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Chapter 7

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Quantum Theory and the Electronic Structure of Atoms

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Properties of Waves

Wavelength () is the distance between identical points on successive waves.

Amplitude is the vertical distance from the midline of a wave to the peak or trough.

Frequency () is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s).

The speed (u) of the wave = x

Review of ConceptWhich of the waves shown has (a) the highest frequency (b) the longest wavelength (c) the greatest amplitude?

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Maxwell (1873), proposed that visible light consists of electromagnetic waves.

Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves.

Speed of light (c) in vacuum = 3.00 x 108 m/s

All electromagnetic radiation x c

Example 7.1

The wavelength of the green light from a traffic signal is centered at 522 nm. What is the frequency of this radiation?

Pg 279

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Mystery #1, “Heated Solids Problem”Solved by Planck in 1900

Energy (light) is emitted or absorbed in discrete units (quantum).

E = h x Planck’s constant (h)h = 6.63 x 10-34 J•s

When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths.

Radiant energy emitted by an object at a certain temperature depends on its wavelength.

E = hc / λBecause = c/λh = 6.63 x 10-34 J•s

Review of Concept

Why is radiation only in the UV but not the visible or infrared region responsible for sun tanning?

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Example 7.2

Calculate the energy (in joules) of

(a) a photon with a wavelength of 5.00 × 104 nm (infrared region)

(b) a photon with a wavelength of 5.00 × 10−2 nm (X ray region)

Pg 282

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Light has both:1. wave nature2. particle nature

Mystery #2, “Photoelectric Effect”Solved by Einstein in 1905

Photoelectric effect phenomenon in which electrons are ejected from the

surface of certain metals exposed to light of at least a certain minimum frequency

(threshold frequency)

Photon is a “particle” of light

h

KE e-

Bohr’s Theory of the Hydrogen atom 12

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Line Emission Spectrum of Hydrogen Atoms

Energize the

sample

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1. e- can only have specific (quantized) energy values

2. light is emitted as e- moves from one energy level to a lower energy level

Bohr’s Model of the Atom (1913)

En = −RH( )1n2

n (principal quantum number) = 1,2,3,…

RH (Rydberg constant) = 2.18 x 10-18J

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E = h

E = h

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Ephoton = E = Ef - Ei

Ef = -RH ( )1n2

f

Ei = -RH ( )1n2

i

i fE = RH( )

1n2

1n2

nf = 1

ni = 2

nf = 1

ni = 3

nf = 2

ni = 3

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Example 7.4

What is the wavelength of a photon (in nanometers) emitted during a transition from the ni = 5 state to the nf = 2 state in the hydrogen atom?

Pg 288

The duel nature of the electron20

Standing Waves

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De Broglie (1924) reasoned that e- is both particle and wave.

Why is e- energy quantized?

v = velocity of e-

m = mass of e-

2r = n = hmv

Example 7.5 Pg 292

Quantum mechanics24

Heisenberg Uncertainty principle

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Δx Δp ≥ h 4π

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Schrodinger Wave EquationIn 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e-

Wave function () describes:

1. energy of e- with a given

2. probability of finding e- in a volume of space

Schrodinger’s equation can only be

solved exactly for the hydrogen atom.

Must approximate its solution for

multi-electron systems.

Quantum Numbers

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n = 1, 2, 3, 4, ….

n=1 n=2 n=3

distance of e- from the nucleus

principal quantum number n

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Shape of the “volume” of space that the e- occupies

Sublevels:s orbitalp orbitald orbitalf orbital

Sublevels

s orbital (1 orientation: sphere)

p orbital (3 orientations: dumbbells)

d orbital (5 orientations: double dumbbells)

f orbital (7 orientations)

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Spin

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Energy of orbitals in a single electron atom

Energy only depends on principal quantum number n

En = -RH ( )1n2

n=1

n=2

n=3

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Energy of orbitals in a multi-electron atom

Energy depends on n and l

n=1 l = 0

n=2 l = 0n=2 l = 1

n=3 l = 0n=3 l = 1

n=3 l = 2

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Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom.

1s1

principal quantumnumber n

Sublevel (shape)

number of electronsin the orbital

Orbital diagram

H

1s1

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“Fill up” electrons in lowest energy orbitals (Aufbau principle)

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Pauli exclusion principle - no two electrons in an atomcan have the same four quantum numbers.

Each seat is uniquely identified (E, R12, S8).Each seat can hold only one individual at a time.

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Paramagnetic

unpaired electrons

2p

Diamagnetic

all electrons paired

2p

Shielding Effect

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• Why is the 2s orbital lower in energy than the 2p?

• “shielding” reduces the electrostatic attraction

• Energy difference also depends on orbital shape

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The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).

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Order of orbitals (filling) in multi-electron atom

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

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Outermost subshell being filled with electrons

Example 7.11

An oxygen atom has a total of eight electrons. Write the ground state electron configuration and orbital diagram.

Pg 309

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Noble Gas Configuration

Ex: Aluminum

e− configuration: 1s22s22p63s23p1

preceding noble gas is Ne: 1s22s22p6

noble gas configuration: [Ne] 3s23p1

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Example

Write the noble gas configuration and the noble gas orbital diagram for sulfur (S).