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Unformatted text preview: Chem 210 Chapter 6 A / WANG
Waves
Characteristics
Characteristics Chapter 6.1 through 6.3
Electronic
Electronic Structure of Atoms 1. UpandDown motion
Upand• Frequency or
wavelength
• Amplitude or
intensity 6.1 Wave Nature of Light
6.2 Quantized Energy and Photons
6.3 Bohr’s Atomic Model / intro to
Quantum Mechanical Atomic Model
Online practice goal: achieve >90% in Chap 6.
goal:
homework 5 and Quiz 5
http://wps.prenhall.com/esm_brown_chemistry_8e/51/13244/3390683.cw/index.html EOC (endofchapter problems)
(endof6.14, 6.16, 6.36, 6.44, 6.54, 6.64, 6.68, 6.74
(textbook page 253255)
253 due
due date – Wed. Sept. 23rd 2. Forward motion
• Speed or
velocity http://imagers.gsfc.nasa.gov/ Wave Nature of Light
Maxwell proposed(1873) : light consists of
light
electromagnetic waves called:
waves,
electromagnetic radiation.
UpandUpanddown motion composed of 2 waves
composed
perpendicular to each other:
– Electric field + Magnetic field
Magnetic • Forward motion in a
in
vacuum
vacuum moves at the
speed
speed of light: • c = 3.00 x 108 m/sec
3.00 http://math.arizona.edu/~ura/964/
sinclair/diff.html Wave Characteristics of
electromagnetic
electromagnetic radiation How do we know electromagnetic radiation is
composed of waves?
• Electromagnetic radiation shows diffraction
diffraction
patterns characteristic of all waves.
characteristic
waves.
– Two sets of water waves running into each
other will show patterns of destructive and
destructive and
constructive interferences.
constructive interferences.
– Same as rays of light shining through two
tiny holes next to each other.
– We detect common objects by the patterns
patterns
of visible light diffraction along the edges of
diffraction along
these objects.
• Fall 2009 UMSJTU JI • Electromagnetic radiation includes infra red (IR),
includes
ultraviolet (UV), x ray, microwave, gamma ray…..
and visible light.
visible
• Different types of electromagnetic radiation have
electromagnetic
different
different wavelengths, but they all move through
ll
a vacuum at the same speed
vacuum
speed
3.00
3.00 x 108 m/sec http://en.wikipedia.org/wiki/Diffraction Pictures on the left
show typical diffraction
patterns of water
waves going through
slit(s). Note the
diffraction patterns.
Thomas
Young's sketch
of twoslit
twodiffraction,
which he
presented to
the Royal
Society in 1803 Page 1 Chem 210 Chapter 6 A / WANG
Diffraction pattern caused by light passing
light
through two adjacent slits. Wave Characteristics of
electromagnetic
electromagnetic radiation
Further explanation on “electromagnetic waves”.
• Wave characteristics of electromagnetic
radiation come from the periodic oscillations of
periodic
of
its electric and magnetic components.
electric and magnetic components.
– The strengths of electric and magnetic fields
strengths
fields
riseandriseandebb like water waves. Different behaviors of waves and particles. Wave Characteristics of
electromagnetic
electromagnetic radiation Or,
Or, c = λν
Speed of light =
wavelength x
frequency
frequency c=λν
Speed = length / time
(m⋅s1)
Frequency = 1/ time (s1)
Wavelength = length (m,
µm, nm, etc.) Higher frequency ↔
Shorter wavelength Fall 2009 UMSJTU JI Amplitude
(intensity) of a
wave is a
separate
property.
It is independent
of wavelength or
frequency. Page 2 Chem 210 Chapter 6 A / WANG Wavelength (λ) Range of Visible light
λ around 0.4 µm to 0.7 µm
= 400 to 700 nm (1µm = 1000 nm)
(1
= 4000 to 7000 A (1 nm = 10 A)
(1 Frequency (ν) Range of Visible light
Definition of ν, frequency:
frequency:
number
The number of complete waves (cycles) that
passes through a given point in one second.
one
Unit: Cycle per second = sec1 = Hertz (Hz)
sec
Hertz
Visible wavelength range is 400nm – 700 nm.
• at λ = 400 nm
ν=c/λ
(3.00
ν = (3.00 x 108 m sec1) ÷ (400 x 109 m)
sec
ν = 7.50 x 1014 sec1
Hz
ν = 7.50 x 1014 Hz
• at λ = 700 nm
ν = 4.29 x 1014 Hz
Visible light frequency range:
4.29 x 1014 Hz to 7.5x1014 Hz Observation: Coal at 1000 K
Coal
1000 appears red. Filament at
Filament
2000
2000 K appears white. smoldering coal red hot light bulb filament –
white hot Max Planck explained that
“red hot” object releases
releases
mostly lower ν of visible +
lower
Infra red radiation of lower
lower
energy temperature
energy / temperature;
“white” hot object releases
wider
w ider range and higher
and
frequencies at higher
higher
temperature / energy.
energy. Fall 2009 UMSJTU JI Frequency ν ↔wavelength λ
Question: National Public Radio in the U.S.
is heard at FM 91.1. What is the wavelength
of this radio wave?
Hint: FM 91.1 means: 91.1 MHz
= 91.1 x 106 cycles per second
Answer:
λ=? λ=c/ν
= (3.00 x 108 m sec1) ÷ (91.1 x 106 sec1)
= 3.29 m
The wavelength of this radio wave is 3.29 m. Max Planck’s “Quantum”
Max Planck related energy to frequency,
and first used the term quantum in 1900
quantum
to denote “the smallest quantity of
quantity
energy that can be emitted or absorbed
by atoms as electromagnetic radiation.”
electromagnetic
He proposed that energy (E) of a quantum is
proportional to its frequency:
its E = h ⋅ν He was awarded the
1918 Nobel Prize in
Planck’s constant
physics for this work on
h = 6.63 x 1034 Js.
6.63
the Quantum theory.
Quantum theory. Page 3 Chem 210 Chapter 6 A / WANG Einstein’s “Photon”
experimental evidence of
quantum theory
Einstein
Einstein applied (1905)
Planck’s quantum theory
quantum
to explain the photoelectric
photoelectric
effect and received the
1921 Nobel Prize in physics
for this interpretation (NOT
for the relativity theory!).
• PAGE 222 TEXT
TEXT
• Quick Time movie
photo_ef
photo_ef. ParticleParticleWaves Duality: Is light a
Is
wave or a particle?
• Light has wave characteristics –
diffraction patterns of electromagnetic
radiation. Energy of “photon” or “quantum”
E = hν
Find the energy of a quantum of x ray with
ν = 3 x 1018 s1. How much energy is in 1 mole of this type
of photons? Further Observation of light Spectrum
continuous spectrum – Produced by the sun • Light also has particle characteristics photoelectric effect and the quantum
theory.
• Particlewave duality is established
Particlewith respect to light: Line Spectrum –
Produced from atoms (gas) of discharge tubes – It’s both a w ave and a particle! Sun
Sun light or light from heated solids
or
appears white, which separates into
which
a continuous spectrum. Fall 2009 UMSJTU JI Light emitted from heated gases in sodium
gases
or neon lamps or discharge tubes
separates into a Line Spectrum,
Line
unique to each element! Page 4 Chem 210 Chapter 6 A / WANG The line spectra of several
elements versus sun light. strontium 38Sr copper 29Cu Sun light
mercury
strontium Line spectra and Fireworks
Emission spectrum of sodium atoms. hydrogen Bohr’s interpretation of the line spectrum Bohr’s Atomic Model
• • In 1914, Niels Bohr published his explanation of
Niels
the Hydrogen line spectrum in relation to the
electronic structure of the atom, and received
the 1922 Nobel prize in physics for this work.
Bohr’s
The basic assumptions of Bohr’s atomic model:
1. Electrons move in circular orbits around the
nucleus (planetary model)
2. Only orbits of certain radii, corresponding to
specific allowed energy states are permitted. An atom normally is in the ground state. All electrons are arranged in
lowest possible energy levels in the atom, one of which is shown here. 0 E
ground level excited level
E* E0 excited level Light!
ground level Bohr’s Atomic Model
Bohr’s Model
explained
explained the
hydrogen spectral
lines observed by
Balmer (1885) in the
visible region as
resulting from
electrons jumping
from n = 5 2, 4 2,
2,
2,
3 2.
2. Fall 2009 UMSJTU JI When energy is supplied by a flame or in an electrical discharge
tube, the electron jumps to a higher energy level. The atom is now in an excited state, which is not very stable.
The electron will not stay in the higher energy levels very
long.
The excited electron returns back to the original energy level by
releasing the amount of energy that is equal to the difference
between the two levels: E*  E0 = light.
Emitting energy (E*E0) to produce
a spectral line in the line spectrum.
The atom itself returns to the original ground state. Bohr’s
model also
explained
other
known
series of
spectral
lines in the
emission
spectrum
of the
Hydrogen
atom. Page 5 Chem 210 Chapter 6 A / WANG
A quantum
staircase
showing how
an electron
can move up
(absorbs
energy) or
down (emits
energy)
between
energy levels
in Bohr’s
atom. Bohr’s equation for calculating
electron energy in the Hydrogen atom Bohr’s Atomic Model
Bohr’s Model succeeded in:
1. The idea of “only quantized energy states are
quantized
permitted.”
2. Explained the Hydrogen line spectrum:
Hydrogen
– Heating “excites” the electron to larger
orbits.
emitted
– Light of specific wavelength is emitted when
the electron returns from the higher energy
orbit (excited state) back to a lower energy
orbit (ground state). Calculate spectral line between ni & nf
by Bohr’s equation
ni
1 Ef =  RH ( nf )
2 nf Ei =  RH ( 1 )
ni 2 RH = 2.18×1018 J (Rydberg’s constant)
(Rydberg’s
n is called the “principal quantum number”. • The first orbit has n = 1, is closest to the
first
closest
nucleus, and has negative energy by
convention. E1 =  2.18×1018 J
• The furthest orbit has n close to infinity
furthest
and corresponds to zero energy. E∞ = 0. Question: Calculate the wavelength of light
involved for an electron transition in the
Hydrogen atom from n = 5 to n = 2. ν= ν= ∆E RH
=
h h 1 1 2 − 2 ni n f ∆E
2.18 × 10 −18 J 1 1 =
−
= −6.90 × 1014 ⋅ s −1
h
6.63 ×10−34 J ⋅ s 52 22 ∆E R H
=
ν=
h h −7 = 4.33 ×10 m = 433nm Fall 2009 UMSJTU JI 1 1 2 − 2 n
nf i • When ni > nf, energy is emitted (negative value).
emitted (negative
• When nf > ni, energy is absorbed (positive
absorbed (positive
value).
value) Fill in the blank:
The electron transition in the Hydrogen atom
from n = ? to n = 2 corresponds to this red line.
red E = Enf Eni =  h (c/λ)
=  6.63 x1034 (3.00x108 / 656 x109)
656
19
= 3.032×10
1
1
= 2.18×1018 × (n 2 − n 2 )
f λ = c ν = 2.99 ×108 m / s ÷ 6.9 ×1014 s −1 Spectral line ∆E = E f − Ei = hν i 11
0.139 ~ 2 − 2
32
Answer:
Answer: From n=3 to n=2! Page 6 Chem 210 Chapter 6 A / WANG Bohr’s Atomic Model
Limitations of Bohr’s Model:
Can only explain oneelectron atoms or
oneions.
Such as H, He+1 or Li+2
Cannot explain the line spectrum of
atoms with more than one electron.
Such as: He, C, or Na+1
Bohr’s model fails to explain elements other
as
than hydrogen because electrons have, as
light has, both particle and wave properties. Modern Concept of the Atom
QM atomic model uses wave or quantum
quantized
mechanics (QM) to determine the quantized
electron energy levels by considering
electrons as “waves”, which provides the
probability of finding an electron in certain
orbitals
regions around the nucleus, called orbitals.
http://chemmovies.unl.edu/ChemAnime/index.htm
http://chemmovies.unl.edu/ChemAnime/UNCTMD/UNCTMD.html Electrons are:
“particles in orbits” in Bohr’s model vs.
Bohr’s
“waves / orbitals” in QM model. The “s” orbital Electron probability in
the groundstate H
groundatom. Fall 2009 UMSJTU JI Page 7 ...
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This note was uploaded on 07/30/2011 for the course CHEM 210 taught by Professor Zhang during the Spring '09 term at Shanghai Jiao Tong University.
 Spring '09
 zhang
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