Transcript Wave Nature of Light

Wave Nature of Light
• Rutherford’s model of the atom could not
explain chemical behavior
• Bohr and others described the arrangement
of electrons around the nucleus
• These arrangements could account for
differences between the elements
• Bohr’s model was based on spectroscopic
evidence
Electromagnetic Radiation
• Light can be described as though it is a
wave
Parts of a wave
• Amplitude and wavelength
Crest
Trough
Wave Stuff
• Amplitude: Vertical distance from crest to
midline (brightness/intensity)
• Wavelength: Horizontal distance from crest
to crest (meters) (color)
• Velocity: Rate at which wave travels
(3.00x108 m/s in a vacuum) (constant)
• Frequency: # waves that pass a given point
per unit time (waves/sec, cps, hertz, s-1)
Electromagnetic Spectrum
High frequency
Low frequency
Wave Math
• Velocity = wavelength x frequency
• Velocity = c
Wavelength = l
Frequency = n
• c = ln
• Since c is constant, l and n are inversely
related
Example problems
• Find the frequency of purple light
(wavelength 455 nm).
• Solution: c = ln, or n = c/l
Wavelength must be in meters, since c is in
m/s: 455 nm = 4.55x10-7 m
n = (3.00x108 m/s)/(4.55x10-7 m) =
6.59x1014s-1
Example #2
• Find the wavelength of red light with a
frequency of 4.56x1014s-1.
• c = ln or l = c/n
• l = (3.00x108 m/s)/(4.56x1014s-1) =
6.58x10-7m (658 nm)
Particle Nature of Light
• Light also acts as a particle: proposed by
Newton
• Max Planck and glowing blackbodies:
energy is quantized
• Smallest energy unit available is a quantum
• Energy of quanta depends on the frequency
of the energy:
E = hn
Particle Nature of Light
• h is Planck’s constant: 6.626x10-34Js
• Energy is directly proportional to frequency
• Energy is inversely proportional to
wavelength:
E = hn
and n = c/l
so E = hc/l
Light Particle Sample Problem
• Find the energy of a microwave photon
having a wavelength of 3.42x10-2m.
• Solution: E = hc/l
= (6.626x10-34Js)(3.00x108m/s)/3.42x10-2m
= 5.81x10-24J
Photoelectric Effect
• Certain metals will
eject electrons when
exposed to light
• Number of electrons
ejected depends only
on the intensity of
light
• No electrons ejected
by light below certain
frequency
Photoelectric Effect
• Could not be
explained by wave
model of light
• Einstein explained
effect using quantum
theory of light
• He won the Nobel
Prize for his work (not
for relativity)
Photoelectric Effect Simulator
Atomic Emission Spectra
• When elements are zapped with energy,
they give off light
• Light is first shone through a slit
• When light is shone through a prism, colors
are separated
• Only some of the colors appear as fine lines
against a dark background
Emission spectra of common
fluorescent bulbs
Emission Spectrum Setup
Absorption Spectra
• In absorption spectra, light is shone through
cold gas or liquid
• Light then goes through a slit and prism or
grating
• Resulting spectrum is continuous except for
dark lines
Absorption Spectrum
Absorption Spectrum of Chlorophyll
Liquids tend to have less distinct absorption spectra
Gas Absorption Spectra
Absorption Spectrum Setup
Spectra Types
Bohr Model of the Atom
• Bohr wanted to explain the presence of sharp lines in
the hydrogen spectrum
• He proposed that hydrogen’s electron could only have
certain distinct energies
• These energies were integral multiples of some
minimum energy
• The energy levels correspond to differently sized
orbits
Bohr’s Atom
• Spectral lines were due to
electrons jumping from one
level to another.
• Incoming energy promotes
an electron to a higher
energy level
• When the electron returns
to the lower level it
releases energy
Quantum Numbers
• Bohr assigned the energy levels numbers
• The Principle Quantum Number (n) represents
the main energy level
• n can only have non-zero integral values
• n = 1, 2, 3, ...
Why quantum numbers?
•
•
•
•
Louis de Broglie: Wave-particle duality
As a wave: E = hc/l
As a particle: E = mc 2
Combined: hc/l = mc 2
l = hc/mc 2 = h/mc
• For objects moving slower than light, replace c with
v (velocity): l = h/mv
Particle wavelength problems
• Every particle has a wavelength
• The larger the particle, the shorter the wavelength
• Example: Calculate the wavelength of an electron
moving at 0.80c (mass = 9.109×10-31 kilograms).
• Solution: l = h/mv
= 6.626x10-34Js/[(9.109×10-31kg)(0.80)(3.00x108m/s)]
= 3.0x10-12m (smaller than an atom, bigger than a
nucleus)
Particle wavelength problems
• Find the wavelength of a baseball (145g) thrown
toward home plate at 95.0 mph (42.5 m/s)
• Solution: l = h/mv
= 6.626x10-34Js/[(0.145kg)(42.5m/s)]
= 1.08x10-34m (much smaller than a nucleus)
Back to quantum numbers
• Only certain orbits are
allowed because they are
the only ones in which an
integral number of
wavelengths can “fit”.
• “In-between” orbitals would
require a fractional number
of wavelengths.
“I think it is safe to say that no one understands quantum mechanics.” Physicist Richard P. Feynman
Heisenberg Uncertainty Principle
• It is impossible to know both the position and
momentum of an electron simultaneously
• Electrons are both particles and waves
• It’s in their nature to be indeterminate
• Can be thought of as being “smeared out” over a
region of space
• Indeterminacy is related to Planck’s constant
More Energy Levels
• The fine lines in emission spectra are actually made
up of several even finer lines
• Each energy level has sublevels
• Each sublevel has a shape
• Each sublevel has one or more orbitals
• Each orbital holds two electrons
• How do we sort all this out?
Using Quantum Numbers!
• Four quantum numbers are needed in Schrödinger’s
equation to describe the probability function of an
electron
• n = principle quantum number = 1, 2, 3, ...
Main energy level – determines size of orbital
• l = azimuthal quantum number = 0, 1, ... n-1
Sublevel – determines orbital shape
Well-used quantum numbers
• s:
p:
d:
f:
• m
l = 0 (first two columns of PT)
l = 1 (last six columns of PT)
l = 2 (middle ten columns of PT)
l = 3 (bottom two rows of PT)
= magnetic quantum number = - l to +l
Specifies orbital – determines orientation
• s = spin quantum number = ±½
Specifies spin
Orbital shapes
• s orbital: spherical
• Every energy level has an s
orbital: 1s, 2s, etc.
• Higher level s orbitals are lobed
• Nodes are areas of minimum
electron density
• One node is added for each level
• s sublevel: one orbital, two
electrons
p orbital
• p orbitals are dumbbell
shaped
• p sublevel (l = 1) consists
of three orbitals: px py pz
(six electrons)
• Three p orbitals are
orthogonal to each other
• Only present after first
main energy level (n>1)
d orbital
• d orbital is cloverleafshaped
• Five orbitals, ten electrons
make up d sublevel
• Only available when n>2
f orbitals
• Complicated shape
• Seven orbitals, fourteen
electrons
• Only available when n>3
Allowed quantum number combinations
• Pauli exclusion principle: no two electrons can have
the same set of four quantum numbers
• Aufbau principle: electrons fill the lowest energy
state available first
• Lower numbers mean lower energy (n and l)
• Various m and s states are degenerate (of equal
energy)
Allowed Quantum Number Combinations
n
l
1
0
1
0
1s sublevel –
m
0
0
2e-
s
+½
-½
2
0
0
2
0
0
2s sublevel – 2e-
+½
-½
n
l
2
1
2
1
2
1
2
1
2
1
2
1
2p sublevel –
m
-1
0
1
-1
0
1
6e-
s
+½
+½
+½
-½
-½
-½
Allowed Quantum Number Combinations
3s and 3p are
and 2p
3d sublevel:
n
l
3
2
3
2
3
2
3
2
similar to 2s
m
-2
-2
-1
-1
s
+½
-½
+½
-½
n
l
3
2
3
2
3
2
3
2
3
2
3
2
3d sublevel -
m
0
0
1
1
2
2
10e-
s
+½
-½
+½
-½
+½
-½
Electron configurations
• Electron configurations show the location of every
electron in the atom
• Electrons follow three rules: Pauli exclusion principle,
Aufbau principle, Hund’s rule
• Each orbital is represented by a box and a symbol,
and each electron by an arrow.
Electron configurations
More Electron Configurations
Hund’s rule: When putting electrons into degenerate
orbitals, do not pair them until necessary.
More Electron Configurations
More Electron Configurations
Add non-standard configurations
• And reason for 4s-3d order
Orbital filling diagrams
Orbital filling diagrams
Noble Gas Shorthand Structures
• Noble gas symbols can be used to represent the core
electron structure
• Manganese (25 e-): 1s2 2s2 2p6 3s2 3p6 4s2 3d5
• Equivalent to [Ar] 4s2 3d5
Electron Dot Structures
• Electron dot structures represent only the valence
electrons
• Valence electrons are the electrons in the outermost
energy level (highest value of n)
• The maximum number of electrons allowed in the
valence shell is 8
Electron dot structures
• Consists of the element’s symbol and dots
representing the valence electrons
Hydrogen: H
Helium: He
Lithium:
Beryllium:
Sodium:
Be
Na
Nitrogen:
Iron:
N
Fe
Li
Neon:
Ne
Lead:
Pb