1 © 2009 brooks/cole - cengage test ii raw grades: hi92 lo9 average:37.3 curve 25 pt. grades...

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© 2009 Brooks/Cole - Cengage

Test IITest II

Raw grades:Raw grades:HiHi 9292LoLo 99Average:Average: 37.337.3Curve Curve 25 pt.25 pt.

Grades (curved) are posted on BlazeVIEWGrades (curved) are posted on BlazeVIEWLook at tests/ask questions after class or Look at tests/ask questions after class or Wednesday 9 – 1pm (in my office)Wednesday 9 – 1pm (in my office)

Analysis/solutions session can be scheduled if Analysis/solutions session can be scheduled if there is interest (there is interest (email [email protected])email [email protected])

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Midterm GradesMidterm Grades

Based only on Test 1 (75.7%) and Based only on Test 1 (75.7%) and OWL (24.2%)OWL (24.2%)

The last day to drop without academic penalty: The last day to drop without academic penalty: March 3d, by 11:59 pm; March 3d, by 11:59 pm; limited to five withdrawals per college lifelimited to five withdrawals per college life

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Chapter 6Chapter 6

Chem 1211

Class 13

Atomic Structure

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Atomic Line Spectra and Atomic Line Spectra and Niels BohrNiels Bohr

Atomic Line Spectra and Atomic Line Spectra and Niels BohrNiels Bohr

Bohr’s theory was a great Bohr’s theory was a great accomplishment.accomplishment.

Rec’d Nobel Prize, 1922Rec’d Nobel Prize, 1922

Problems with theory —Problems with theory —

• theory only successful for H.theory only successful for H.

• introduced quantum idea introduced quantum idea artificially.artificially.

• So, we go on to So, we go on to QUANTUMQUANTUM or or WAVE MECHANICSWAVE MECHANICSNiels BohrNiels Bohr

(1885-1962)(1885-1962)

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Quantum or Wave Quantum or Wave MechanicsMechanics


de Broglie (1924) de Broglie (1924) proposed that all proposed that all moving objects have moving objects have wave properties. wave properties.

For light: E = mcFor light: E = mc22

E = hE = h = = hc / hc /

Therefore, mc = h / Therefore, mc = h / and for particlesand for particles

(mass)(velocity) = (mass)(velocity) = h / h /

de Broglie (1924) de Broglie (1924) proposed that all proposed that all moving objects have moving objects have wave properties. wave properties.

For light: E = mcFor light: E = mc22

E = hE = h = = hc / hc /

Therefore, mc = h / Therefore, mc = h / and for particlesand for particles

(mass)(velocity) = (mass)(velocity) = h / h /

L. de BroglieL. de Broglie(1892-1987)(1892-1987)

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Baseball (115 g) Baseball (115 g) at 100 mphat 100 mph

= 1.3 x 10= 1.3 x 10-32-32 cm cm

e- with velocity e- with velocity = =

1.9 x 101.9 x 1088 cm/sec cm/sec

= 3.88 x 10= 3.88 x 10-10-10 m m = 0.388 nm= 0.388 nm

Experimental proof of waveExperimental proof of waveproperties of electronsproperties of electrons



PLAY MOVIE

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Uncertainty PrincipleUncertainty PrincipleProblem of defining Problem of defining nature of electrons in nature of electrons in atoms solved by W. atoms solved by W. Heisenberg.Heisenberg.

Cannot simultaneously Cannot simultaneously define the position and define the position and momentum (= m•v) of an momentum (= m•v) of an electron.electron.

We define e- energy We define e- energy exactly but accept exactly but accept limitation that we do limitation that we do not know exact not know exact position.position.

Problem of defining Problem of defining nature of electrons in nature of electrons in atoms solved by W. atoms solved by W. Heisenberg.Heisenberg.

Cannot simultaneously Cannot simultaneously define the position and define the position and momentum (= m•v) of an momentum (= m•v) of an electron.electron.

We define e- energy We define e- energy exactly but accept exactly but accept limitation that we do limitation that we do not know exact not know exact position.position.

W. HeisenbergW. Heisenberg1901-19761901-1976

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Schrodinger applied idea of Schrodinger applied idea of e- behaving as a wave to e- behaving as a wave to the problem of electrons in the problem of electrons in atoms.atoms.

He developed the He developed the WAVE WAVE EQUATIONEQUATION

Solution gives set of math Solution gives set of math expressions called expressions called WAVE WAVE FUNCTIONS, FUNCTIONS, psipsi))

Each describes an allowed Each describes an allowed energy state of an e-energy state of an e-

Quantization introduced Quantization introduced naturally.naturally.

E. SchrodingerE. Schrodinger1887-19611887-1961



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WAVE FUNCTIONS, WAVE FUNCTIONS,

• is a function of distance and two is a function of distance and two angles.angles.

• • Each Each corresponds to an corresponds to an ORBITALORBITAL — — the region of space within which an the region of space within which an electron is found.electron is found.

• • does NOT describe the exact does NOT describe the exact location of the electron.location of the electron.

• • 22 is proportional to the probability is proportional to the probability of finding an e- at a given point.of finding an e- at a given point.

There is a set of numbers that are There is a set of numbers that are

parameters of parameters of : they are called : they are called quantum quantum numbersnumbers

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QUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERS

The The shape, size, and energyshape, size, and energy of each orbital is a of each orbital is a function of 3 quantum numbers:function of 3 quantum numbers:

nn (principal)(principal) →→ shell shell

ll (angular) (angular) → → subshellsubshell

mmll (magnetic)(magnetic) → → designates an orbital designates an orbital within a subshellwithin a subshell

According to that numbers, electrons in atom According to that numbers, electrons in atom grouped in shells and subshellsgrouped in shells and subshells

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Subshells & Subshells & ShellsShells


• Subshells grouped in shells.Subshells grouped in shells.• Each shell has a number called Each shell has a number called

thethe PRINCIPAL QUANTUM PRINCIPAL QUANTUM NUMBER, NUMBER, nn

• The principal quantum number The principal quantum number of the shell is the number of the of the shell is the number of the period or row of the periodic period or row of the periodic table where that shell begins.table where that shell begins.

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n = 1n = 1

n = 2n = 2

n = 3n = 3

n = 4n = 4

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Types of Types of OrbitalsOrbitals

s orbitals orbital p orbitalp orbital d orbitald orbital

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OrbitalsOrbitals• No more than 2 e- assigned to an orbitalNo more than 2 e- assigned to an orbital

• Orbitals grouped in s, p, d (and f) Orbitals grouped in s, p, d (and f) subshellssubshells

s orbitalss orbitals

d orbitalsd orbitals

p orbitalsp orbitals

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s orbitalss orbitals

d orbitalsd orbitals

p orbitalsp orbitals

s orbitalss orbitals p orbitalsp orbitals d orbitalsd orbitals

No.No.orbs.orbs.

No. No. e-e-

11 33 55

22 66 1010

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SymbolSymbol ValuesValues DescriptionDescription

n (major)n (major) 1, 2, 3, ..1, 2, 3, .. Orbital size Orbital size and energy and energy

where E = -R(1/nwhere E = -R(1/n22))

ll (angular)(angular) 0, 1, 2, .. n-10, 1, 2, .. n-1 Orbital shape Orbital shape or type or type (subshell) (subshell)

mmll (magnetic) (magnetic) -l..-l..0..+0..+ll Orbital Orbital orientationorientation

# of orbitals in subshell = # of orbitals in subshell = 22ll + 1 + 1

QUANTUM NUMBERSQUANTUM NUMBERS

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Types of

Atomic Orbitals

See Active Figure 6.14

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Shells and SubshellsShells and SubshellsShells and SubshellsShells and Subshells

When n = 1, thenWhen n = 1, then ll = 0 and m= 0 and mll = 0 = 0

Therefore, in n = 1, there is 1 Therefore, in n = 1, there is 1 type of type of subshellsubshell

and that subshell has a single and that subshell has a single orbitalorbital

(m(mll has a single value has a single value →→ 1 orbital) 1 orbital)

This subshell is labeled This subshell is labeled ss (“ess”) (“ess”)

Each shell has 1 orbital labeled s, Each shell has 1 orbital labeled s, and it is and it is SPHERICALSPHERICAL in shape.in shape.

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s Orbitals— Always s Orbitals— Always SphericalSpherical

Dot picture Dot picture of electron of electron cloud in 1s cloud in 1s orbital.orbital.

Surface Surface densitydensity

4πr4πr22 versus versus distancedistance

Surface of Surface of 90% 90% probabiliprobability sphere ty sphere

See Active Figure 6.13

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1s Orbital1s Orbital

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22



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p Orbitalsp Orbitalsp Orbitalsp OrbitalsWhen n = 2, then When n = 2, then ll = 0 and = 0 and 11

Therefore, in n = 2 shell Therefore, in n = 2 shell there are 2 types of there are 2 types of orbitals — 2 subshellsorbitals — 2 subshells

For For ll = 0 = 0 mmll = 0 = 0

this is a s subshellthis is a s subshell

For For ll = 1 = 1 mmll = -1, 0, +1 = -1, 0, +1

this is a this is a p p subshellsubshell with with

3 orbitals3 orbitals

When n = 2, then When n = 2, then ll = 0 and = 0 and 11

Therefore, in n = 2 shell Therefore, in n = 2 shell there are 2 types of there are 2 types of orbitals — 2 subshellsorbitals — 2 subshells

For For ll = 0 = 0 mmll = 0 = 0

this is a s subshellthis is a s subshell

For For ll = 1 = 1 mmll = -1, 0, +1 = -1, 0, +1

this is a this is a p p subshellsubshell with with

3 orbitals3 orbitals

planar node

Typical p orbital

planar node

Typical p orbital

See Screen 6.15See Screen 6.15

When When ll = 1, there is = 1, there is a a PLANARPLANAR NODENODE thru the thru the nucleus.nucleus.

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p Orbitalsp Orbitalsp Orbitalsp Orbitals

The three p orbitals lie 90The three p orbitals lie 90oo apart in space apart in space

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2p2pxx Orbital Orbital 3p3pxx Orbital Orbital

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d Orbitalsd Orbitalsd Orbitalsd OrbitalsWhen n = 3, what are the values of When n = 3, what are the values of ss??

ll = 0, 1, 2 = 0, 1, 2 and so there are 3 subshells in the and so there are 3 subshells in the shell.shell.

For For ll = 0, = 0, mmll = 0 = 0

→→ s subshell with single s subshell with single orbitalorbital

For For ll = 1, = 1, mmll = -1, 0, +1 = -1, 0, +1

→→ p subshell with 3 orbitalsp subshell with 3 orbitals

For For ll = 2, = 2, mm l l = -2, -1, 0, +1, +2= -2, -1, 0, +1, +2

→→d subshell with 5 d subshell with 5 orbitalsorbitals

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d Orbitalsd Orbitalsd Orbitalsd Orbitals

s orbitals have no s orbitals have no planar node (planar node (ll = 0) = 0) and so are spherical.and so are spherical.

p orbitals have p orbitals have ll = 1, = 1, and have 1 planar and have 1 planar node,node,

and so are “dumbbell” and so are “dumbbell” shaped.shaped.

This means d orbitals This means d orbitals (with (with ll = 2) have 2 = 2) have 2 planar nodesplanar nodes

typical d orbital

planar node

planar node

See Figure 6.15See Figure 6.15See Figure 6.15See Figure 6.15

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3d3dxyxy Orbital Orbital

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3d3dxzxz Orbital Orbital

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3d3dyzyz Orbital Orbital

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3d3dxx22

- y- y22 Orbital Orbital

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3d3dzz22 Orbital Orbital

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f Orbitalsf Orbitalsf Orbitalsf OrbitalsWhen n = 4, When n = 4, ll = 0, 1, 2, 3 so there are 4 = 0, 1, 2, 3 so there are 4 subshells in the shell.subshells in the shell.

For For ll = 0, m = 0, mll = 0 = 0

→ → s subshell with single orbitals subshell with single orbital

For For ll = 1, m = 1, mll = -1, 0, +1 = -1, 0, +1

→ → p subshell with 3 orbitalsp subshell with 3 orbitals

For For ll = 2, m = 2, mll = -2, -1, 0, +1, +2 = -2, -1, 0, +1, +2

→ → d subshell with 5 orbitalsd subshell with 5 orbitals

For For ll = 3, m = 3, mll = -3, -2, -1, 0, +1, +2, = -3, -2, -1, 0, +1, +2, +3+3

→ → f subshell with 7 f subshell with 7 orbitalsorbitals

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f Orbitalsf Orbitals

One of 7 possible f orbitals.

All have 3 planar nodal surfaces.

Can you find the 3 surfaces here?

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Spherical NodesSpherical Nodes

•Orbitals also have spherical Orbitals also have spherical nodesnodes•Number of spherical nodes Number of spherical nodes = n - = n - ll - 1 - 1•For a 2s orbital:For a 2s orbital: No. of nodes = 2 - 0 - 1 = 1 No. of nodes = 2 - 0 - 1 = 1

2 s orbital

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Arrangement of Arrangement of Electrons in AtomsElectrons in Atoms

Arrangement of Arrangement of Electrons in AtomsElectrons in Atoms

Electrons in atoms are arranged asElectrons in atoms are arranged as

SHELLSSHELLS (n) (n)

SUBSHELLSSUBSHELLS ( (ll))

ORBITALSORBITALS (m (mll))

1 © 2009 brooks/cole - cengage test ii raw grades: hi92 lo9 average:37.3 curve 25 pt. grades...

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