KI1101-2012-KD Lec04a TheQuantumMechanicsOfAtom

8/11/2019 KI1101-2012-KD Lec04a TheQuantumMechanicsOfAtom

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Chapter 8Chapter 8

The Quantum Mechanical AtomThe Quantum Mechanical Atom

Achmad Rochliadi


2/75

Summary HighlightSummary Highlight

Model of Atomic Theory Electromagnetic Energy

Atomic Spectra

Matter Wave

Electron Configuration

Shape of !r"ital

Atomic propertie


3/75


4/75

&alton ' Each element i compoed of mall particle

called atom,

Atom are neither created nor detroyed inchemical reaction,

All atom of a given element are identical

Compound are formed +hen atom of more

than one element com"ine


5/75

Thompon ' The atom of the element conit of a

num"er of negatively electrifiedcorpucle encloed in a phere ofuniform poitive electrification,


6/75

Rutherford The atom of an element conit of a mall* poitively

charged nucleu in the centre* +hich carrie almot theentire ma of the atom,

The electron are revolving around the nucleu at high

peed, The num"er of electron in an atom i e/ual to the

num"er of proton, Hence it i electrically neutral, The volume of the nucleu i negligi"ly mall

compared to the volume of the atom, Mot of the pace in the atom i empty


7/75

Rutherford Simple &eignRutherford Simple &eign


8/75

(iel -ohr' Atom i a mall* poitively charged nucleu

urrounded "y electron that travel in circular

or"it around the nucleu0imilar in tructure

to the olar ytem* "ut +ith electrotatic force

providing attraction* rather than gravity,


9/75

The Quantum Mechanical AtomThe Quantum Mechanical Atom

-y the late $8%%1 it +a clear that claicalphyic +a incapa"le of decri"ing atom

and molecule

E)periment ho+ed that electron actedli2e tiny charged particle in ome

e)periment and +ave in other

The phyic that decri"e o"3ect +ithwave/particle dualityi called quantum

mechanicsor quantum theory


10/75

Energy can "e tranferred "et+een thing a

light or radiation Radiation carrie energy through pace a

wavesor ocillation moving out+ard from

a ditur"ance Electromagnetic +ave 4radiation5 may "e

characteri6ed "y their .height7 or

amplitudeand the num"er that occur perecond or frequency4v5


11/75 11

ight Act A A Waveight Act A A Wave

Wavelength ()the ditance light travel tocomplete one cycle

Frequency () the num"er of +ave cyclein one econd

unit are cycle per econd 4cp5* Hert6 4H65 H6 9 :$


12/75 Electromagnetic radiation provides the clue to the electronic structures of

atoms12

Frequency And Wavelength Are RelatedFrequency And Wavelength Are Related

(ote that a the fre/uency of the +aveincreae* the +avelength decreae

Regardle of the fre/uency* light travel at

the ame peed* c

c9;,??@?>B8 < $%8m

Learning Check' Df the fre/uency of a radiotation i %%, MH6* +hat i the +avelength

in mF 0.999 m


13/75

7.1 Electromagnetic radiation provides the clue to the electronic structuresof atoms

13

Radiant nergy !pectrumRadiant nergy !pectrumhigh energy,

short waves

low energy,

long waves

"h t l t i ff t #" ti l $h %f"h t l t i ff t #" ti l $h %f


14/75

@,$ Electromagnetic radiation provide the clue to the electronic tructure of atom $

"hotoelectric ffect #"article $heory %f"hotoelectric ffect #"article $heory %f

Light&Light&

Al"ert Eintein 4$?%B5 E9h= Shining light on a clean metal urface may

e3ect electron

There i a threhold level needed to e3ect theelectron 4a +or2 function pecific to the

metal5

Dncreaing intenity doe not caue the effect

Dncreaing thefrequencyof the light doe


15/75

The unit of fre/uency are the hert'4('5

The minimum and ma)imum amplitude of

electromagnetic radiation are evenly paced

The pea2:to:pea2 ditance i called thewavelength

5econd4$$$H6$ :$

54


16/75

The product of fre/uency and +avelength

give the peed of light 4c5

Electromagnetic radiation come in a "roadrange of fre/uencie called the

electromagnetic spectrum

The electromagnetic pectrum i dividedinto region according to the +avelength

of radiation

m$%,%% 8 c


17/75

What +e call lighti a mall lice of the

electromagnetic pectrum +ith +avelength"et+een a"out %% and @%% nm

Thi i called the visi)le region"ecaue +e can

.ee7 thee +avelength of the electromagneticpectrum

Gamma ray* ray* and ultraviolet radiation

have +avelength horter than the vii"le region

Micro+ave* infrared radiation* and radio +avehave +avelength longer than vii"le light


18/75

The +ay a u"tance a"or"

electromagnetic radiation can "e ued to

characteri6e it

Ior e)ample* each u"tance a"or" a

uni/uely different et of infrared

fre/uencie

A plot of +avelength a"or"ed veru the

a"orption i called an infrared a)sorption

spectrum

Dt can "e ued to identify a u"tance


19/75

The ocillating magnetic and electric field

of an electromagnetic +ave interact +ith

particle that it pae

A charged particle can pic2 up energy at the

e)pene of the radiation ource

Infraredasorptionspectrum

of woodalcohol!methanol".


20/75

The energy tranfer i not decri"e correctly

"y claical phyic

Dn $?%% the German cientit Ma) #lanc2

propoed that the electromagnetic radiation

could "e vie+ed a a tream of tiny energy

pac2et or quanta+e no+ call photons

#hoton travel at the peed of light

#lanc2 propoed* and Eintein confirmed*that the energy of a photon is proportional

to its frequency


21/75

Thi mean that )othelectron and

electromagnetic radiation can "e

repreented a either +ave or particle The vii"le pectrum i a continuous

pectrum "ecaue it contain a continuou

ditri"ution of light of all color E)cited atom can emit light

J$%K,K>Kcontant#lanc2L

photonofenergy

:

h

hE


22/75

>>

Ilame EmiionIlame Emiion Element e)hi"it characteritic color +hen

"urned

The characteritic pectra are alo o"erved

+hen element are u"3ect to trong electrical

field a in ga dicharge tu"e,

(ote that the

light from the

dicharge tu"e i

actually everal

different colored

line a een on

the urface of the

C&


23/75

The atomic spectrumor emission

spectrumi a erie of individual linecalled a line spectrum

Atomic pectra are uni/ue for each element

#ight emitted y

e$cited atoms is

comprised of a

few narrow eams

with fre%uencies

characteristic of

the element.


24/75

Dn general* the line pectrum of an element

i rather complicated

The line pectrum of hydrogen* +ith a

ingle electron* i the implet

The Ryd)erg equationcan "e ued to

calculated all the pectral line of hydrogen

n1and n> are poitive integers

#attern Dn Atomic ine Spectra

$

=

RH$

n$>

$

n>>


25/75


26/75

The firt theoretical model that uccefully

accounted for the Ryd"erg e/uation +a

propoed in $?$ "y (iel -ohr

&ontinuous !a" and discrete

!" potential energy of a

tortoise. 'he potential energy

of the tortoise in !" is

%uanti(ed.


27/75

@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie >8

Electron move around the nucleu in fi)edpath or orbitsmuch li2e the planet move

around the un

!r"it poition* la"eled +ith the integer n*have pecific potential energy

The lo+et energy tate of an atom i called

theground state4an electron +ith n9 $ for ahydrogen atom5

-ohr1 Model !f The Atom-ohr1 Model !f The Atom


28/75

@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie >?

A"orption And EmiionA"orption And Emiion

Electron thatabsorbenergy areraied to a higherenergy level

A particularfre/uency of light iemitted+hen an

electron fall to alo+er energy level


29/75

@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie %

Thi e/uation allo+ the calculation of the energy*

E* of any or"it

"9 -ohr1 contant

n i the or"it location

J$%>,$8"

n"E

$8

>

-ohr E/uation 4$?$5-ohr E/uation 4$?$5


30/75

@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie $

-ohr1 4theoretical5 e/uation e)plain thee)perimental 4empirical5 Ryd"erg e/uation

The com"ination of contant* b/hc* ha a

value +hich differ from the e)perimentallyderived value ofRH"y only %,%BN

>>

>>

>>

$$$$

$$

or

+ith

54

hl

hl

lh

nnhc

b

lhnn

n

b

n

blh

hc

nnb

EEE

-ohr1 Model #redict Energy evel-ohr1 Model #redict Energy evel


31/75

@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie >

Oour TurnNOour TurnN

Which energy i not poi"le according to -ohr1ModelF

A, :B,B


32/75

@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie

Theory +a not

a"le to e)plain

the pectra of

atom +ith more

than one electron Theory doen1t

e)plain the

collaping atom

parado)

-ohr1 Model Iail-ohr1 Model Iail


33/75

@, Electron have propertie of "oth particle and +ave

ight E)hi"it Dnterferenceight E)hi"it Dnterference

Constructive interference:+ave .in:

phae7 create +ave of greater amplitude

4 they add5 estructive interference: +ave .out:of:

phae7 create +ave of lo+er amplitude

4they cancel out5


34/75

@, Electron have propertie of "oth particle and +ave B

ight e)hi"it interference* and it alo haparticle nature

Electron* 2no+n to "e particle* alo

demontrate interference

&iffraction And Electron&iffraction And Electron


35/75


36/75

An electron that .ecape7 from the nucleu

ha infinity for it /uantum num"er and6ero energy

-ohr1 4theoretical5 e/uation e)plain the

4empirical5 Ryd"erg e/uation

>>

>>

>>

$$$$

$$

or

+ith

54

hl

hl

lh

nnhc

b

lhnn

n

b

n

blh

hc

nnb

EEE


37/75

The com"ination of contant* b/hc* ha a

value +hich differ from the e)perimentallyderived value ofRH"y only %,%B

-ohr1 effort to develop a general theory

of electronic tructure +a doomed "y the+aveparticle duality of electron

&e -roglie uggeted that the +avelength

of a particle of ma mmoving at peed v i

mvh


38/75

Thi relation provide the lin2 "et+een the

decription a a particle and a a +ave Heavy o"3ect have very .hort7

+avelength o their matter +ave and the

+ave propertie go unnoticed Tiny particle +ith mall mae have

.long7 +avelength o their +ave propertie

are an important part of their "ehavior Wave com"ine in t+o +ay


39/75

The contructive and detructiveinterference i called diffraction

Electron produce imilar pattern

!a" )aves in phase interfere constructively. !" *ut of phase

waves produce destructive interference. !c" )aves passing

through holes fan out and produce an interference pattern.


40/75

There are t+o type of +ave' traveling

and standing

A tanding +ave i produced +hen a guitar

tring i pluc2ed' the center of the tringvi"rate* "ut the end remain fi)ed

#oint of 6ero +ave amplitude are called

nodes

'he wind produces

traveling waves on the

surfaces of la+es and

oceans.


41/75

Ior guitar tring the only +ave are thoefor +hich a half:+avelength i repeated

e*actlya +hole num"er of time

Ior a trength of length+ith nan integerthi can "e +ritten

tanding waves on a guitar

string.

nn >

>'grearranginor


42/75

Thee reult can "e ued to ho+ ho+

/uantum theory unite the +ave and particle

decription of a "ound electron

Conider the claical particle model of the

."ead on a +ire7

Df the electron 4particle5 ha ma mand

peedv

The 2inetic energy of the moving electron i

>

>$ mvE


43/75

The &e -roglie relation connect model

4a5 and 4"5

!a" - classical model of theelectron as a ead on a wire. -nyenergy is possile and position ise$actly +nown. !" &lassicalmodel of the electron as astanding wave. !c" uantummechanical model comines !a"and !". /ar+ areas indicate

proale electron positions.


44/75


45/75

The electron energy i /uanti6ed "ecaue it

depend on the integer n

The lo+et energy allo+ed i for n9$ or

E!h"/#m"4the energy cannot )e 'ero5

>

>>

>

>

8

>

>

>

>$>

>$

giveuing

'ngu"titutior

m

hn

n

m

hmh

mh

mvh

E

mmvE

v


46/75

Electron trapped on a +ire have ome

reidual 2inetic energy* 3ut li2e electrontrapped in atom

'he spacing

etween levels is

proportional to

#

2

.

!a" - long wire. !"

- short wire.

'he

onger the wire, the

sma er the spacing

etween a owed

energy eve s.


47/75

The +ave that correpond to the electron i

called a wave function The amplitude of the +ave function at a

given point can "e related to the

pro)a)ilityof finding the electron there

According to /uantum mechanic there are

region of the +ire +here the electron +ill

not "e found

Region of 6ero +ave function amplitude

are called node


48/75

Dt i generally true that the more nodes an

electron has, the higher its energy Er+in SchrPdinger +a the firt to

uccefully apply the concept of the +ave

nature of matter to electronic tructure

He developed an e/uation that can "e

olved to give +ave function and energy

level for electron trapped in them

Wave function for electron in atom are

called or)itals


49/75

!r"ital are characteri6ed "y a et of three

/uantum num"er'

n9 principle /uantum num"er, All

or"ital +ith the ave principle

/uantum num"er are in the ame shell,Allo+ed value' the et of poitive

integer,

l 9 econdary /uantum num"er +hichdivide the or"ital in a hell into

maller group called su)shells,

Allo+ed value' from % to 4n $5,


50/75

1elationships etween

n

, , and

m

.

umer of

n m

ushell *ritals

0 0 s

2 0 0 2

s

, 0, 2

p

3

3 0 0 3s

, 0, 3p 3

2 2, , 0, , 2 3d 4

5 0 0 5s

, 0, 5

p

3

2 2, , 0, , 2 5d 4

3 3, 2, , 0, , 2, 3 5f 7


51/75

The appro)imate energie of the u"hellin an atom +ith more than one electron'

Electron "ehave li2e tiny magnet

'he %uantum

numersassociated withthe first twoshells areshown.


52/75

Electron +ithin atom interact +ith amagnet field in one of t+o +ay'

Electron pin i important in determiningelectronic tructure

Electrons can spin in either

direction in the presence of an

e$ternal magnetic field. 'his

gives rise to the spin %uantum

numer,

m

s

with allowed

values of 6 2 !spin up8" or 9

2 !spin down8".


53/75

According to the "auli e*clusion principle

no two electrons in the same atom can haveidentical values for all four quantum

numbers

Thu t+o electron can occupy the ame

or"ital only if they have oppoite pin and

are aid to "e paired

A u"tance +ith more pin in one direction

i aid to contain unpairedelectron


54/75

Su"tance +ith unpaired electron arelightly attracted to a magnet and are called

paramagnetic

Su"tance in +hich all electron are pairedare called diamagnetic

The ditri"ution of electron among the

or"ital of an atom i called the electronic

structureor electronic configuration


55/75

To indicate the ground tate electronconfiguration +e can'

$5 it the u"hell that contain electron andindicate their electron population +ith aupercript,

>5 Repreent each or"ital +ith a circle and uearro+ to indicate the pin of each electron,

Electron configuration mut "e conitent+ith the #auli principle* auf"au principle*and Hund1 rule

E)ample' ( $s>>s>>p* (a $s>>s>>pKs$


56/75

Electron configuration e)plain the

tructure of the periodic ta"le

'he periodic tale isdivided into regionsof 2, :, 10, and 15columns which is

the ma$imumnumer of electronsin s, p, d, and fsulevels.

ushells that fillacross the periods.


57/75

Ior the repreentative element 4A Group5

the electron +ith the highet n value or

valence shellare normally the only

electron important for chemical propertie

Ior thee element the valence electrons

consist of just the s and p subshells

encountered crossing the period that

contains the element in question

E)ample' the valence configuration of"romine i

-r s>pB


58/75

There are fe+ important e)ception to the

.e)pected7 electronic figuration of

commonly encountered element

Iollo+ing the rule for Cr* Cu* Ag* and Au

uing no"le ga notation'

$$%>?

$$%>?

$$%>?

$B>

KSeTBKSeTBCu

BSUrTBSUrTAg

SArTSArTCu

SArTSArTCr

alE)perimentE)pectedElement

sdsd

sdsd

sdsd

sdsd


59/75

Apparently* half:filled and filled u"hell

are particularly ta"le

Similar irregularitie occur among the

lanthanide and actinide element

The poition of an electron mut "e

decri"ed +ith pro"a"ilitie

Heien"erg1 uncertainty principleay

that it i impoi"le to meaure +ith

complete preciion the velocity andpoition of a particle imultaneouly


60/75

Thee limitation are not important for large

o"3ect "ut are very important for mall

particle li2e electron

Quantum mechanic re/uire that +e tal2

a"out the pro"a"ility of finding an electron

in a particular region of pace

Thi pro"a"ility i often repreented a an

electron clouda"out the nucleu

The pro"a"ility varie +ith ditance from

the nucleu


61/75

Thi type of plot ho+ that electron

densityvarie from place to place Electron denity variation define the hape*

i6e* and orientation of or"ital

!a" - dotdensity

diagram for an

electron in a

s

orital. !" ;raph

of proaility

versus distance.


62/75

por"ital are /uite different fromsor"ital

They poe a nodial plane +hich include

the nucleu and eparate the .lo"e7 ofhigh pro"a"ility

*ritals get larger as the

principle %uantum numer n

increases. odes, or regions

of (ero electron density,

appear eginning with the 2s

orital.


63/75

Recall that there are three different or"italin eachpu"hell

/otdensity diagrams of

the cross section of the

proaility distriution of a

single !a" 2pand !" 3p

orital showing the nodal

plane.

'he directions of ma$imum electron

density lie along lines that are

mutually perpendicular. It is

convenient to lael the oritals as p

$

,

p

y

, and p

(


64/75

The hape and orientation of dor"ital are

more complicated than forpor"ital

Shape and directional propertie of the

five dor"ital in a du"hell, Thefor"ital are even more comple) than

the dor"ital


65/75

The amount of poitive charge .felt7 "y

outer electron in atom other than

hydrogen i called the effective nuclearcharge

Dt i lo+er than the atomic num"er "ecaue

of shielding

If the 2 charge of the1s2core of lithium were100< effective at

shielding the 2selectronfrom the nucleus, thevalence electron wouldsee8 a charge of 61.


66/75

The effective nuclear charge felt "y outer

electron i determined primarily "y the

difference "et+een the charge on the

nucleu and the charge on the core

Effective nuclear charge control a num"er

of propertie

Atomic i6e increae top to "ottom in a group

"ecaue of increaing n and get maller left to

right in a group "ecaue the effective nuclearcharge increae


67/75

Variation in atomic and ionic radii, Value

in picometer 4$%:$>m5


68/75

The i6e trend in ion can "e ummari6ed'

#oitive ion are al+ay maller than the atom

they are formed

(egative ion al+ay larger than the atom

from +hich they are formed

-dding electrons leads toan increase in si(e of aparticle, as illustrated for

fluorine. emoving electronsdecreases the si(e of theparticle, as shown forlithium and iron.


69/75

+oni'ation energy4DE5 i the energy

re/uired to remove an electron from an

iolated* gaeou atom

Succeive ioni6ation are poi"le until no

electron remain

The trend in DE are the oppoite of thetrend in atomic i6e

eg$g$ 5454


70/75

=ariations in first

ioni(ationenergies.

Elements with the

largest ioni(ation

energies are in the

upper right of the

periodic tale. 'hose

with the smallest

ioni(ation energy are

at the lower left.


71/75

=ariations in

successive

ioni(ation

energies. ote

that it is

e$tremely

difficult to rea+

into the nole

gas core !2

nd

through >

th

ioni(ations for #i

through ?,

respectfully.


72/75

The electron affinity4EA5 i the potential

energy change aociated +ith the addition

of an electron to a gaeou atom or ion in it

ground tate

The addition of one electron to a neutral

atom i e)othermic for nearly all atom

The addition of more electron re/uire

energy

5454 g$eg$


73/75

Conider the addition of electron to

o)ygen'

The reult for firt electron affinitie can

"e generali6ed

: :

: : >:

: >:

Change EA42Jmol5

!4g5 e ! 4 5 :$$

! 4g5 e ! 4 5 8

(et' !4g5 >e ! 4 5 @%

g

g

g

+

+ +

+ +


74/75

Dn general' EA increae from left to right in a period

EA increae "ottom to top in a group

Meauring atomic maeMeauring atomic mae


75/75

Meauring atomic maeMeauring atomic mae

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KI1101-2012-KD Lec04a TheQuantumMechanicsOfAtom