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8/3/2019 3.2 AE&PT the Quantum Mechanical Model of the Atom June 17, 2011
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3.2
ATOMS, ELECTRONS,
and PERIODIC
TRENDS:
The Quantum
Mechanical
Model of the
Atom
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DevelopingQuantumMechanics
Scientists
attempt toexplainelectronbehaviour of
atoms what andwhere
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Louis de Broglie (1892-1987)
Wave Nature of Electron1924 light not only entity to exhibit
wave-particle duality
ordinary particles such as electrons can
also exhibit wave characteristics in certain circumstances
electron has associated with it a system of"matterwaves"
waves possess crests that disappear at one point andappear an instant later at another point
distance between successive crests (P) is the de Brogliewavelength and is calculated from P = h/mv, where h isPlanck's constant and mvis momentum
wavelength associated with an electron and derived from itsmomentum yields a standing-wave pattern identical to
Bohr's allowed energy levels
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Erwin Schrdinger (1887-1961)
Wave Equation1926 used dual nature of
particles to produce
basic equation of quantummechanics
equation treats electrons as matterwaves
equation described ]as the densitydistribution--some regions rich inelectron matter while others scarce
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Max Born (1882-1970)Probability Density
figured out what the waveequation actually predicts
concept of the electron as
a point particle moving in a well-defined path around the nucleus is replacedin wave mechanics by clouds thatdescribe the probable locations of
electrons in different statesBorn'sprobability density most
dramatic change in viewing our world sinceNewton and gravity.
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Werner Heisenberg (1901-1976)
Uncertainty Principleact of measuring an electron's
properties by hitting it with gamma
rays alters electron's behavior
you couldmeasure the position
of an electron (or other particle)
OR you couldmeasure its momentum
more precisely you measure one property,
the more you throw the other off
placed concept in an equation using Planck'sconstant, and called it the uncertainty principle
many resisted this idea, it eventually became
accepted as a fundamental law of nature.
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Uncertainty principle
A free electron moves into
the focus of a hypothetical
microscope (a) and is struck
by a photon of light; thephoton transfers
momentum to the electron.
The reflected photon is seen
in the microscope (b), butthe electron has moved out
of focus. The electron is not
where it appears to be.
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Quantum Numbers:
The Bohr modelwasa
one-dimensional model
that used one quantum
number to describe theelectrons in the atom.
Only the size of the orbit
was important, which
was described by the nquantum number.
Schrodingerdescribed
an atomic modelwith
electrons in three
dimensions. This modelrequired three
coordinates, orthree
quantum numbers, to
describe whereelectronscould befound.
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Quantum Numbers:
The three coordinates from Schrodinger's
wave equationsare the
principal (n),
angular (l),
and magnetic (m) quantum numbers.
These quantum numbers describe the size,
shape, and orientation in space of theorbitals on an atom.
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Four Quantum Numbers:
Four numbersare used to describe
electrons in the modern model ofan atom.
1. Principal quantum number - n
Describes the energy level within the
atom.y Energylevelsare 1 to 7y Maximum number of electrons in n is 2 n 2
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Four Quantum Numbers:
2. Secondary (orbital-shape) quantumnumber - lDescribes the sublevel in ny Sublevels in the atoms of the known elementsare s - p - d - f(l= 0, 1, 2, and 3 respectively)
y Each energylevel hasn sublevels.y Sublevels of different energylevels may have
overlapping energies.
The secondary quantum number alsodescribes the shape of the orbital.
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Four Quantum Numbers:
3. Magnetic quantum number ml
Describes the orbital within a sublevels (l= 0) has 1 orbital (ml = 0)p (l= 1) has 3 orbitals (ml = -1,0,+1)d (l= 2) has 5 orbitals (ml = -2,-1,0,+1,+2)f (l= 3) has 7 orbitals (ml =-3,-2,-1,0,+1,+2,+3)Orbitals contain 1 or 2 electrons, nevermore.
mlalso describes the direction, or
orientation in space for the orbital.
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Four Quantum Numbers:
4. Spin quantum number - ms
This fourth quantum number describes
the spin of the electron.y Electrons in the same orbital must have
opposite spins.
Possible spinsare clockwiseorcounterclockwise.
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Rules governing the
combinations of quantumnumbers:
The first three quantum numbers n, l,and m
lare integers.
The principal quantum number (n)cannot be zero.
y n must be 1, 2, 3, etc...
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Rules governing the
combinations of quantumnumbers:
The secondary quantum number (l) can
be any integer between 0 and n - 1.Forn = 3, lcan be either0, 1, or2.
The magnetic quantum number (ml) canbe any integer between -land +l.
Forl= 2, m can be either -2, -1, 0, +1, or+2.
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Rules governing the
combinations of quantumnumbers:
The spin quantum number (ms) is
arbitrarily assigned the values
+1
/2 and -1
/2.
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Allowed combinations of Quantum
Numbers:
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Quick Calculations with the
Principal Quantum Number:
n2 = total number of orbitals in a shell
(or energy level)
2n2 = total number of electrons inorbitals of a shell (or energy level)
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Quick Calculations with the
Quantum Numbers:1.Whichofthe following combinationsofquantum numbers are possible /
impossible?Ifa combination is impossible,correct it.
(a, b, and c are answered.)
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Quick Calculations with the
Quantum Numbers:
a.n = 2, l= 2, ml= -1, m
s= -1/2 ___1______
b.n = 3, l= 2, ml= -3, ms = +1/2 ___-2_____c.n = 4, l= 2, m
l= -1, m
s= -1/2 _possible__
d.n = 0, l= 1, ml= -1, m
s= -1/2 ___________
e.n = 5, l= 3, ml= -1, ms = -1/3 ___________
f. n = 6, l= 5, ml= +4, m
s= +1/2 ___________
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Quick Calculations with the
Quantum Numbers:
d.n = 0, l= 1, ml= -1, m
s= -1/2 2,3,4,5,6, or7
e.n = 5, l= 3, ml= -1, m
s= -1/3 __ +/-1/2 __
f. n = 6, l= 5, ml= +4, ms = +1/2 __possible__
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Quick Calculations with the
Quantum Numbers:
2. Howmany electronscan have the quantumnumbers n = 5, m
l= +1?
Answer:3. Howmany orbitalscan have the designationn = 3?
Answer:4. Howmany electronscan have the designationn = 3?
Answer:
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Quick Calculations with the
Quantum Numbers:
2.Howmany electronscan have the quantum numbersn = 5, l = 4, m
l= +1?
Answer: ms
= +1/2 or -1/2 2 electrons
3. Howmany orbitalscan have the designation n = 3?
Answer: n2 = 32 = 9 orbitals
4. Howmany electronscan have the designation n = 3?
Answer: 2n2 = 2 x 32 = 18 electrons
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Electron Orbitals
Orbits and orbitals
When a planet movesaround the sun, you canplot a definite path for it
which is called anorbit. This is similar tothe motion of anelectron in a Bohr atom.
An electron of an atomis located in a region of
space known as anorbital. It is a sort of3D map of the placesthat an electron is likelyto be found.
Diagrams of orbitals
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Electron Orbitals
Shapes of the s orbitalsRepresentations of (a) 1s, (b) 2s, and (c)3s orbitals. Cutaway views of these
sphericalorbitals are shown on thetop, with the probability of finding an
electron represented by the density ofthe shading. Electron probabilitydistribution plots of y2 as a function ofdistance from the nucleus are shown onthe bottom. Note that the 2s orbital hasburied within it a spherical surface ofzero probability (a node), and the 3sorbital has within it two spherical
surfaces of zero probability. The differentcolors of different regions in the 2s and3s orbitals correspond to differentalgebraic signs of the wave function,analogous to the different phases of awave,
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Electron Orbitals
Shapes of the p-orbitalsThe three 2p orbitals. Part (a) isa plot giving the probability offinding a 2p electron as afunction of its distance from thenucleus. Part (b) shows
representations of the three 2porbitals, each of which isdumbbell-shapedandoriented in space along one ofthe three coordinate axes x, y, orz. Each p orbital has two lobes ofhigh electron probabilityseparated by a nodal planepassing through the nucleus. Thedifferent shadings of the lobesreflect different algebraic signsanalogous to the differentphases of a wave.
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Electron Orbitals
Shapes of the dorbitalsRepresentations of the five3d orbitals. Four of theorbitals are shaped like a
cloverleaf(a-d), and thefifth is shaped like anelongated dumbbellinside a donut(e). Alsoshown is one of the seven4f orbitals (f). As with porbitals, the differentshadings of the lobesreflect different phases.
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Cool Stuff To See And Do
Web Videos
The Quantum Number Rag
http://www.youtube.com/watch?v=Tilkl4lRqzo
The Quantum Number Rag - Michael Offutt
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Cool Stuff To See And Do
Web Simulations
Atomic orbitals (USEFUL)http://micro.magnet.fsu.edu/electromag/java/atomicorbitals/Observe s, p, d, and f orbitals.
http://michele.usc.edu/105a/atomic_structure/orbitals/orbitals.html (DOWNLOAD CHIME FIRST)On this advanced page, you can view
representations of various orbitals and theequations that describe them (from theUniversity of Southern California site).
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3.2 Section Review(p.138):
#1,2,3, 5, and 6