Atomic Structure I
It’s not about Dalton anymore…
http://plus.maths.org/latestnews/may-aug07/strings/atoms.jpg
First…
• To understand the electronic structure
of the atom we need to review the
properties of electromagnetic radiation.
The Wave Nature
of Light
Figure 7.1
Frequency and
Wavelength
c = ln
l = wavelength
n = frequency
C = speed of light
Amplitude (intensity) of a wave.
The waveheight or amplitude determines radiation intensity.
The wavelength is related to the energy of the radiation.
λ, ν, and Energy
• As λ decreases and ν increases, what
happened to the energy of the
radiation?
E=hn =
hc
l
where h = Planck’s constant
(6.626 × 10-34 m2 kg/s)
The infinite number of wavelengths of
electromagnetic radiation have been classified
into groups as shown below.
Regions of the electromagnetic spectrum.
Interconverting Wavelength and Frequency
PROBLEM:
o
A dental hygienist uses x-rays (l= 1.00A) to take a series of
dental radiographs while the patient listens to a radio station (l =
325 cm) and looks out the window at the blue sky (l= 473 nm).
What is the frequency (in s-1) of the electromagnetic radiation
from each source? (Assume that the radiation travels at the
speed of light, 3.00x108 m/s.)
Use c = ln
SOLUTION:
o
-10
-10
1.00A 10 o m = 1.00x10 m
1A
3x108 m/s
= 3x1018 s-1
n=
1.00x10-10 m
-2
325 cm 10 m = 325x10-2 m
1 cm
3x108 m/s
= 9.23x107 s-1
n=
325x10-2 m
10-9 m
473nm
= 473x10-9 m
1 nm
3x108 m/s = 6.34x1014 s-1
n=
473x10-9 m
Calculating the Energy of Radiation from Its Wavelength
PROBLEM:
A cook uses a microwave oven to heat a meal. The wavelength of
the radiation is 1.20cm. What is the energy of one photon of
this microwave radiation?
After converting cm to m, we can use the energy equation, E = hn
combined with n = c/l to find the energy.
SOLUTION:
E=
E = hc/l
6.626X10-34J*s x 3x108m/s
1.20cm
10-2m
cm
= 1.66x10-23J
Particle or Wave?
Different
behaviors
of waves
and
particles.
The diffraction pattern caused by light
passing through two adjacent slits.
Light is a wave…right?
• Light falling on alkali
metals causes electrons
to be released from the
metal.
• The # of electrons
depends on the intensity
of light.
• There are specific
wavelengths of light that
cause the release of e-.
• This is called the
photoelectric effect.
Light is a wave…right?
• Einstein’s interpretation of the
photoelectric effect (1905) was that
light is quantized in packets of set
energy called photons. (He won the
Nobel Prize for this.)
• This meant that light had
characteristics of particles!
Electrons are particles…right?
• In 1925, de Broglie stated that all
particles have a wavelength described
by the equation:
λ = h/p where p= momentum
• Electrons show diffraction pattern
when passing through a slit
• So light and particles have a dual
nature.
Back to atomic structure…
• We already know an atom contains a
nucleus with p+ and no. Electrons orbit
the nucleus.
• It was known that atoms emit a unique
spectrum of lines when excited.
Rydberg derived an equation that
related the lines.
Rydberg equation
1
l
=
R
1
1
n12
n22
• R is the Rydberg constant = 1.096776x107 m-1
Flame test colors derive from electrons changing energy
levels.
Atomic emission spectra
Clockwise from lower left:
neon, helium, hydrogen,
mercury, nitrogen
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/atspect2.html
Spectra Site
• http://jersey.uoregon.edu/vlab/element
s/Elements.html
Absorption and emission spectra for
element arranged on the periodic table
Back to atomic structure…
• Bohr theorized that the emission
spectra of atoms described by
Rydberg’s equation were caused by the
transition of electrons between specific
energy levels (orbits).
• http://www.upscale.utoronto.ca/General
Interest/Harrison/BohrModel/Flash/Bo
hrModel.html
Electron locations
• When an electron occupies its usual
energy level it is in the ground state.
• When an electron absorbs a photon and
moves to a higher energy level it is in an
excited state.
• The energy levels are “quantized”.
Atoms can only transition between set
levels.
• Why are the levels set where they are?
More on electrons as waves
• Since electrons have wave motion
Schrödinger applied the classic wave
equations to the motion of a hydrogen
electron. Certain wavelengths
reinforced each other and were allowed.
• This generated regions occupied by an
electron of set energy termed orbitals.
Wave motion in
restricted systems.
More on electrons as waves
• Heisenberg stated that in measuring
the electron there is uncertainty so we
can only calculate a probable location
for the electron. This is called the
Heisenberg Uncertainty Principle.
Electron probability in the
ground-state H atom.
The 2p orbitals.
The 3d orbitals.
F orbitals
CLASSICAL THEORY
Matter
particulate
, massive
Energy
continuous,
wavelike
Summary of the major observations
and theories leading from classical
theory to quantum theory.
Since matter is discontinuous and particulate
perhaps energy is discontinuous and particulate.
Observation
Theory
blackbody radiation
Planck:
Energy is quantized; only certain values
allowed
Einstein: Light has particulate behavior (photons)
photoelectric
effect
atomic line
spectra
Bohr:
Energy of atoms is quantized; photon
emitted when electron changes orbit.
Since energy is wavelike perhaps matter is wavelike
Observation
Theory
Davisson/Germer:
deBroglie: All matter travels in waves; energy of
electron
atom is quantized due to wave motion
diffraction
of electrons
by metal crystal
Since matter has mass perhaps energy has mass
Observation
Compton: photon
wavelength increases
(momentum
decreases) after
colliding with electron
Theory
Einstein/deBroglie: Mass and energy are
equivalent; particles have wavelength and
photons have momentum.
QUANTUM THEORY
Energy same as Matter
particulate, massive, wavelike