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Chapter Six (1)
Atomic Structure
Chapter 6
Slide 1 of 82
Introduction
The chapter consists of three parts:
– The discovery of the electron and
the determination of its properties
– Understanding the nature of light
– The behavior of electrons in atoms
Chapter 6
Slide 2 of 82
Cathode Rays
Electric Discharge Tube
Chapter 6
Slide 3 of 82
Cathode Rays
• Cathode rays are the carriers of electric current from
cathode to anode inside a vacuumed tube
• Cathode rays have the following characteristics:
– Emit from the cathode when electricity is passed
through an evacuated tube
– Emit in a direction perpendicular to the cathode
surface
– Travel in straight lines
– Cause glass and other materials to fluoresce
– Deflect in a magnetic field similarly to negatively
charged particles
Chapter 6
Slide 4 of 82
Cathode rays deflect in a magnetic field
S
N
magnet
Chapter 6
Slide 5 of 82
Thomson’s Mass-to-Charge Ratio
Apparatus
me /e = –5.686 X 10-12 kg/C
Chapter 6
Slide 6 of 82
Millikan’s Oil Drop Experiment
e = -1.602 X 10-19 C
Chapter 6
Slide 7 of 82
Determined Values
• J.J. Thomson devises an experiment telling the
ratio of the cathode ray particle’s mass to the
charge expressed:
me /e = –5.686 X 10-12 kg/C
• George Stoney names the particle an electron
• Robert Millikan then determines a value for
the charge
e = -1.602 X 10-19 C
• From these two values the mass of an electron:
me = 9.109 X 10-31 kg/electron
Chapter 6
Slide 8 of 82
J.J. Thomson’s Model
• J.J. Thomson proposed an atom with a positively
charged sphere containing equally spaced electrons
inside
– Proposed for a Hydrogen atom that there was one
electron at the exact center of the sphere
– Proposed for a Helium atom, that two electrons
existed along a straight line through the center,
with each electron being halfway between the
center and the outer surface of the sphere
– Applied this analysis to atoms with up to 100
electrons
Chapter 6
Slide 9 of 82
Thomson’s
Raisin Pudding Model
Chapter 6
Slide 10 of 82
Rutherford’s Alpha Scattering
Experiment
Chapter 6
Slide 11 of 82
Rutherford’s Model
• Ernest Rutherford discovered the positive charge of
an atom is concentrated in the center of an atom,
the nucleus
– An atom, can be visualized as a giant indoor
football stadium
– The nucleus can be represented by a pea in the
center of the stadium,
– The electrons are a few bees buzzing throughout.
The roof of the stadium prevents the bees from
leaving.
Chapter 6
Slide 12 of 82
Chapter 6
Slide 13 of 82
Chapter 6
Slide 14 of 82
The Wave Nature of Light
• Electromagnetic waves originate from the
movement of electric charges
– The movement produces fluctuations in electric
and magnetic fields
– Electromagnetic waves require no medium
• Electromagnetic radiation is characterized by its
wavelength, frequency, and amplitude.
Chapter 6
Slide 15 of 82
An Electromagnetic Wave
Chapter 6
Slide 16 of 82
Wavelength And Frequency
• Wavelength (λ ) is the distance between any two
identical points in consecutive cycles, and is
measured in nanometers and angstroms
• Frequency (v ) of a wave is the number of cycles of
the wave that pass through a point in a unit of time,
and is measured in hertz (s-1)
• Amplitude (I) of a wave is its height: the distance
from a line of no disturbance through the center of
the wave peak.
Chapter 6
Slide 17 of 82
The Electromagnetic Spectrum
Chapter 6
Slide 18 of 82
Continuous and Line Spectra
• White light passed through a prism produces a spectrum of
rainbow colors in continuous form. The different colors of
light correspond to different wavelengths and frequencies.
• When light is produced through an element, a discontinuous
spectrum is displayed.
• The pattern of lines produced by the light emitted by excited
atoms of an element is call a line spectrum.
• Emission Spectroscopy is the analysis of light emitted from a
strongly heated or energized element
• A photograph or other record of the emitted light is called
emission spectrum.
Chapter 6
Slide 19 of 82
Continuous
Spectra
Line Spectra
Chapter 6
Slide 20 of 82
Emission Spectrum of Hydrogen
in Visible Light Region
Chapter 6
Slide 21 of 82
Emission Spectrum of Helium
Chapter 6
Slide 22 of 82
Line Spectra of Some Elements
Chapter 6
Slide 23 of 82
Planck’s Constant
• Planck’s quantum hypothesis states that energy can
be absorbed or emitted only as a quantum or as
whole multiples of a quantum, thereby making
variations discontinuous, changes can only occur in
discrete amounts.
• The smallest amount of energy, a quantum, is given
by:
E = hv
as Planck’s constant, h = 6.626 X 10-34 J s.
Chapter 6
Slide 24 of 82
The Photoelectric Effect
• Albert Einstein considered electromagnetic energy
to be bundled in to little packets called photons.
Energy of photon = E = hv
– Photons of light hit surface electrons and transfer
their energy
hv = B.E. + K.E.
hv
e- (K.E.)
– The energized electrons overcome their attraction
and escape from the surface
Chapter 6
Slide 25 of 82
Photoelectric Effect Illustrated
Chapter 6
Slide 26 of 82
Chapter 6
Slide 27 of 82
Bohr’s Hydrogen Atom
Postulations
• Rutherford’s nuclei model
• The energy of an electron in a H atom is quantized
• Planck & Einstein’s photon theory
E = hv
• Electron travels in a circle
• Classical electromagnetic theory is not applied
Z
v
r
• e-
Orbit
Chapter 6
Slide 28 of 82
(1) Classical physics
centripetal force = Coulombic attraction
mv2/r = Ze2/r2
(2) Total energy
E = 1/2 mv2 - Ze2/r
Quantum number
(3) Quantizing the angular momentum
mvr = n (h/2π )
E = - ( 2π2 mZ2e4)/(n2 h2)
when n =1, E(1)= - (2π2 mZ2e4)/( h2)
E = E (1) /n2
r = (n2 h2)/ (4π2 mZe2)
Bohr’s Hydrogen Atom
• Niels Bohr found that the electron energy (En) was
quantized, that is, that it can have only certain specified
values.
• Each specified energy value is called an energy level of
the atom
En = - B/n2
– n is an integer, and B is a constant which equals
2.179 x 10-18 J
– The energy is zero when the electron is located
infinitely far from nucleus
– The negative sign represents the forces of attraction
Chapter 6
Slide 30 of 82
The Bohr Model
Chapter 6
Slide 31 of 82
Bohr Explains Line Spectra
• Bohr’s equation is most useful in determining the
energy change (∆Elevel) that accompanies the leap of
an electron from one energy level to another
• For the final and initial levels:
Ef = -B / nf2
Ei = -B / ni2
The energy difference between nf and ni is:
∆Elevel = Ef - Ei
= ( -B / nf2 ) – (-B / nf2 )
= B(1/ni2 – 1/nf2)
Chapter 6
Slide 32 of 82
Energy Levels and Spectral Lines for
Hydrogen
Chapter 6
Slide 33 of 82
Ground States and Excited States
• When an atom has its electrons in their lowest
possible energy levels, it is in its ground state
• When an electron has been promoted to a higher
level, it is in an excited state
– Electrons are promoted through an electric
discharge, heat, or some other source of energy
– An atom in an excited state eventually emits
photons as the electron drops back down to the
ground state
Chapter 6
Slide 34 of 82
λ= ? nm
Chapter 6
Slide 35 of 82
Chapter 6
Slide 36 of 82
Problems of
Bohr’s Model of Atom
• The energy levels of Bohr’s H atom cannot
be applied to other atoms.
• The orbit of electrons cannot of defined.
Chapter 6
Slide 37 of 82
De Broglie’s Equation
• Louis de Broglie speculated that matter can behave
as both particles and waves, just like light
• He proposed that a particle move with a mass m
moving at a speed v will have a wave nature
consistent with a wavelength given by the equation:
p = mc
E = mc2 = pc = hν
p = hν /c = h/ λ
λ = h/p = h/mv
• De Broglie’s prediction of matter waves led to the
development of the electron microscope
Chapter 6
Slide 38 of 82
Experimental Determination
of Crystal Structures
Bragg’s Law
2 d sinθ = n λ
Chapter 6
Slide 39 of 82
X-Ray Diffraction Image & Pattern
Single crystal
Powder
Chapter 6
Slide 40 of 82
What is the speed of an electron to have a
wavelength of X-ray?
Wavelength of X-ray ~ 0.10 nm = 1.0 x 10-10 m
Mass of electron = 9.11 x 10-31 kg
Planck constant h = 6.626 x 10-34 Js (kg m2/s)
<Answer>
λ= h/p = h/mv
v = h/m λ = (6.626 x10-34)/[(9.11 x10-31)(1.0 x 10-10)]
= 7.3 x106 m/s
Chapter 6
Slide 41 of 82
How to achieve the speed of an electron of
7.3 x106 m/s?
V
<Answer>
E= eV= ½ mv2
V = ½ mv2 /e = ½ (9.11 x10-31)(7.3 x106)2 /(1.6022 x 10-19)
V = 150 V
(1 eV = 1.6022 x 10-19 J)
Chapter 6
Slide 42 of 82
Electron diffraction
In 1927, Davisson and Germer of the Bell
Laboratories investigated the scattering of
electrons from various surfaces.
Chapter 6
Slide 43 of 82
The Uncertainty Principle
• Werner Heisenberg’s uncertainty principle states
that we can’t simultaneously know exactly where a
tiny particle like an electron is and exactly how it is
moving
(∆Px) (∆x) > h/4π, Px = mvx
• The act of measuring the particle actually interferes
with the particle
• In light of the uncertainty principle, Bohr’s model of
the hydrogen atom fails, in part, because it tells more
than we can know with certainty.
Chapter 6
Slide 44 of 82
Uncertainty Principle Illustrated
Chapter 6
Slide 45 of 82
Wave Functions
• Quantum mechanics, or wave mechanics, is
the treatment of atomic structure through the
wavelike properties of the electron
• Wave mechanics provides a probability of
where an electron will be in certain regions of
an atom
Chapter 6
Slide 46 of 82
• Erwin Schrödinger developed a wave equation to
describe the hydrogen atom
• An acceptable solution to Schrödinger’s wave
equation is called a wave function
• A wave function (ψ) represents an energy state of the
atom
ψ ( x, y , z )
∫
+∞
−∞
2
: the probability of finding an
electron
at (x, y, z) position in an atom
ψ ( x, y , z ) dτ = 1
2
Chapter 6
The probability of finding
an electron in the universe
is equal to 1.
Slide 47 of 82
y
x
Traveling wave
y(x, t) = y0sin(kx−ωt)
y: amplitude of the wave
If y is a function of x only,
then, y(x) = y0sinkx
n=1
n=2
n=3
L x
0
L
Standing wave
y(x) = y0sinkx
Boundary condition:
y = 0, when x = 0
y = 0, when x = L
kL = nπ, k = nπ/L
n = integers (quantum number)
y(x) = y0sin[(nπ/L) x]
Standing Waves & Quantum Number
Chapter 6
Slide 49 of 82
Wave Mechanics
Schrödinger equation
one-dimensional
d 2ψ 8π 2 m
[E − U (x )]ψ = 0
+
2
2
dx
h
three-dimensional
∂ 2ψ ∂ 2ψ ∂ 2ψ 8π 2 m
[E − U (x , y , z )]ψ = 0
+
+ 2 +
2
2
2
∂x
∂y
∂z
h
• ψ : amplitude of the wave
• The probability that a particle will be detected is
proportional to
.2
ψ
Boundary condition for solving ψ in
Schrödinger eq. :
•
∫
+∞
ψ ( x , y , z ) d τ = 1 (normalization)
−∞
2
• ψ(x,y,z) is a single valued function w.r.t. the
coordinates
• ψ(x,y,z) is a continuous function
• ψ(x,y,z) is a finite function
For H atom
− Ze 2 − e 2
U =
=
r
r
To solve the equation more easily,
Cartesian coordinates x, y, z are
transformed to polar coordinates r, θ, φ.
ψ ( x, y, z ) = ψ (r ,θ , φ )
= R (r )Θ(θ )Φ (φ )
= R (r )Υ (θ , φ )
Wavefunctions of Hydrogen Atom
4πr (Rnl )
2
2
Chapter 6
Slide 54 of 82
Chapter 6
Slide 56 of 82
Quantum Numbers and
Atomic Orbitals
• The wave functions for the hydrogen atom contain
three parameters that must have specific integral
values called quantum numbers.
• A wave function with a given set of these three
quantum numbers is called an atomic orbital.
• These orbitals allow us to visualize the region in
which there is a probability of find an electron.
Chapter 6
Slide 57 of 82
Quantum Numbers
When values are given to quantum numbers, a specific
atomic orbital is defined
The principal quantum number (n)
– Can only be a positive integer
n = 1, 2, 3 · · · ·
– The size of an orbital and its electron energy
depend on the n number
– Orbitals with the same value of n are said to be in
the same principle shell
Chapter 6
Slide 58 of 82
Quantum Numbers (continued)
• The orbital angular momentum quantum number (l)
– Can have positive integral values
0≤ l ≤ n-1
– Determines the shape of the orbital
– All orbitals having the same value of n and the
same value of l are said to be in the same subshell
– Orbitals and subshells are also designated by a
letter:
Value of l
0
1
2
3
Orbital or subshell
s
p
d
f
Quantum Numbers (continued)
• The magnetic quantum number (ml):
– Can be any integer from -l to +l
-l ≤ ml ≤ l
– Determines the orientation in space of the
orbitals of any given type in a subshell
– The number of possible value for ml = 2l + 1,
and this determines the number of orbitals in a
subshell
Chapter 6
Slide 60 of 82
The relationship between quantum numbers
0≤ l ≤ n-1
1s- orbital
For example: n= 1, l= 0
n= 2, l= 1, 0 2p, 2s- orbitals
n= 3, l= 2, 1, 0 3d, 3p, 3s- orbitals
-l ≤ ml ≤ l
For example: l= 1, ml = -1,0,1 px, py, pz- orbitals
l= 2, ml = -2,-1,0,1,2
dxy, dyz, dzx, dz2, dx2-y2
orbitals
Quantum Numbers Summary
Chapter 6
Slide 62 of 82
The 1s Orbital
3/ 2
⎛Z ⎞
⎛ ρ⎞
⎟
⎜
R10 (r ) = ⎜ ⎟ 2 exp ⎜ − ⎟
⎝ 2⎠
⎝ a0 ⎠
Υ0, 0(θ,φ) = 1/2π1/2
2 Zr
ρ=
a0
a 0 = 52 .92 pm
• The 1s orbital has spherical symmetry.
• The electrons are more concentrated near the center
Chapter 6
Slide 63 of 82
The 2s Orbital
3/ 2
⎛ Z ⎞ ⎛1
⎛ ρ⎞
⎞
R20 (r ) = ⎜⎜ ⎟⎟ ⎜
2 ⎟ (2 − ρ ) exp ⎜ − ⎟
⎝ 2⎠
⎠
⎝ a0 ⎠ ⎝ 2
Υ0,0(θ,φ) = 1/2π1/2
(+)
r
0
(-)
0
node
0
The 2s Orbital
• The 2s orbital has two regions of high electron
probability, both being spherical
• The region near the nucleus is separated from the outer
region by a spherical node- a spherical shell in which
the electron probability is zero
node
Chapter 6
Slide 65 of 82
Chapter 6
Slide 66 of 82
The Three p Orbitals
Chapter 6
Slide 67 of 82
The Five d Orbital Shapes
Chapter 6
Slide 68 of 82
The Seven f Orbital Shapes
Chapter 6
Slide 69 of 82
Chapter 6
Slide 70 of 82
Electron Spin – the 4th Quantum
Number
• The electron spin quantum number (ms) explains
some of the finer features of atomic emission spectra
– The number can have two values: +1/2 and –1/2
( ms= ½ , -½ )
– The spin refers to a magnetic field induced by the
moving electric charge of the electron as it spins
– The magnetic fields of two electrons with opposite
spins cancel one another; there is no net magnetic
field for the pair.
Chapter 6
Slide 71 of 82
The Stern-Gerlach Experiment
Chapter 6
Slide 72 of 82
Hydrogen atom and Schrödinger equation
• energy is quantized (n)
• magnitude of angular momentum is
quantized (l)
• the orientation of angular momentum is
quantized (ml)
Electron has spin (ms)
⎛ 2π 2 me 4
E = ⎜⎜ −
2
h
⎝
⎞⎛ Z 2
⎟⎟⎜⎜ 2
⎠⎝ n
⎞
⎟⎟
⎠
hydrogen atom
Chapter 6
Slide 74 of 82
Chapter 6
Slide 75 of 82
light-emitting diode (LED)
• A light-emitting diode (LED) is a semiconductor device
that emits incoherent narrow-spectrum light when electrically
biased in the forward direction.
• This effect is a form of electroluminescence.
• The color of the emitted light depends on the chemical
composition of the semiconducting material used.
AlGaAs - red and IR
AlGaP - green
AlGaInP - high-brightness orange-red, orange, yellow,
yellow
and green
GaAsP - red, orange-red, orange, and yellow
GaN - green, and blue
InGaN - near UV, bluish-green and blue
AlN, AlGaN - near to far UV
Chapter 6
Slide 76 of 82
Chapter 6
Slide 77 of 82
Organic Light-Emitting Diodes (OLEDs)
• vs. inorganic LEDs
Flexibility
Simple and easy thin film fabrication and micronscale patterning
(vs. wire-bonded epitaxial AlGaAs or group III nitride discrete
semiconductor LEDs)
• vs. liquid crystal display, LCD
Wide viewing angle
Very bright and highly contrast
No back-lighting needed (low energy consumption)
Fast switching times (video-rate display)
Multicolor emission (RGB)
Thin and light weight
Foldable, very thin screen possible
Chapter 6
Slide 78 of 82
比一比看誰炫
液晶顯示器 Ｌ(ＣＤ
有機發光二極體 Ｏ(ＬＥＤ
)
)
Chapter 6
Slide 79 of 82
Summary
• Cathode rays are negatively charged fundamental particles
of matter, now called electrons.
• An electron bears one fundamental unit of negative electric
charge.
• A nucleus of an atom consists of protons and neutrons and
contains practically all the mass of an atom.
• Mass spectrometry establishes atomic masses and relative
abundances of the isotopes of an element
• Electromagnetic radiation is an energy transmission in the
form of oscillating electric and magnetic fields.
Chapter 6
Slide 80 of 82
Summary (continued)
• The oscillations produce waves that are characterized by
their frequencies (v), wavelengths (λ), and velocity (c).
• The complete span of possibilities for frequency and
wavelength is described as the electromagnetic spectrum.
• Planck’s explanation of quantums gave us E = hv
• The photoelectric effect is explained by thinking of quanta
of energy as concentrated into particles of light called
photons.
• Wave functions require the assignment of three quantum
numbers: principal quantum number, n, orbital angular
momentum quantum number, l, and magnetic quantum
number, ml.
Chapter 6
Slide 81 of 82
Summary (continued)
• Wave functions with acceptable values of the three
quantum numbers are called atomic orbitals.
• Orbitals describe regions in an atom that have a high
probability of containing an electron or a high electronic
charge density.
• Shapes associated with orbitals depend on the value of l.
Thus, an s orbital (l = 0) is spherical and a p orbital (l = 1)
is dumbbell-shaped.
• A fourth quantum number is also required to characterize
an electron in an orbital - the spin quantum number, ms.
Chapter 6
Slide 82 of 82