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Chapter Seven

The Electronic Structure of Atoms

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Wave TheoryWave

Repeating disturbance spreading out from a defined originCharacterized by wavelength, frequency and amplitude

Wavelength ()Distance between identical ptsUnits some form of meters

Frequency ()Number of waves that passthrough a point in 1 secondUnits of cycles/sec or Hz

AmplitudeHeight of wave from center ptIntensity of wave

3Electromagnetic RadiationElectromagnetic Radiation

Emission/transmission of energy in the form of waves with both electrical and magnetic components

Travels at the speed of light, cc= 3.00 x 108 m/s

Frequency & wavelength linked c=

4

What is the wavelength of an FM-radiowave with a 94.9 MHz frequency?

c = =3.00 x 108 m/s = c/

94.9M Hz = 94.9 x 106 Hz = 94.9 x 106/s

mxsx

smx 16.3

109.9411000.3

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8

5

Quantum Theory and

the Photoelectric Effect

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Max Planck’s Quantum TheoryMeasurements show amount of energy emitted by an

object at a certain temperature is directly related to its wavelength

Theorized that the energy must be in discrete amounts.May be in multiples of these discrete amounts

E = h, E = 2h, E = 3h …

Called the smallest amount of energy a Quantum: Planck’s constant: h = 6.63 X 10-34 J s

Didn’t know why , but math worked over entire spectrum

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Einstein and the Photoelectric EffectExperiment to prove why E= h

Full spectrum light hits metal surface Energy transferred to electrons in metalElectrons break free and escape to anodeFlow of electrons recorded with voltmeter

ResultsLight energy must have a certain threshold frequency to dislodge electronsLight energy has wave properties: E = h

Light energy as a particle: E= KEelectron + w(work needed to dislodge electrons)

These particles of light later called “photons”

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Practical Examples of the Photoelectric EffectWhat is the energy of a radiowave with a frequency of 94.9 MHz?

What is the energy per photon and per mole of photons of violet light, with a wavelength of 415 nm?

What wavelength has an energy of E = 1.00 x 10-20J?

JxsxxJsxhEphoton

26634

1023.6109.94110626.6

Jxmx

xs

mxxJsxhcE photon19

9

834

1079.41041511000.3

110626.6

mxJx

xs

mxxJsx 520

834

1099.11000.111000.3

110626.6

molJx

molphotonsxx

photonJxEmol

52319 1088.21

1002.61079.4

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Bohr’s Theory of the Hydrogen Atom

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Emission SpectraPattern of radiation that is emitted when photons are

removed from a substanceProcedure

Add energy to a substancePhotons are emitted as a beam of lightSeparate wavelengths through a prismRecord pattern on a photographic plate

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Continuous vs. Line SpectraContinuous spectrum:

Occurs when all visible light is present: white light

Line SpectrumOccurs when light is produced through an elementShows a pattern of lines characteristic of that elementCan be used for identification

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Elemental Line Spectra

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Bohr’s Hydrogen AtomNiels Bohr (1913): Electron energy (En) was quantized

Only certain specified values allowedStable levels called energy levelsPhoton moves from 1 level to another

The energy of each stable orbit En = –RH/n2

n is the quantum number of the level integers only, 1,2 3..

Proportionality constant RHRydberg constantRH = 2.18 X 10-18 J

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Energy Level CalculationsAll calculations done by comparing energy levels

Electron moves between levelsE = RH (1/ni

2 – 1/nf2)

Energy emitted or absorbedHigh to low level

energy released (-)

Low to high levelenergy absorbed (+)

Ground state: The lowest possible energy level Excited state: All other levels

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Calculate the wavelength of the electron shift from n = 4 to n =2. Is light emitted or absorbed?

22

11

fiH nn

RE

JxJxxE 1922

18 1009.421

411018.2

so E Ehchc

mxJx

xs

mxxJsx 719

834

1086.41009.411000.31063.6

= 486 nm Visible blue green light is emitted (higher to lower n)

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Quantum Numbers

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Quantum Numbers and Atomic OrbitalsAtomic orbital

A region in space with a high probability of finding an electron.Identified by 4 quantum numbers.

Four Quantum Numbers1. The principal quantum number (n)2. The angular momentum quantum number (l)3. The magnetic quantum number (ml)4. The electron spin quantum number (ms)

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The Principal Quantum Number (n)Restricted to the positive integers: 1, 2, 3, 4, 5, 6 or 7Indicates the shell or level of the orbital

Indicates the size of the orbitalIntegers correspond to row numbers in periodic table

n=1n=2n=3

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The Angular Momentum Quantum Number (l)Indicates orbital shape

Designation: s, p, d or fDesignates the subshell

Values range from 0 to n-1

l= 0 are called s orbitalsSpherical

l = 1 are called p orbitals2 teardrops joined at center

I= 2 are d orbitalsl= 3 are f orbitals.

level 0 1 2 3Name s p d f

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The Magnetic Quantum Number (ml):Determines the orientation in space of the orbitals

Integers from -l to +l

Determines the number of orbitals in a subshellThe number of possible values for ml = 2l + 1

l = 1 # values = 3 Range: -1 to 1

ml -1 0 1

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Electron Spin Quantum Number (ms)A magnetic field is induced by the moving electric charge

of the electron as it spinsSpins cancel one another No net magnetic field for the pairAllows 2 electrons to occupy 1 orbital

Designationtwo values: +1/2 and –1/2

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Quantum Numbers Summary

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Electron ConfigurationsThe energy of an electron is defined by both n and l

Principle shellsn = 1,2, 3, 4 or 5

Subshellsl = 0, 1, 2, or 3depends on ns p d orbitals present(f subshell not shown)

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Orbital Filling in Multi-electron AtomsFill low to high with 2 electrons per orbitalUse chart to account for overlap of n values

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6sFormat: nl#e-

1s22s22p63s23p64s23d104p65s24d10…

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Electronic ConfigurationDefines the orbital for each electron

# electrons = atomic number (Z) of atomspdf Notation

n designates subshellLetter designates l

Use superscript for # electrons

Ne: Z = 101s22s22p6

Na: Z = 111s22s22p63s1

orNa: [Ne]3s1

Orbital DiagramShow boxes or lines for levelsPlace designate electrons2 electrons allowed per orbital

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Hund’s Rule and the Aufbau PrincipleHund's rule: Electrons in the same subshell occupy degenerate orbitals

singly, before pairingOxygen, O Z = 8

The Aufbau Principle: Electron configuration of each element is based on the electron

configuration of the element just before it in the periodic table. (Z = 1) H 1s1

(Z = 2) He 1s2

(Z = 3) Li 1s22s1

11222 22221 zyx pppss

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Magnetism in Multi-electron Atoms+1/2 & -1/2 spins will cancel if electrons pairedNo magnetic properties without spin present

# unpaired electrons proportional to magnetic properties

ParamagneticAt least 1 unpaired electron

Na: 1s22s22p63s1

Diamagnetic All electrons paired

Ne: 1s22s22p6

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Exceptions To The Aufbau PrincipleElements will fill out a lower energy subshell when possibleCr and Cu fill out their 3d shell before the 4s shell. Elements in the same family as Cr &Cu behave in same way.

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Quantum Numbers and the Periodic TablePrinciple quantum number, n

Row number of periodic table, values of 1-7Angular momentum quantum number, l

Specific area of periodic table, spdfNumber of orbitals and electrons, ml & ms

ml: Count blocks and divide by 2 ms: Count blocks

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Electronic Configurations and the Periodic TableAdd 1 electron for each block in the periodic table