) 1 0 -1 1s
c) 5 2 0 5d
c) Fill in the quantum numbers or sublevel names:
n l ml Sublevel
name
a) 4 1 +1 ?
b) ? 3 -2 6f
c) 5 0 ? 5s
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Shapes of Atomic Orbitals
s orbital l=0, no node
p orbital l=1, 1 nodal
plane
d orbital l=2, 2 nodal
planes
f orbital l=3, 3 nodal
planes
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Size and Shape of Atomic Orbitals
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Figure 7.21 Energy levels of the H atom.
The Special Case: Energy Level in Hydrogen Atom
Hydrogen is
the only atom
whose energy
state depends
completely on
the principal
quantum
number n.