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Strange Days Max Planck (1894) studied black-
body radiation (when solids are heated to
incandescence) Results could not be explained by
the physics of the day. Based on his experiments, energy
can only be transferred in discrete (quantized) amounts (1899)
Called these small packets of energy “Quanta” (singular = quantum)
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The Cat’s out of the Bag
Einstein proposed that electromagnetic radiation itself is quantized and can be thought of as a stream of “particles” or photons (1905).
E = h & c = E = hc/ Neils Bohr attempted to explain the stability of
the atom and the Hydrogen Emission spectrum using the idea of quantized energy (1913).
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Bohr’s Model
Electrons only in permitted circular orbits The Ground State is the open orbit closest to
nucleus (lowest available energy) The Excited State is an orbit farther away
from nucleus (it has higher energy) Principal Quantum # (n) given to determine orbit
Small n means a small radius, closer to the nucleus Value: n > 0
n = 1n = 2
n = 3
Nucleus
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Light Emission occurs when Electrons absorb energy and
Jump to a higher energy level (excited state) Electrons then release energy
Fall to a lower energy levelEmit photon of lightCalculate the difference using E = h
n = 2
n = 3
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Something’s Rotten in Denmark
Bohr’s model works perfectly…for hydrogen.
More precise measurements of line spectra of higher elements reveal more lines.
Arnold Sommerfeld (1868-1951) suggests elliptical orbits.
Remember, more lines= more Energy Levels!
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Old SpectroscopyTerms
Shape Matters
Azimuthal Quantum # (l) given to determine shape of the electron’s orbit
0 l (n – 1) l = 0 s (spectral) l = 1 p (principal) l = 2 d (diffuse) l = 3 f (fine) l = 4 g (but we don’t have enough ‘s)
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More Lines Still – Zeeman Effect
When atoms were placed into a magnetic field, triplets were formed from singlets
Sommerfeld chimes in again, in 1916, saying orientation in space must matter
Singlet
Triplet More Energy More Energy Levels!?!Levels!?!
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Orient This, Baby!
Magnetic Quantum # (ml) given to determine orbital’s orientation in space
- l ml l For s orbitals (l = 0), only 1 possibility For p orbitals, 3 possible suborbitals For d’s, 5 For f’s, 7 s-orbitalpx-orbitalpy-orbital
pz-orbital3 p-orbitals
z
x
y
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You Guessed it…still more lines
AZE – Anomalous Zeeman Effect = even more lines under certain circumstances
Wolfgang Pauli (1900 – 1958) proposed a hidden rotation
Unfortunately, Pauli is unable to visualize it, so Uhlenbeck & Goudsmit get credit for it (leading to a Nobel Prize) Wolfgang Pauli
I’ll Be Back!Just You
Wait!
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You Spin Me Right ‘Round…
Spin Quantum # (ms) given to electrons to specify additional angular momentumNothing to do with the orbitals
Two values, +1/2 or -1/2Also called Up or DownNot literally true – have to be spinning ~10x
speed of light to account for extra momentum
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Now have 4 Quantum Numbers
Specify location of electrons in atomn = energy level (n > 0)
lower the number, closer to the nucleus
l = orbital shape (0 l [n – 1]) Shapes are abbreviated s p d f…
ml = suborbital orientation (- l ml l) s 1 possible, p 3, d 5, f 7…
ms = spin (+1/2, -1/2) Up & Down
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Size Still Matters
Principal Quantum # (n) Integer from 1 to 7 (theoretically more)The larger n is, the larger the orbit
n = 1
n = 2
n = 3
n = 4
Also, the larger the n, the more energy that is “stored” by the electron.
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Shapes Determined w/ Azimuthal (l)
“s” orbitals – spherical, Larger n = bigger sphere
“p” orbitals – dumbbell shapedLarger n = bigger dumbbell
1s2s
3s
2p 3p 4p
Also, the more complex the shape, the more energy that is “stored” by the electron.
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Every Which Way (But Loose)
n > 1
You Will Have toDraw These!
Each type of orbital has multiple orientations possible (except s)
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Crazy Orbital Shapes
“d”orbitals Only possible when
n > 2 You don’t have to
draw all of these!!! Just this one!
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A Closer Look
An orbital is the probable location of the electron90% of time e- is in the orbital (other 10%?)
A node is the position within an orbital where the probability of finding an electron is 0.
2px orbital
Node:Electron is Never There!
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So Far What We Know
Electrons are in orbitalsOrbitals differ in:
Size (n) Shape (l) Orientation (ml)
Electrons have spins (ms) Why do they matter?
(Photons do not obey this principle)22
Knock, Knock!!!
Pauli Exclusion Principle – no two electrons can have the same 4 quantum numbers!
Electrons cannot stack up on each other.
If an orbital is full, the next e- must go to a higher orbital.
This is what makes matter solid!!!
I Told You I’d Be Back!And this time, I got my
Nobel Prize!!!Mwah-ha-ha!!!Guess Who’s
Back…
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Pauli’s Revenge Each e- must have a different set of Q#’s (0 ≤ l ≤ n-1) (-l ≤ ml ≤ l) (+1/2 or -1/2)
n(level)
l(orbital)
ml
(suborbital)
ms
(spin)
# e-s Possible
1 0 (s) 0 +½, -½ 2
20 (s) 0 +½, -½ 2
1 (p) -1,0,1 3(+½, -½) 6
3
0 (s) 0 +½, -½ 2
1 (p) -1,0,1 3(+½, -½) 6
2 (d) -2,-1,0,1,2 5(+½, -½) 10