3.2 AE&PT the Quantum Mechanical Model of the Atom June 17, 2011

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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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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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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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


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


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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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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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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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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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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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

3.2 AE&PT the Quantum Mechanical Model of the Atom June 17, 2011

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