Download Bohr`s Model of the Atom - Mr. Walsh`s AP Chemistry

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The Bohr Model of the Hydrogen Atom
Unit 6A: Atomic Theory (Quantum/Electronic Structure)
Knowledge/Understanding Goals:
 developments leading to the Bohr model of the atom
 the Bohr model and its limitations
 how the modern quantum mechanical model of the atom grew out of the
Bohr model
Skills:
 calculate the frequency/wavelength of light emitted using the Rydberg
equation
 calculate the energy associated with a quantum number using Bohr’s
equation
Significant Developments Prior to 1913
Discovery of the Electron (1897): J.J. Thompson determined that cathode
rays were actually particles emitted from atoms that the cathode was
made of. These particles had an electrical charge, so they were named
“electrons”.
Cathode Ray Experiment:
https://www.youtube.com/watch?v=GzMh4q-2HjM
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The Bohr Model of the Hydrogen Atom
Discovery of the Nucleus (1909): Ernest Rutherford’s famous “gold foil
experiment” determined that atoms contained a dense, positively-charged
region that comprised most of the atom’s mass. This region was named
the “nucleus”, after the nucleus of a cell.
Gold Foil Experiment:
http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/ruther14.swf
Rutherford (“Planetary”) Model of the Atom (1911): The atom was believed
to be like a miniature solar system, with electrons orbiting the nucleus in
much the same way as planets orbit the sun. Electrons could be found
orbiting anywhere within the low density “electron cloud” region.
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The Bohr Model of the Hydrogen Atom
Rydberg Formula (1888): Johannes Rydberg developed a generalized
formula that could describe the wavenumbers of all of the spectral lines
in hydrogen (and similar elements).
There are several series of spectral lines for hydrogen, each of which
converge at different wavelengths. Rydberg described the Balmer series
in terms of a pair of integers (n1 and n2, where n1 < n2), and devised a
single formula with a single constant (now called the Rydberg constant)
that relates them. (RH = 1.097 x 107 1/m)
 1
1
1
 RH  2  2
λvac
 n1 n2



Rydberg’s equation was later found to be consistent with other series
discovered later, including the Lyman series (in the ultraviolet region;
first discovered in 1906) and the Paschen series (in the infrared region;
first discovered in 1908).
Those series and their converging wavelengths are:
Series
Wavelength
n1
n2
91 nm
1
2→∞
Balmer
365 nm
2
3→∞
Paschen
820 nm
3
4→∞
Lyman
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The Bohr Model of the Hydrogen Atom
Bohr’s Model of the Atom (1913)
In 1913, Niels Bohr combined atomic, spectroscopy, and quantum theories
into a single theory. Bohr hypothesized that electrons moved around the
nucleus as in Rutherford’s model, but that these electrons had only certain
allowed quantum values of energy, which could be described by a quantum
number (n). The value of that quantum number was the same n as in
Rydberg’s equation, and that using quantum numbers in Rydberg’s equation
could predict the wavelengths of light emitted when the electrons gained or
lost energy by moved from one quantum level to another.
Bohr’s model gained wide acceptance, because it related several prominent
theories of the time. The theory worked well for hydrogen, giving a
theoretical basis for Rydberg’s equation. Bohr defined the energy
associated with a quantum number (n) in terms of Rydberg’s constant:
En  
RH
n2
http://highered.mheducation.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0072482621/59229/
Bohr_Nav.swf::The%20Bohr%20Atom
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The Bohr Model of the Hydrogen Atom
The Bohr model worked well for hydrogen. However, the equations could not
be solved exactly for atoms with more than one electron, because of the
additional effects that electrons exert on each other (Coulomb force
kq q
F  d12 2 ).
By the mid-1920s, quantum physics was changing. The concept of “allowed
states” gave way to probability distributions, governed by Werner
Heisenberg’s uncertainty principle, which states that there is a limit on how
much certainty can exist in the state of a sub-atomic particle.
For example, the more exactly an electron’s position is specified, the
less the exactly the velocity or momentum can be specified.
Or, as soon as you observe light energy, it loses its duality. (must act
as either a wave or a particle)
In 1925, Erwin Schrödinger used the “wave equation”—an equation that
describes how a wave changes with time—to describe where electrons would
be found (in terms of probability) if the electron behaved as a wave rather
than as a particle.
Schrödinger found that by treating each electron as a unique wave function
governed by the wave equation, the energies of the electrons could be
predicted by the solutions to the wave equation without the need for an
empirically-derived number (the Rydberg constant). This use of
Schrödinger’s equation to construct a probability map for the electrons in an
atom is the basis for the modern quantum-mechanical model of the atom.
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The Bohr Model of the Hydrogen Atom
Probability Maps: graphical depictions of where certain electrons are likely
to be found at any given moment around the nucleus.
Each map represents a specific orbital, capable of holding 2 electrons. The
shapes of each orbital are determined using Schrödinger’s equation.
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