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Electrons and Atoms
 Properties of electromagnetic radiation
wavelike behavior described by wavelength, frequency, and amplitude.
students should know the general spectrum of light from radio waves
to cosmic rays. Visible light = ROY G BIV
c  
 Observations regarding light.
A solid heated to incandescence emits all wavelengths of visible light.
The spectrum is continuous.
Gases under low pressure under high voltage emit discontinuous light.
Bright lines are seen generating atomic spectra or line spectra. They are
unique to each atom.
 1885: Apparently through trial and error, Johann Balmer determines an
equation that accurately predicts the four visible lines in the H spectra. The
equation is: (where n greater than 2)
 1
1 


22 n 2 
  3.2881x1015 s 1 
 1900: Max Planck, after evaluating the spectra of Black body radiation
which did not correlate to the classical physics model ( which placed no limit on the
E of a system) proposes that E is discontinuous. The difference between specific
values is a quantum and it is proportional to frequency.
E  h
where h = 6.626 x 10-34 J s
 1905: Einstein explains the photoelectric effect which had been observed
decades earlier. When visible light shines on certain metals, electrons
are ejected from the surface. The stunning observation was that super
bright red light would result in no electrons leaving the surface of the metal, but
extremely faint blue light would cause some electrons to leave the surface and
they all possessed the same KE. Classical physics had always related the E of
light as a function of brightness (amplitude) but not its frequency. Einstein
proposes that light has particle like
properties which we call photons. The number of electrons ejected
depends on the intensity but the KE of the electrons depends on the
frequency of the light. The fundamental interpretation relevant to
electrons is that they are not capable of accumulating energy. They are
restricted to certain allowed energies -- and can make quantum jumps.

 The Rutherford Model of the atom
Rutherford's model derived from the classic gold foil experiment with
Alpha particles was that the atom is a vast empty space with
electrons traveling around an extremely tiny unbelievably dense
nucleus. But a charged particle that is in a circular path radiates
energy and thus should fall into the nucleus (Classical Physics)
 1913: The Bohr Model of the atom
Bohr is aware of this inconsistency as well as Planck's and Einstein's proposals. He
asserts the following and thus creates a replacement
model of the atom.
1. e- are in circular orbits (their motion is classically defined)
2. e- has a fixed set of allowed orbits and no energy is emitted
as the electron moves. Arbitrarily, he states that angular
momentum is quantized.
mvr 
nh
2
3. e- may pass from one allowed orbit to another but only if fixed
discrete quantities of E (quanta) are involved (h). These
orbits are described with values of n, where n = 1, 2, 3, 4.....
Bohr defines the energy of a hydrogen electron as
En 
 RH
2
n
where RH is equal to 2.179 x 10-18 J
Most often we are interested in ∆E so the useful equation is:
18
E  2.179x10
 1
1 

J  2  2 

ni n f 
As an electron approaches a nucleus, it drops in potential energy and
emits light. Thus, the energy of the electron becomes negative.
Notice the resemblance to Balmer's equation for the hydrogen line spectrum
calculated almost 30 years earlier!
Although the Bohr model was impressive it failed to predict bright line
spectra for elements beyond H. The failure increased dramatically with
increased atomic number. Why would the model fail for multi-electron
species?
 1924-27:
Louis De Broglie proposes that e- may display wave like character.
According to his hypothesis, the wavelength of a particle is related to the
particle momentum, p, and Planck's constant, h. Momentum is the product
of mass and velocity. Lambda is the wavelength of the matter wave.

h
h

p mv
note that the units work. Also note that the velocity in this equation is not to be
confused with the velocity term for the KE of an electron.
It is only when wavelengths are comparable to ~ atomic dimensions that waveparticle duality is important. If m is large, lambda is not measurable.
If electrons were treated as 3D standing waves, then they could only
constructively interfere if crest met crest; the number of wavelengths
that fit a given circumference must be an integral number:
2r  n
Since we already know the De Broglie equation, substitute the equation:
2 r 
nh
mv
Rearrange and voila, the Bohr postulate:
mvr 
nh
2
 If an electron behaves as a wave, how do you specify a position of a wave
at a particular moment? Maybe its wavelength, E, and amplitude could
be measured, but the idea of position becomes nebulous.
Heisenberg uncertainty principle: there is a limit to which both the eposition and momentum can be known. If you can't say where the electron is, we
certainly don't know how it got there.
 Wave Mechanics
Schrodinger proposed various complex mathematical equations that
described 3D wave patterns. They required a set of quantum numbers
and produce a "wave function." When specific terms are assigned for
these quantum numbers, an orbital is defined. Orbital: a region of
space around the nucleus where the probability of finding an electron
is >90%.