Download 3-Bohr Model of Atom

Intro Questions
1. Describe the “Plum Pudding” model
of the atom
2. Describe the Rutherford model of
the atom and the problems with it
3. Explain what an emission spectrum
is and what creates it
Atomic Spectra (Review)
Balmer and Rydberg discovered
mathematical relationship
 1/λ
1/λ = R (1/22 – 1/n2)
R (Rydberg
(Rydberg Constant) = 1.096 x 107 m -1
Bohr Model Postulates:
Bohr’
Bohr’s first “quantum condition”
condition”--Angular
--Angular
momentum (L) is quantized
– L = mvrn = n(h/(2π
n(h/(2π))
Bohr’
Bohr’s second “quantum condition”
condition”-electrons only jump from one “orbital”
orbital” to
another and they give discrete amounts of
energy when they do this
– rn = (0.53 x 10-10m)n2
N = 1, 2, 3…
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The Bohr Model of the Atom
Syllabus References:
13.1.8: Outline a laboratory procedure for
producing and observing atomic spectra
13.1.9: Explain how atomic spectra provide
evidence for the quantization of energy in
atoms.
13.1.10: Calculate wavelengths of spectral
lines from energy level differences and vice
versa.
13.1.11: Explain the origin of atomic energy
levels in terms of the “electron in a box”
model.
Niels Bohr model
Planetary model is good, but should
incorporate the recent quantum theories of
Planck and Einstein, and should explain
atomic spectra.
Bohr Model Postulates:
The orbits have energy described by:
 E = k/n2
K = -13.6 eV for Hydrogen
– The energy of the atom is quantized!
– This is the ionization energy
Photons are emitted when electrons drop
energy levels (orbits) or absorbed when
they jump orbits. The frequency can be
calculated using E = hf
 ΔE = k (1/n2f – 1/n2i)
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Bohr Model:
Complies with observed spectra of
Hydrogen and made predictions of lines
later to be discovered
Assumptions:
– Fixed electrons do not emit radiation
– Angular momentum is quantized
– Can’
Can’t explain how electrons move from one
energy state to the next
Won Nobel Prize in 1922 (37 yrs old!)
Limitations of Bohr’s Model
Doesn’t work with atoms with multiple
electrons
Didn’t explain relative brightness of lines
Didn’t explain bonding
No experimental evidence for the
postulates
De Broglie’s hypothesis
Particles (like electrons) have wave nature
 λ = h/p
 Bohr’
Bohr’s postulate: mvr = n(h/(2π
n(h/(2π)) 
rearrange to get 2πr = nλ
nλ
Each energy level is the circumference
that allows for standing waves
– 2πrn = nλ
nλ
– Substitution with above equation yields Bohr’
Bohr’s
Quantum Condition!!
Explains why electrons have specific
orbitals
Energy of the electron
“Electron in a Box” model
Kinetic Energy of an electron:
Ek = (n2h2)/(8meL2)
– n is the orbital
– h is Planck’s constant
– me is mass of electron
– L is length of “box” or orbital circumference
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One final question
If electrons are waves, what exactly is
doing the “waving?”
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