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Electrons in Atoms
Cartoon courtesy of NearingZero.net
1.
Unanswered Questions
Rutherford’s model was incomplete because it did
not explain:
• How an atom’s electrons are arranged in space
surrounding the nucleus
• Why electrons did not spiral into the positively
charged nucleus
• The differences in chemical behavior between the
different elements
2. Early in the twentieth century a new atomic
model developed based on the absorption and
emission of LIGHT.
Wave-Particle Duality
J.J. Thomson won the Nobel prize for describing the
electron as a particle.
His son, George Thomson won the Nobel prize for
describing the wave-like nature of the electron.
The
electron is
a particle!
The
electron is
an energy
wave!
The Wave Description of Light.
Before the 1900’s,
scientists thought light
behaved only as waves.
The electron propagates
through space as an energy
wave. To understand the
atom, one must understand
the behavior of
electromagnetic waves.
Louis deBroglie
Electromagnetic radiation -
energies that have wave-like properties/behavior while
traveling trough space.
Electromagnetic spectrum includes:
Characteristic Parts/Properties of a electromagnetic
(light) waves
amplitude– the height of a crest or trough - directly proportional to
the amount of energy.
Wavelength -units = m, cm, nm; symbol = lambda =  ;
Distance between two consecutive corresponding points on a wave.
Frequency – units = Hz, s-1 (waves/s); symbol = nu =  ;
Number of complete waves that pass a point in 1 s time.
Electromagnetic radiation:
Wavelength and frequency are mathematically related.
c=
 ·  ; inverse proportion
c = speed of light= 3.00 x 10 8 m/s (speed in a vacuum)
.
Long
Wavelength
=
Low Frequency
=
Low ENERGY
Short
Wavelength
=
High Frequency
=
High ENERGY
Wavelength Table
Continuous spectrum
Light beam passing through a prism is refracted
(bent) twice, separating into all colors of the
rainbow (continuous spectrum.) A continuous
spectrum is referred to as the rainbow.
The Particle Description of Light
In the early 1900’s, scientists conducted
experiments involving the interactions of light
and matter that could not be explained by the
wave model of light.
One experiment involved the phenomenon known
as the photoelectric effect.
Photoelectric Effect
The emission of electrons from the surface of a metal when light of a certain,
minimum frequency shines on it
Planck (1900)
By studying the heating of solid objects Planck’s work
showed the following:
 Matter can gain or lose energy only in small specific
amounts- i.e. each frequency (color of light) had a set
amount of energy.
 Light consists of particles called quanta (a quantum)
 These particles contain the minimum amount of energy
that can be lost or gained by an atom.
 A direct mathematical proportion existed between
frequency and energy of emitted radiation:
E = h
• E = Energy, in units of Joules
• h = Planck’s constant (6.626 x 10-34 J·s)
•  = frequency, in units of hertz (Hz or s-1)
Einstein (1905)
• Expanded on Planck’s theory by introducing the idea that
electromagnetic radiation has a dual wave-particle nature.
• While light exhibits many wavelike properties, it can also be
thought of as a stream of particles.
• Einstein called these particles photons- particles of
electromagnetic radiation with no mass that carry quantums of
energy
• Summary – Photoelectric Effect
The energy of a photon must have a certain minimum, or threshold, energy to
cause the ejection of a photoelectron
(i.e. red photons were low in energy and did not produce the photoelectric
effect while violet light which is high in energy did produce the photoelectric
effect)
•
Remember:
Spectroscopic analysis of the visible spectrum…
…produces all of the colors in a continuous spectrum
Hydrogen Line-Emission Spectrum
• The lowest energy state of an atom is its ground state.
• A state in which an atom has a higher potential energy than it has in its
ground state is an excited state.
• When an electron falls to a lower energy level, a photon is emitted, and the
process is called emission.
• Energy must be added to an atom in order to move an electron from a lower
energy level to a higher energy level. This process is called absorption.
Hydrogen’s Line-Emission Spectrum
• The line- (or atomic-) emission spectrum of
an element is the set of frequencies of the EM
waves emitted by atoms of the element.
– Each element’s atomic emission spectrum is
unique and can be used to determine if that
element is present in a compound or to identify an
element.
Atoms give off Line Spectrums
•What does this mean?
•Neils Bohr solved this
in 1913
•He said the spectrums
showed that electrons
jumped from level to
level as they moved
The Bohr Model of the Atom
• Bohr proposed that the H
atom has only certain
allowable energy levels (the
lowest = the ground state)
• He related the energy levels
to the movement of e- in only
certain allowed circular paths,
or orbits, around the nucleus
• He assigned a quantum
number, n, to each orbit
Bohr’s Explanation
• At first Bohr’s model appeared promising- it
fits the hydrogen atom very well.
• BUT, when applied to other atoms, it did NOT
work.
• Further experiments showed it was
fundamentally incorrect- electrons do not
move around the nucleus in circular orbits!
• His model did though pave the way for later
theories…………
Quantum Mechanical Model of the Atom
• Mathematical laws can identify the regions
outside of the nucleus where electrons are most
likely to be found.
• These laws are beyond the scope of this class
and includes the work of DeBroglie, Heisenberg,
Schrodinger and others.
• Like Bohr, the quantum mechanical model lead to
quantized energy levels. Unlike Bohr, the quantum
mechanical model does not define an exact
pathway for electrons.
• The quantum mechanical model is concerned with
the probability of finding an electron.
• At this point, electrons can be explained in terms
of waves, particles and beyond.
Louis de Broglie
If waves can have particle
like behavior, could the
opposite be true?
De Broglie derived an
equation that predicts all
moving particles (including
electrons) have wave
characteristics
Heisenberg Uncertainty Principle
“It is impossible to know
precisely both the velocity and
position of a particle at the
same time.”
You can find out where the
electron is, but not where it
is going.
Werner
Heisenberg
OR…
You can find out where the
electron is going, but not
where it is!
Schrodinger (1926)
Wave Equations

d
h

 V   E
8  m dx
2
2
Erwin Schrodinger
2
2
Derived equations for the
probability of finding
electrons.
Described mathematically the
wave properties of electrons.