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Chap 5: Periodicity & Atomic Structure

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Chapter 5. Periodicity & Atomic StructureChapter 5. Periodicity & Atomic Structure

Why do elements have periodic properties?

Why do elements and compounds have characteristic colors?

Demo (Q224): colored balloon explosions

Wave PhenomenaWave Phenomena

Classical wave description of light explains refraction, interference, diffraction

 Diffraction of light

When light passes through a large slit ,

the edges cast shadows and the light

that goes through is a distinct replica

of the slit.

(A beam of classical particles would

also behave this way.)

However, when the slit is small,(<100l) the beam is diffracted ,

it spreads out.

DiffractionDiffraction

Light passing through a narrow slit spreads out.

This is purely a wave phenomenon.

 A beam of classical particles would make a shadow pattern.seat activity

single slit diffraction

Photoelectric EffectPhotoelectric Effect

KE(electron)

frequency of incident light

However, the color of the incident light affected the electron energy

• Einstein proposed the energy of light is carried in packets (photons).

• The amount of energy in a photon depends on the frequency:

E = hn = hc/ l 

where h = 6.63 x 10-34 J-s (Planck’s constant)

Photoelectric effect explanation:

hn > W  electron emittedhn < W  no electron emitted

(in this picture, intensity is related to the number of photons/s)

Photon EnergyPhoton Energy

E photon= hn = hc/ l 

E photo

n

Matter WavesMatter Waves

• Matter classically considered to be composed of “particles” – p, n, e –

• Beams of these “particles” display wavelike phenomena (e.g. diffraction)

deBroglie suggested a particle wavelength by analogy with light

photon energy: E = hn = hc/ l   (Planck)

and E = pc  (Relativity) where p is momentum

gives l = h/p

classical momentum of a particle:  p = mv 

deBroglie wavelength of a particle l = h/p = h/mv 

Some phenomena are consistent with a particle “picture.”Other phenomena are consistent with a wave “picture.”

But a theory is useful only if it is predictive, these pictures must be unified!

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Chap 5: Periodicity & Atomic Structure

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Quantum MechanicsQuantum Mechanics

• Wave and particle descriptions are based on intuition developed from

macroscopic observations.

• Inconsistency with experiments on light and elementary particles

suggests that these pictures fail in the microscopic realm.

 A postulate of QM: An electron (or other system) is described by a wavefunction (y ) like

that used to describe light classically. The wavefunction isdetermined by solving a wave equation. The probability of finding

the electron in a given location is equal to the square of the value of the wavefunction (y 2) at that location.

 A wavefunction for an atom or molecule is also called an orbital .

QuantizationQuantization

 An important consequence of the postulate is that the possible measured

values of many quantities (e.g. energy, momentum, angular momentum)are quantized , i.e. only certain discrete values can be measured.

Consider an e – confined within a 1-d “box” of length a.

The probability of finding the electron outside the box iszero, so the wavefunction must vanish at both ends.

Therefore, only certain discrete wavelengths are allowed(l = 2a, a, 2a/3, a/2, etc.). Each possibility is called a

state and designated by a quantum number (n),i.e. l n=2a/n where n = 1, 2, 3, etc.

The electron momentum and energy are related to thewavelength:

 p = h/ l E= h2  /2ml 2 

Energy Levels

E n = h2 n2  /4ma2 

WavefunctionWavefunction & probability distribution& probability distribution

P.I.B. wavefunction

y 3

Probability distribution

 y 3

2

high

probability

“nodes”

zero probability

ClassicalClassical ““uncertaintyuncertainty””

Diffraction

• The “uncertainty” of the vertical position of aphoton (Dy) is the size of the slit.

• The “uncertainty” of the direction of flight is

related to the angular spread of the diffractedbeam (Dq).

Dq ~ 1/ Dy or Dy Dq = const.

(Dq is related to the uncertainty of the

y-component of photon momentum)

Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle

Consider an electron with a wavefunction

and probability distribution like these

D x 

the electron will almost always

be found within this range

Uncertainty principle:

 A wavefunction with a small D x results

in a large uncertainty in momentum, D p,

and vice versa.

 D x D p ≥ h /4p 

Summarize QMSummarize QM

1. Possible “states” of a system are quantized; each discrete state is

assigned a quantum number and each is associated with a

particular value of a measurable quantity like energy.

2. States are related to a wavefunction (also called orbitals). The

probability that a measurement of position will yield a specific result

can be determined by the shape of the wavefunction squared.

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Chap 5: Periodicity & Atomic Structure

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H-atom Energy LevelsH-atom Energy Levels

E n = –¬ hc 

n2 (n = 1, 2, 3, …)

¬= 1.097 x 107 m-1

h = 6.626 x 10-34 J•sc = 2.998 x 108 m/s

¬ hc = 2.179 x 10-18 J

= 1,312 kJ/mol

n=1 (ground state)

n=2 (1st excited state)

n=3 (2nd excited state)

n=4 (3rd excited state)

Atomic Emission SpectraAtomic Emission Spectra

UV

visible

IR

When an electron falls (decays) from a higher energy state to one of 

lower energy, the excess energy is emitted as a photon:

visible

part

Some atomic emission spectraSome atomic emission spectra

H

He

O

N

Fe

Na

Xe

“Fingerprints” for elemental analysis.

Quantum NumbersQuantum Numbers

n = 1, 2, 3, … principal quantum number  H-atom energy depends only on n

specifies electron shell 

determines size of orbital

l = 0, 1, … n-1 angular momentum quantum number  specifies sub-shell 

n and l determine orbital shape

l = 0 = s subshell

l = 1 = p subshell

l = 2 = d subshell

l = 3 = f  subshell

m = -l, -l +1, …, l-1, l  magnetic quantum number 

specifies direction (orientation) of orbital in space

(i.e. x, y, z)

ss Orbital ShapesOrbital Shapes

The s orbitals are spherical. Probability of finding s electrondepends only on distance from nucleus, not on angular position.

 

y 1s = Ae

-r /a0

 

y 2s = A(2 - r /a0 )e-r /2 a0

 

a0 = 0.53 Å (Bohr radius)

 p p Orbital ShapesOrbital Shapes

The p orbitals are dumbbell–shaped.

This representation of orbital shapes simply draws a surface to show

where the probability of finding the electron decreases beyond some

arbitrarily small value (e.g. there is a 95% probability of finding theelectron withing the dumbbell). It gives you a good feeling for the angular 

dependence of the orbital shape but not the radial-dependence (distance

from the nucleus).

 

y 2 p = A(r /a0 )e-r /2 a0 cosq 

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Chap 5: Periodicity & Atomic Structure

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d d Orbital ShapesOrbital Shapes

d orbitals have two different shapes. Most have 4 lobes (regions of high

electron density).

This is an f orbital.It has 8 regions of electron density.

Dot-density representationsDot-density representations

In these cross-sectional views,

the density of dots represents

the probability of finding the

electron in that location.

They give a better feeling for how the wavefunction varies

with distance from the nucleus.

MultielectronMultielectron AtomsAtoms

 Approximation: Assume orbitals are similar to those in H-atom.

More than one orbital will be occupied by electrons in a given atom.

Sub-shell energies are no longer exactly equal (degenerate)

because of interactions between electrons (shielding ).

H-atommulti-electron atom

(not on same energy scale)

Ground State Electron ConfigurationsGround State Electron Configurations

electronconfig

• Aufbau Principle:• Lower energy orbitals fill first.

• Orbitals only hold two electrons, andeach should have different spin.

• Degenerate orbitals are filled withelectrons until all are half filled beforepairing up of electrons can occur (Hund’s Rule).

1s2s 2p3s 3p 3d4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d7s 7p

I  n c r  e  a  s i  n gE n e r  g y

[He]

[Ne]

[Ar]

[Kr]

[Xe]

[Rn]

Core

n+l “rule”

 An atom or molecule with one or more

unpaired electrons is paramagnetic and

is attracted to a magnetic field.

Some Electron ConfigurationsSome Electron Configurations

1s 2s 2 p

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø

↑Ø ↑Ø ↑Ø ↑Ø

↑Ø ↑Ø

↑Ø

↑

↑

↑

↑ ↑

↑ ↑ ↑

↑ ↑

↑

H 1s1

He 1s2

Li 1s2 2s1 = [He] 2s1

Be 1s2 2s2 = [He] 2s2

B 1s2 2s2 2 p1 = [He] 2s2 2 p1

C 1s2 2s2 2 p2 = [He] 2s2 2 p2

N 1s2 2s2 2 p3 = [He] 2s2 2 p3

O 1s2 2s2 2 p4 = [He] 2s2 2 p4

F 1s2 2s2 2 p5 = [He] 2s2 2 p5

Ne 1s2 2s2 2 p6 = [He] 2s2 2 p6

Chromium should be [Ar]4s23d 4, but is [Ar]4s13d 5

Copper should be [Ar]4s23d 9, but is [Ar]4s13d 10

 A few elements have

anomalous e – configs

paramagnetic

paramagnetic

paramagnetic

paramagnetic

paramagnetic

paramagnetic

paramagnetic

Atomic RadiiAtomic Radii

Radii

 Atomic radius determined by outermost orbital occupied

Increase down group due increasing n (additional outer shell).

Decrease across row due to increasing nuclear charge.