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Modern Atomic Model
Or “this is really freaking me out”
Bohr Model of the Atom

How are electrons
arranged around the
nucleus so that they
do not fall in?



Planetary Model
Electrons are in
circular “orbits”
around nucleus
Would eventually
collapse
e-
e-
e-
e+
o o+ o +
+ o +o
+ oo
o
e-
e-
Matter or Energy

Louis de Broglie (1923)

Max Planck said that waves actually act like
small particles
Energy came in small bursts or packets
 Called “photons”


de Broglie said that particles (matter) could
likewise have the properties of waves
(energy)
Figure 11.6: Photons of red and
blue light.

Mathematical Proof
E=mc2
Einstein
E=hυ
Planck
∴mc2 = hυ
Substituted
v-speed of particle for
c-speed of light
∴mv2 = hυ
c=λυ  υ=c/λ
speed of wave

wavelength of wave
speed of particle

wavelength of particle
OR
∴mv2 = h(v/λ)
Rearrange and cancel
one velocity
Planck’s Constant (Js)
h
λ 
mv
Wavelenth
(nm)
Velocity of Particle
(m/s)
Mass of Particle (g)

Experimentally proven that electrons have
characteristics of waves

Wave/Particle Duality of Nature
Everything in nature (matter and
energy) can be treated as a particle or
a wave