Bohr

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Quantum Mechanics
Through the Looking Glass
2
This is how the model of the atom has developed
so far
3
Understanding Radiant Energy
c ?? where c 2.99 x 108 m/s
4
Sample Problem The yellow light given off by a
sodium lamp has a wavelength of 589 nm. What is
the frequency of this radiation?
c ??, where c 2.99 x 108 m/s
x ?
2.99 x 108 m/s 589 nm x
? 5.08 x 1014 s 1-
5
Plancks Theory Energy is released
incrementally as as individual packets of energy
called quanta where the change in energy of a
system is ?E h?, 2h?,n h? and h (planks
constant) 6.63 x 10-34 J-s
Sample Problem Calculate the smallest increment
of energy that an object can absorb from yellow
light whose wavelength is 589 nm
we know from the previous problem c ??, that ?
5.08 x 1014 s 1-
since ?E h? and h (planks constant) 6.63 x
10-34 J-s
?E (6.63 x 10-34 J-s )(5.08 x 1014 s 1- )
?E 3.37 x 1019 J
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A Continuous Spectrum
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Light is a form of ...
Electromagnetic Radiation
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An Emission Spectrum...
is produced when a gas is placed under reduced
pressure...
...and a high voltage is applied
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Balmers Description of the Emission Spectrum of
Hydrogen
-
where n 3, 4, 5, 6 and C 3.29 x 1015 s-1
? C
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Bohrs Model of the Atom (1914)
Limited the path of electrons to circular orbits
with discrete energy (quantum energy levels)
Explained the emission spectrum of hydrogen
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Radii and Energies of the Three Lowest Energy
orbits in the Bohr Model
0

En -RH
n 3
-0.242 x 10 -18 J
n 2
-0.545 x 10 -18 J
where RH 2.18 x 1018J
En -RH
n 1
-2.18 x 10 -18 J
o
0 A
o
o
0.53 A
2.12 A
4.77 A
radius n2 (5.3 x 10-11m)
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Hydrogens Spectrum is Produced When
Electrons appear in excited state
electrons transfer from an excited state
Electrons are excited from their ground state
Electrons return to their ground state
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Pashen Series

• Infrared

Balmer Series

• Visible and Ultraviolet

Lyman Series

• Ultraviolet

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Explaining the Emission Spectrum of Hydrogen
since ?E E f - E i
-
then ?E
-RH
-

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Sample Problem Calculate the wavelength of
light that corresponds to the transition of the
electron from the n 4 to the n2 state of the
hydrogen atom.
-
2.18 x 10-18J
?E
-4.09 x 10-19 J
?E
-4.09 x 10-19 J
? ?E

h
6.63 x 10-34 J-s
? 6.17 x 1014 s -1
? c
3.00 x 108 m/s
4.86 x 10-7 m 486 nm (green)
?
6.17 x 1014 s -1
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ON TO PARTICLE WAVES