CHAPTER 7: ATOMIC STRUCTURE ELECTROMAGNETIC SPECTRUMnicholschem1.weebly.com/uploads/1/2/4/9/12497207/... · Page 4 PARTICLE PROPERTIES OF LIGHT Photoelectric Effect: Electrons can

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

Page 2

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

Page 3

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

Page 4

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

Page 5

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

Page 6

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

Page 7

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

Page 8

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

Page 9

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

Page 10

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

Page 11

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