CHAPTER 7: ATOMIC STRUCTURE ELECTROMAGNETIC SPECTRUMnicholschem1.weebly.com/uploads/1/2/4/9/12497207/... · Page 4 PARTICLE PROPERTIES OF LIGHT Photoelectric Effect: Electrons can
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Page 1
CHAPTER 7: ATOMIC STRUCTURE
ELECTROMAGNETIC SPECTRUM
“Light” (referred to generically) includes any type of
electromagnetic (EM) radiation
X-rays Ultraviolet (sunburns) Visible Microwaves (ovens and cell phones)
Radio
WAVE PROPERTIES OF “LIGHT”
Wavelength:
Frequency:
Amplitude:
Speed:
ddistance crest to crest 4 HzD 5cm microwave
8HZI
u xcycles per second wave rate
V 4 cycles sec 4 Is 4 s t 4 Hertz Hz
height of wave
Related to intensity dim bright
how fast wave propagates forwardAll EM radiation travels at speed of lightC 2.998 108 mls
102.1 MHZ 102,100,000 HZ
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RELATIONSHIPS
c = l·v
l = wavelength (m) v = frequency (s–1) c = speed of light, 2.998 ×108 m/s
E = h·v
E = !"#
E = energy of EM radiation (J) h = Planck’s constant, 6.626 ×10–34 J·s
vs.
LETE
I I
smaller X larger Ahigher v tower v
Xt u are inversely proportional as XP Vd
Energy is quantized in multiples of h
Quantized means it can only be certainnotany
E h V as v P E P
E he as XP E fI
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Sample Problem:
A red and green laser pointer have listed specifications of 650. nm (red) and 532 nm (green). Calculate the frequency and energy of each color.
DIFFRACTION, INTERFERENCE PROPERTIES Diffraction:
Interference Pattern:
Constructive Interference: waves add
Destructive Interference: waves cancel
pwavelength
C d V
TYE f 14.61 10142
Iso.mnoanmmy
N WVgreen 15.64101472
gEred h V 6,626 10 34 f 4.61 10144 13.05 101912Egreen 13.74 1077
Infrared Visible Ultraviolet
LE ROY GBV TE
spread.is
Phase up or do n
out is
II II
D I
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PARTICLE PROPERTIES OF LIGHT
Photoelectric Effect: Electrons can be emitted from the surface of a metal when the wavelength of light is lower than a certain threshold.
Einstein: light is quantized as “photons,” which have both wave and particle properties.
Albert Einstein (1905)
If A too high too low At tu e emailedno e are emitted
Intensity doesnt matter
1V
When photon particle frequency is too low
each photon doesnt have enough E to causeejection of e
7 Intensity you T plutons not E
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THE NATURE OF MATTER
ATOMIC EMISSION SPECTRA
Electricity passed through tubes filled with a gaseous element cause emission of light! Left = Hg, right = H.
QUANTIFYING HYDROGEN EMISSION SPECTRUM
%# = RH & %
'()*+− %
'!-.!+ / l = wavelength (m) n = integer (1, 2, 3…) RH = Rydberg constant, 1.097 ×107 m–1
Sample Problem:
Calculate the wavelength of light in the hydrogen emission spectrum associated with n=3 and n=2 in the Rydberg equation.
Johannes Rydberg (1888)
yEmissionSpectrum quantized
colors
r
Ionlyfor H integers n 2 to n 6
f 1.097 107 m
f 1,523,611 m D 1 I1,523,61T
_16.563 1072656.3hm
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BOHR MODEL
Photon Absorption – Emission Event:
Transitions that produce visible light: Other transitions:
n = 2
n = 3
n = 4n = 5n = 6n = 7
n = 2
n = 3
n = 4n = 5n = 6n = 7
n = 2
n = 3
n = 4n = 5n = 6n = 7
n = 2
n = 3
n = 4n = 5n = 6n = 7
Niels Bohr (1913)
n = 2
n = 3
n = 4n = 5n = 6n = 7
n = 1
Bohr ModelElectrons exist incertain orbits aroundnucleus not true
Electrons can only havecertain energies ye tree
e
e f fDE pos 8Ehye e
ground state excited state
Light is emitted when e transitionsfrom high to low C level
e
T ne
Iii
h 6 02 h B 02
Different colors as diff E are lost
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For H atom: Eelectron = – 0∙2∙3456
Eelectron = – (8.8:8×<=>?@A∙B)(:.DDE×<=FG/B)(<.=DI×<=JG>K)
56
Eelectron = –2.179 × 10–18 J L %'+M En = energy of electron at “n” level n = integer
DE = –2.179 × 10–18 J & %'N-'O(+ − %
'-'-P-O(+ / DE = change in energy for a transition (J)
Sample Problem:
Calculate the energy of an electron in the hydrogen atom at the n=4 and n=1 state.
Calculate the change in energy that accompanies an electronic transition in a hydrogen atom from the n=3 to n=2 level, and the associated wavelength of light (in nm) either produced or absorbed.
D Defined as 4 Represents boefinafon
E 2.179 10185 441 1 1.362 1019572
E 2.179 10185 Y 1 2.179 1071Bothare negative IE than 0 at h Sn I lower C as closer to nucleus
3WOEoE 2.179 10 J
n na aZ
3.026 101957DE he
A he oE releasing.FI
D h 998xl083 026 x lo 19J
ad theesnes6.565 10 m
1656.5mL
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ELECTRONIC DIFFRACTION + INTERFERENCE
(Left) Electron beam through a double slit; electron beam through beryl crystal (middle), and Ni (right).
DE BROGLIE
SCHRÖDINGER EQUATION + HEISENBERG UNCERTAINTY PRINCIPLE
QRΨ = UΨ
Ĥ = Hamiltonian, an operator (like multiplication, derivative, or integral)
V = Wave equation for an electron (“orbital”); sample below
E = eigenvalue, solution to the equation
(Dx)(Dmv) ≥
0WX
The more precisely you know an electron’s position (Dx << 1) the greater the uncertainty in the momentum (Dmv >> 1).
POSITIONAL PROBABILITIES
€
Ψ2p =1
4 2πzao
$
% &
'
( )
3 / 2
z rao
$
% &
'
( ) e−zr / 2ao cosθ
Louis De Broglie
Werner Heisenberg Erwin Schrödinger
Interference patternmeans e are
waves
e are standing waves
maforwaves
i
42 probability of finding eat certainspot
porbital
I shape nLee e foudto N 904 of time
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QUANTUM MECHANICAL MODEL
ORBITAL ENERGIES
ELECTRONIC QUANTUM NUMBERS
An electron can be described by four quantum numbers (n, l, ml, ms), solutions to the Schrödinger equation.
= (1, 0, 0, +½)
Principle QN
n Angular Momentum QN
l Magnetic QN
ml Spin QN
ms
Size and energy Shape Orientation spin
n = 1, 2, 3…∞ l = 0, 1, 2, … (n–1) ml = –l …0…+l ms = +½ or –½
QUANTUM NUMBER n
O
e quantum number
h I 2,3called a shell or E level
As h P
energy typically 9a e tend to be furtherfrom nucleusi bigger orbitalw 35 compared to 25
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QUANTUM NUMBER l
n l orbitals
1
2
3
4
QUANTUM NUMBER ml
QUANTUM NUMBER ms
0 Is0 I 25,2ps
fl 0 l I l 2 1 3 0,1,23s3p3dS p d f 0,1 34s4p4d4f
l shape of orbital l 0 1,2 n l
me orientation me l 0 tl
3typeIs
generic
sorb Me 0 I 0 t me I O tt
1 0 porb l I Px Py Pe
Z I I z me 2 I O l 2
d orb l z 5 types d
3 2 I O l 2 37 types off
Ms spinIz or f fIz Mg 12 hrs Iz
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ELECTRON CONFIGURATIONS
A set of quantum numbers describes one electron; electron configurations describe an entire atom or ion.
Aufbau Principle:
Pauli Exclusion Principle:
Hund’s Rule:
PS d
n l IS Isn 22525 donelower Zpn 3 35 f thannow zp45 3d 4ps55 4d 5p
Jdbass6
µJf
f blockfill lower E orbitals first ground state
no two e can have the same 4 quantum s
or e 1h same orbital must be spin paired
y y.pen 1l F Me 0ms tYz 1,0 0,11121
DL h I l me p ms Yz 1,0 O 12
lowest E situation is when e in degenerateequal E orbitals are unpaired w same spin
not 94 t T
p
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