Download 2_Lecture BOHR.pptx

Structure of the atom
•  What IS the structure of an atom?
•  What are the properties of atoms?
REMEMBER: structure affects function!
•  Important questions:
Where are the electrons?
What is the energy of an electron?
Chapter 3 Part 1
Dual Nature of Light
λν=c
E = hν
Line Spectrum
Bohr Model of Hydrogen Atom
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Light behaves as a wave! Or does it???
Several phenomena were inconsistent with the wave nature of light.
Blackbody radiation
Photoelectric effect
Line spectrum of atoms
The color of the heating element
changes with temperature from
black (cold) to “white” hot.
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Black body radiation
Intensity of emitted light predicted by the wave mechanics differs from
experiment.
Planck shows:
E= n hν
n = integer
ν = frequency of emitted light
h = Planck s constant
= 6.626 × 10−34 J-s
Observed (solid lines) and predicted
(classical, non-quantum model) spectra
of radiating black-bodies at 5000 K (red)
and 7000 K (blue). The sun has blackbody temperature of 5780 K.
Energy = hν
photon
energy
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frequency of
photon
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Photon energy
What is the energy of a green photon (wavelength
equal to 523 nm)?
1. 
2. 
3. 
4. 
5. 
5.74 × 10+14 J
3.80 × 10−19 J
5.23 × 10−29 J
1.90 × 10−19 J
3.80 × 10−28 J
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Spectroscopy: light interacting with matter
λ
Common use
Dangerous or not???
Energy
Interaction with matter
gamma
X-Ray
ultraviolet
visible
infrared
microwave
radio
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Photoelectric effect: Classically, expect metal to soak up
energy of light until e– binding energy (Eb) is overcome.
BUT
–  No e– s emitted until ν = ν0
–  No waiting time
–  Kinetic energy of e– = h(ν– ν0)
= ½ mv2
where v = speed of electron emitted
Ephoton = hν = Eb + ½ mv2
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Metal atoms absorb
only 1 quantum of
energy: it happens all
at once as if struck by
a particle è photon
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Visible (white) light contains a continuous distribution
of frequencies of electromagnetic radiation.
Spectrum: distribution of ν in emitted radiation
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Different types of light produce different spectra
DEMONSTRATIONS: How can we explain all of this?
Examples
Laser
Spectrum Type
ν’s
Light bulb
Hg vapor
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Hg vapor spectrum
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Observation of line spectra implies that atoms
have discrete (quantized) energy levels.
Excited state (E3)
Excited state (E2)
absorption
ΔE = hν
emission
ΔE = hν
Ground state (E 1)
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There are only 4 emission lines in the visible
spectrum of hydrogen
H2 discharge tube
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Each element has a unique line spectrum.
(Structure affects function)
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To explain this phenomenon, we start with the
simplest atom (hydrogen) and try to understand it.
H atom has 1 proton (+) and 1 electron ( – ) .
Where is the proton? Where is the electron?
Bohr Model of H atom (1913)
Bohr proposes that the electron
is in one of several possible
“orbits” around the proton.
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If the electron is in an “orbit”, what is it’s energy?
Bohr used the line spectrum to figure out the energy differences between
“orbits” and then deduced the energy of the electron in each orbit.
⎛ 1⎞
En = − RH ⎜ 2 ⎟
⎝n ⎠
∞
n = 6n = 5
n=4
n=3
n = 1, 2, 3, …..
principal quantum number
Energy
n=2
RH = Rydberg constant
RH = 2.18x10–18J
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n=1
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Energy of an Electron (Bohr Model)
Energy is given off when an electron is put into orbital.
Coulomb’s Law helps
where
E∝
Q1Q2
d
Q1 = charge of electron (negative)
Q2 = charge of proton (positive)
d = orbit radius (distance between nucleus and electron)
•  Put electron into the orbital: attractive interaction
Energy will be negative (means energy is given off)
•  Reverse the process: try to remove the electron
Energy will be positive (energy is absorbed)
Note: Orbit energy in Bohr Model is negative, so it must correspond to
energy needed to put electron into the orbit.
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Recall the Goal
•  What IS the structure of an atom?
•  What are the properties of atoms?
REMEMBER: structure affects function!
•  Important questions:
Where are the electrons?
What is the energy of an electron?
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Review Quantized Energy
•  Energy comes in discrete packets, or “quanta”
•  Energy of a quantum ε is
ε = hν
ν = frequency of light
h = Planck’s constant = 6.63 × 10−34 J·s
•  Total energy in light beam is nhν (n = 1, 2, 3, …)
Dual Nature of Light
Wave
λν = c
Particle
E = hν
Experimental support:
•  black-body radiation (Planck, 1900)
•  photoelectric effect (Einstein, 1905)
•  line spectra of hydrogen (Bohr, 1913)
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Bohr Model of H atom (1913)
Line spectrum is due to electronic transitions
Atoms absorb or emit light when e− changes its orbit
ΔE = Ef – Ei = hν
⎛1
1⎞
hν = ΔE = RH ⎜⎜ 2 − 2 ⎟⎟
⎝ ni nf ⎠
where ni and nf are integers.
This predicts the H-atom spectrum EXACTLY!
Note:
nf > ni
nf < ni
ΔE is +
ΔE is –
(absorbs photon)
(emits photon)
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Energy levels in Bohr Model
∞
n = 6n = 5
n=4
n=3
Energy
n=2
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n=1
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Be able to use the Bohr Model to solve
problems describing electronic transitions in
the Hydrogen atom.
If ni = 2 and nf = 1, is energy emitted or absorbed?
1  . emitted
2  . absorbed
Of the following transitions in an H-atom, which one
results in the emission of the highest energy photon?
1. n=1 è n = 6
2. n=6 è n = 3
3. n=3 è n = 6
4. n=1 è n = 4
5. n=6 è n = 1
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The Bohr model explained some experimental
evidence for hydrogen atom, but it failed for other
atoms.
From Orbits to Orbitals :
DeBroglie (1924): if light has dual wave/particle behavior, perhaps
matter does also.
Wavelength of matter waves:
λ = h/mv
·  Electron waves discovered in 1927 (Davidson and Garmer)
(Basis for electron microscope)
·  For a baseball and bacteria, λ is too small to observe, but for
electrons λ is of atomic size producing profound effects.
Electrons in atoms behave as "standing" waves. (Schrödinger
equation, 1926)
Enter the Quantum World…
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There is experimental evidence for the wave
behavior of electrons
X-Ray diffraction
electron diffraction
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Electron microscope provides
experimental evidence that particles have wave
properties.
Electrons diffract when interacting with matter.
Used to image some of the tiniest objects.
Image of HIV budding from T-cell
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Heisenberg Uncertainty Principle
It is NOT possible to simultaneously know the position &
velocity (momentum, mv) of a particle with complete certainty
•
Derives from wavelike nature of matter
This really becomes important when dealing with subatomic matter
• All electrons have a velocity, therefore, you cannot specify their
exact location
•  Contradicts Bohr’s planetary model of the hydrogen atom
In other words: It is not appropriate to imagine e– moving in nice
little orbits around the nucleus
Can we say anything about where the e– are?
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Solutions of Schrödinger equation are
wavefunctions (Ψ)
H Ψ= E Ψ
Ψ(x,y,z) = wavefunction (no physical significance)
Ψ2(x,y,z) = probability of finding one electron in a region of space,
also called electron density
Think of electrons as clouds of electron density.
Orbitals = Ψ2(x,y,z)
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Prepare for recitation tomorrow
BRING
•  Chem 110 Student packet
•  textbook
•  Calculator
•  Completed homework (pp. 26-27)
–  Explain your reasoning!
–  Use Problem Solving Guidelines in the student packet (p 16,
sample problems on pp 17-19)
You will be working on the recitation worksheet found
on page 28-29. (Don’t do it ahead of time…)
•  First RQ will be at the beginning of recitation tomorrow
•  First Quiz on Angel tomorrow
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