# 3.20 x 10 11 s -1

```Energy and Electrons
Wave-Particle Duality
JJ 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-like Electron
The electron propagates
through space as an energy
wave. To understand the atom,
one must understand the
behavior of electromagnetic
waves.
Louis deBroglie
through space as a wave moving at the
speed of light.
c = 
C = speed of light, a constant (3.00 x 108 m/s)
 = frequency, in units of hertz (hz, sec-1)
 = wavelength, in meters
Key to Understanding Electron Paths
• Early scientists discovered that
Electromagnetic radiation (light) is given off
by atoms of an element when they have
been excited by some form of energy
• Furthermore, atoms of different elements
give off different colors of light when they
are excited.
When salts
containing Li,
Cu, and Na
dissolved in
methyl alcohol
are set on fire,
brilliant colors
result.
Cu
Li
Na
Spectral Analysis of Emitted
Light from Excited Atoms
 When the emitted light from excited atoms was
passed through a prism, a curious spectrum of
discrete lines of separate colors, separate
energies, was observed rather than a continuous
spectrum of ROY G BIV.
 Furthermore, different elements show totally
different line spectra.
 In fact, line spectra are used to identify the presence
of different elements
Interpretation of Atomic
Spectra
• The line spectrum must be related to energy transitions in
the atom.
• Absorption = atom gaining energy
• Emission = atom releasing energy
• Since all samples of an element give the exact same
pattern of lines, every atom of that element must have
only certain, identical energy states
• The energy of an atom is quantized – limited to discrete
values
• If the atom could have all possible energies, then the
result would be a continuous spectrum instead of lines
Continuous Spectrum
Atomic Line Spectrum
Na
Energy Equation
Max Planck, a German Physicist, studied the emission of
light by hot objects. He determined that there is a
minimum amount of energy lost or gained by an atom,
called a quantum of energy.
E = h
E = Energy, in units of Joules (kg&middot;m2/s2)
h = Planck’s constant (6.626 x 10-34 J&middot;s)
 = frequency, in units of hertz (hz, sec-1)
Long
Wavelength
=
Low Frequency
=
Low ENERGY
Short
Wavelength
=
High Frequency
=
High ENERGY
Wavelength Table
Calculating Energy
What is the energy of a photon of microwave
radiation with a frequency of 3.20 x 1011 s-1 ?
E = h
h = 6.626 x 10-34 J x s
 = 3.20 x 1011 s-1
E = (6.626 x 10-34 J x s)(3.20 x 1011 s-1)
E = 2.12 x 10-22 J
Calculating frequency
Orange light has a wavelength of 6.20 x 10-7 m.
What is the frequency?
c = speed of light = 3.00 x 108 m/s
𝒗 = 𝒄/𝝀
8 m/s
3.0
x
10
𝛎=
6.2 x 10-7 m
= 4.8 x 1014 s-1
Relating Frequency, Wavelength
and Energy
c 
E  h
Common re-arrangements:
E
hc

hc

E
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