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Electromagnetic Spectrum
Light as a Wave - Recap
Light exhibits several wavelike
properties including
Refraction: Light bends upon
passing from one substance to
another)
Dispersion: White light can be
separated into colors.
Diffraction: Light sources
interact to give both constructive
and destructive interference.
c = ln
l = wavelength (m)
n = frequency (s-1)
c = speed of light
(3.00  108 m/s)
Blackbody Radiation & Max Planck
The classical laws of physics do
not explain the distribution of
light emitted from hot objects.
Max Planck solved the problem
mathematically (in 1900) by
assuming that the light can only
be released in “chunks” of a
discrete size (quantized like
currency or the notes on a piano). l = wavelength (m)
We can think of these “chunks” as n = frequency (s-1)
particles of light called photons. h = Planck’s constant
E = hn
E = hc/l
(6.626  10-34 J-s)
Photoelectric Effect
In 1905 Albert
Einstein explained the
photoelectric effect
using Planck’s idea of
quantized photons of
light. He later won
the Nobel Prize in
physics for this work.
Line Spectrum of Hydrogen
n=6 n=5
n=4
n=3
In 1885 Johann Balmer, a Swiss
schoolteacher noticed that the frequencies
of the four lines of the H spectrum obeyed
the following relationship:
n = k [(1/2)2 – (1/n)2]
Where k is a constant and
n = 3, 4, 5 or 6.
Rydberg Equation
When you look at the light given off by a H atom outside
of the visible region of the spectrum, you can expand
Balmer’s equation to a more general one called the
Rydberg Equation
n = (cRH)[(1/n1)2 – (1/n2)2]
1/ l = RH[(1/n1)2 – (1/n2)2]
E = (hcRH)[(1/n1)2 – (1/n2)2]
Where RH is the Rydberg constant (1.098  107 m-1), c is
the speed of light (3.00  108 m/s), h is Planck’s constant
(6.626  10-34 J-s) and n1 & n2 are positive integers
(with n2 > n1)
Bohr Model of the Atom
In 1914 Niels Bohr proposed that the
energy levels for the electrons in an
atom are quantized
En = -hcRH (1/n)2
En = (-2.18  10-18 J)(1/n2)
Where n = 1, 2, 3, 4, …
n=1
n=2
n=3
n=4
Louis DeBroglie & the WaveParticle Duality of Matter
While working on his
PhD thesis (at the
Sorbonne in Paris)
Louis DeBroglie
proposed that matter
could also behave
simultaneously as an
particle and a wave.
l = h/mv
l = wavelength (m)
v = velocity (m/s)
h = Planck’s constant
(6.626  10-34 J-s)
This is only important for matter that has a very small
mass. In particular the electron. We will see later that
in some ways electrons behave like waves.
Electron Diffraction
Electron Diffraction
Pattern
Transmission Electron Microscope
Werner Heisenberg & the
Uncertainty Principle
While working as a
postdoctoral
assistant with Niels
Bohr, Werner
Heisenberg
formulated the
uncertainty principle.
We can never precisely
know the location and the
momentum (or velocity or
energy) of an object.
This is only important for
very small objects.
Dx Dp = h/4p
Dx = position uncertainty
Dp = momentum uncertainty
(p = mv)
h = Planck’s constant
The uncertainty principle means
that we can never simultaneously
know the position (radius) and
momentum (energy) of an
electron, as defined in the Bohr
model of the atom.
Schrodinger and Electron Wave
Functions
In Schrodinger’s wave mechanics
the electron is described by a
wave function, Y. The exact
wavefunction for each electron
depends upon four variables,
called quantum numbers they are
Erwin Schrodinger, an
Austrian physicist,
proposed that we think of
the electrons more as
waves than particles.
This led to the field
called quantum mechanics.
n = principle quantum number
l = azimuthal quantum number
ml = magnetic quantum number
ms = spin quantum number
Y2 = Probability density
s-orbital Electron Density
(where does the electron
spend it’s time)
# of radial nodes = n – l – 1
Velocity is proportional
to length of streak,
position is uncertain.
Position is fairly certain,
but velocity is uncertain.
Schrodinger’s quantum mechanical picture of the atom
1. The energy levels of the electrons are well known
2. We have some idea of where the electron might be at a
given moment
3. We have no information at all about the path or trajectory
of the electrons
s & p orbitals
d orbitals
# of nodal planes = l
Electrons produce a magnetic field.
All electrons produce a magnetic
field of the same magnitude
Its polarity can either be + or -,
like the two ends of a bar magnet
Thus the spin of
an electron can
only take
quantized values
(ms=+½,-½),
giving rise to the
4th quantum
number
Single Electron Atom
Multi Electron Atom