ITT Chng Ch 07 Electronic Structure of Atoms

7/29/2019 ITT Chng Ch 07 Electronic Structure of Atoms

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Quantum Theory and theElectronic Structure of Atoms


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Properties of Waves

Wavelength() is the distance between identical points onsuccessive waves.

Amplitudeis the vertical distance from the midline of a

wave to the pea or trou!h.".#


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Properties of Waves

Frequency() is the number of waves that pass throu!h a

particular point in # second ($% & # cycle's).

The speed (u

) of the wave &

".#


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awell (#*"+), proposed that visible li!ht consists of

electroma!netic waves.

Electromagnetic

radiationis the emission

and transmission of ener!y

in the form of

electroma!netic waves.

Speed of li!ht (c) in vacuum & +.-- #-*m's

Allelectroma!netic radiation

= c".#


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".#


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x= c

= c/

= +.-- #-*m's/.- #-/$%= 0.- #-+m

1adio wave

A photon has a fre2uency of .- #-/$%. 3onvert

this fre2uency into wavelen!th (nm). 4oes this fre2uency

fall in the visible re!ion5

= 0.- #-#6nm

".#


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ystery 7#, 89lac 9ody Problem:

Solved by Planc in #;--

Ener!y (li!ht) is emitted or

absorbed in discrete units

(2uantum).

E & h

Planc?s

".#


8/43

@i!ht has both

#. wave nature

6. particle nature

h& BE C 9E

ystery 76, 8Photoelectric Effect:

Solved by Einstein in #;-0

Photonis a 8particle: of li!ht

BE & h= 9E

h

BE e=

".6


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E & h

E & .+ #-=+/(>?s) +.-- #- *(m's) ' -.#0/ #-=;(m)

E & #.6; #- =#0>

E & h c '

".6

When copper is bombarded with hi!h=ener!y electrons,

D rays are emitted. 3alculate the ener!y (in oules)

associated with the photons if the wavelen!th of the D

rays is -.#0/ nm.


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".+

@ine Emission Spectrum of $ydro!en Atoms


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".+


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#. e=can only have specific(2uanti%ed) ener!y

values

6. li!ht is emitted as e=

moves from one ener!y

level to a lower ener!y

level

Bohrs Model of

the Atom (1913)

En& =1$ ( )

#

n6

n(principal 2uantum number) & #,6,+,F

1$(1ydber! constant) & 6.#* #-=#*>

".+


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E & h

E & h

".+


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Ephoton& E & Ef= Ei

Ef& =1$ ( )#

n6f

Ei& =1$ ( )#

n6i

i f

E & 1$( )#

n6#

n6

nf & #

ni & 6

nf & #

ni & +

nf & 6

ni & +

".+


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Ephoton& 6.#* #-=#*

> (#'60 = #';)Ephoton& E & =#.00 #-

=#;>

& .+ #-=+/(>?s) +.-- #-* (m's)'#.00 #-=#;>

*- nm

3alculate the wavelen!th (in nm) of a photon

emitted by a hydro!en atom when its electron

drops from the n& 0 state to the n& + state.

Ephoton& h c '

& h c ' Ephoton

i f

E & 1$( )#

n6#

n6Ephoton&

".+


16/43

4e 9ro!lie (#;6/) reasoned

that e=is both particle and

wave.

Why is e=ener!y 2uanti%ed5

"./

u & velocity of e=

m & mass of e=

2r & n =h

mu


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= h'mu

= .+ #-=+/' (6.0 #-=+ #0.)

= #." #-=+6m & #." #-=6+nm

What is the de 9ro!lie wavelen!th (in nm)

associated with a 6.0 ! Pin!=Pon! ball

travelin! at #0. m's5

m in !h in >?s u in (m's)

"./


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Chemistry in Action: Laser The !lendid Li"ht

@aser li!ht is (#) intense, (6) monoener!etic, and (+) coherent


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Chemistry in Action: #lectron Microsco!y

TM ima"e of iron atoms

on co!!er s$rface

e& -.--/ nm


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Schrodin!er Wave E2uation

Gn #;6 Schrodin!er wrote an e2uation that

described both the particle and wave nature of the e=

Wave function () describes

#. ener!y of e=with a !iven

6. probability of findin! e=in a volume of space

Schrodin!er


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= fn(n, l, ml, ms)

principal 2uantum number n

n& #, 6, +, /, F.

n n&6 n&+

".

distance of e=from the nucleus


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Where ;-H of the

e=

density is foundfor the #s orbital

".


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& fn(n, l, ml, ms)

an!ular momentum 2uantum number l

for a !iven value of n, l& -, #, 6, +, F n=#

n & #, l = 0

n & 6, l& - or#

n & +, l& -, #, or6

Shape of the 8volume: of space that the e=occupies

l& - s orbital

l& # p orbital

l& 6 d orbital

l& + f orbital


".


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l& - (s orbitals)

l& # (p orbitals)

".


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l& 6 (d orbitals)

".


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& fn(n, l, ml, ms)

ma!netic 2uantum number ml

for a !iven value of lml& =l, F., -, F. Cl

orientation of the orbital in space

if l& # (p orbital), ml& =#, -, or#

if l& 6 (d orbital), ml& =6, =#, -, #, or6


".


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ml& =# ml& - ml& #

ml& =6 ml& =# ml& - ml& # ml& 6".


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& fn(n, l, ml, ms)

spin 2uantum number ms

ms& CI or=I


ms& =Ims& CI

".


29/43

Eistence (and ener!y) of electron in atom is described

by its uniquewave function .

Pauli exclusion principle= no two electrons in an atom

can have the same four 2uantum numbers.


& fn(n, l, ml, ms)

Each seat is uni2uely identified (E, 1#6, S*)

Each seat can hold only one individual at a

time

".


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".


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& fn(n, l, ml, ms)

Shell J electrons with the same value of n

Subshell J electrons with the same values of nandl

Krbital J electrons with the same values of n, l, andml

$ow many electrons can an orbital hold5

Gf n, l, and mlare fied, then ms& I or = I

& (n, l, ml, I) or & (n, l, ml, =I)

An orbital can hold 6 electrons ".


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$ow many 6p orbitals are there in an atom5

6p

n&6

l& #

Gf l& #, then ml& =#, -, or C#

+ orbitals

$ow many electrons can be placed in the +d

subshell5

+d

n&+

l& 6

Gf l& 6, then ml& =6, =#, -, C#, or C6

0 orbitals which can hold a total of #- e=

".

Ener!y of orbitals in a single electron atom


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Ener!y of orbitals in a singleelectron atom

Ener!y only depends on principal 2uantum number n

En& =1$ ( )#

n6

n

n&6

n&+

"."

Ener!y of orbitals in a multi electron atom


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Ener!y of orbitals in a multi=electron atom

Ener!y depends on nand l

n l& -

n&6 l& -n&6 l& #

n&+ l& -n&+ l& #

n&+ l& 6

"."

8Lill up: electrons in lowest ener!y orbitals (Aufbau principle)


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Lill up electrons in lowest ener!y orbitals (Aufbau principle)

$ # electron

$ #s#

$e 6 electrons

$e #s6

@i + electrons

@i #s66s#

9e / electrons

9e #s66s6

9 0 electrons

9 #s66s66p#

3 electrons

5 5

".;


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3 electrons

The most stable arran!ement of electrons

in subshells is the one with the !reatest

number of parallel spins (Hunds rule).

3 #s66s66p6

M " electrons

M #s66s66p+

K * electrons

K #s66s66p/

L ; electrons

L #s66s66p0

Me #- electrons

Me #s66s66p

"."

Krder of orbitals (fillin!) in multi electron atom


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Krder of orbitals (fillin!) in multi=electron atom

#s N 6s N 6p N +s N +p N /s N +d N /p N 0s N /d N 0p N s"."


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Electron configurationis how the electrons are

distributed amon! the various atomic orbitals in an

atom.

#s#

principal 2uantumnumber n an!ular momentum2uantum number l

number of electrons

in the orbital or subshell

rbital diagram

$

#s#

".*


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What is the electron confi!uration of !5

! #6 electrons

#s N 6s N 6p N +s N +p N /s#s66s66p+s6 6 C 6 C C 6 & #6 electrons

".*

Abbreviated as OMe+s6 OMe #s66s66p

What are the possible 2uantum numbers for the

last (outermost) electron in 3l5

3l #" electrons #s N 6s N 6p N +s N +p N /s#s66s66p+s6+p0 6 C 6 C C 6 C 0 & #" electrons

@ast electron added to +p orbital

n & + l& # ml& =#, -, or C# ms& I or =I

Kutermost subshell bein! filled with electrons


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Kutermost subshell bein! filled with electrons

".*


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".*


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Paramagneticunpaired electrons

6p

!iamagneticall electrons paired

6p".*


43/43

Chemistry Mystery: %isco&ery of 'eli$m

Gn #**, Pierre >anssen detected a new dar line in the solar

emission spectrum that did not match nown emission lines

Gn #*;0, William 1amsey discovered helium in a mineral of

uranium (from alpha decay).

ystery element was named $elium

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ITT Chng Ch 07 Electronic Structure of Atoms