prentice-hall © 2002general chemistry: chapter 9slide 1 of 50 general chemistry principles and...

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 1 of 50

General ChemistryPrinciples and Modern Applications

Petrucci • Harwood • Herring

10th Edition

Chapter 8: Electrons in Atoms


Contents

8-1 Electromagnetic Radiation

8-2 Atomic Spectra

8-3 Quantum Theory

8-4 The Bohr Atom

8-5 Two Ideas Leading to a New Quantum Mechanics

8-6 Wave Mechanics

8-7 Quantum Numbers and Electron Orbitals


Contents

8-8 Interpreting and Representing Orbitals of the Hydrogen Atom

8-9 Electron Spin: A Fourth Quantum Number

8-10 Multi-electron Atoms

8-11 Electron Configurations

8-12 Electron Configurations and the Periodic Table

Focus on Helium-Neon Lasers


8-1 Electromagnetic Radiation

• Electric and magnetic fields propagate as waves through empty space or through a medium.

• A wave transmits energy.


EM Radiation

Low

High


Frequency, Wavelength and Velocity

• Frequency () in Hertz—Hz or s-1.• Wavelength (λ) in meters—m.

• cm m nm Å pm

(10-2 m) (10-6 m) (10-9 m) (10-10 m)(10-12 m)

• Velocity (c)—2.997925·108 m s-1.

c = λ λ = c/ = c/λ


Electromagnetic Spectrum


RedOrange

Yellow

Green

Blue

Indigo

Violet

Prentice-Hall ©2002 General Chemistry: Chapter 9 Slide 8

ROYGBIV

700 nm 450 nm


Constructive and Destructive Interference


Refraction of Light


8-2 Atomic Spectra


Atomic Spectra


8-3 Quantum Theory

Blackbody Radiation:

Max Planck, 1900:

Energy, like matter, is discontinuous.

Energy quantum: є = h E = n h ν


The Photoelectric Effect

• Light striking the surface of certain metals causes ejection of electrons.

• > o threshold frequency

• e- ~ I• ek ~



Vs stop voltage



• At the stopping voltage the kinetic energy of the ejected electron has been converted to potential.

mv2 = eVs12

• At frequencies greater than o:

Vs = k ( - o)



Eo = hoEk = eVs o = eVo

h

eVo, and therefore o, are characteristic of the metal.

Conservation of energy requires that:

h = mv2 + eVo2

1

mv2 = h - eVo eVs = 2

1

Ephoton = Ek + Ebinding

Ek = Ephoton - Ebinding


General Chemistry: Chapter 9 Slide 19 of 50


8-4 The Bohr Atom (1913)

E = -RH

n2

RH = 2.179.10-18 J


Energy-Level Diagram

ΔE = Ef – Ei = -RH

nf2

-RH

ni2

–

= RH ( ni2

1

nf2

–1

) = h = hc/λ

H atom spectral series



Ionization Energy of Hydrogen

ΔE = RH ( ni2

1

nf2

–1

) = h

As nf goes to infinity for hydrogen starting in the ground state:

h = RH ( ni2

1) = RH

This also works for hydrogen-like species such as He+ and Li2+.

h = -Z2 RH


Emission and Absorption Spectroscopy


Visible atomic emission spectra


8-5 Two Ideas Leading to a New Quantum Mechanics

• Wave-Particle Duality.– Einstein suggested particle-like properties of

light could explain the photoelectric effect.– But diffraction patterns suggest photons are

wave-like.

• deBroglie, 1924– Small particles of matter may at times display

wavelike properties.


deBroglie and Matter Waves

E = mc2

h = mc2

h/c = mc = p

p = h/λ

λ = h/p = h/mu


X-Ray Diffraction


The Uncertainty Principle

Δx Δp ≥ h

4π

• Werner Heisenberg 1927


8-6 Wave Mechanics

2Ln

• Standing waves.– Nodes do not undergo displacement.

λ = , n = 1, 2, 3…


Wave Functions

• ψ, psi, the wave function.– Should correspond to a

standing wave within the boundary of the system being described.

• Particle in a box.

L

xnsin

L

2ψn

En = (n π /L)2 /2


Probability of Finding an Electron

Quantum physics and chemistry

33

E. Schrödinger

EH

The fundamental idea of wave mechanics

Theory of electrons and positrons

P. A. M. Dirac

Operators

• In quantum mechanics operator acts on a function and it transfers the function into another function.

• Typical example: derivation– x2 is transformed to 2x – sin(x) is transformed to cos(x)– ex is transformed to ex

– exk is transformed to k exk


Hamilton operator• Total energy = kinetic + potential

Slide 35 of 60

VTHVTH operátor ˆˆˆ

mp

Tm

pmvT operátor

2ˆˆ

221 22

2

zyxiip ˆ

dxd

ixp ˆ

2

2

2

2

2

222

22

222ˆˆ

zyxmmm

pT

Hamilton operator 2.

• The operator of potential energy, atomic unit

• Nuclear charge:• Electron charge: • rZ is the position of the nucleus: rZ = 0,0,0

Slide 36 of 60

eZ

eZeZ

rrqq

rqq

Vˆˆˆ

ˆ

1Zq

1eq

erVTH

ˆ

12

ˆˆˆ2


Wave Functions for Hydrogen

• Schrödinger, 1927 Eψ = H ψ

– H (x,y,z) or H (r,θ,φ)

ψ(r,θ,φ) = R(r) Y(θ,φ)

R(r) is the radial wave function.

Y(θ,φ) is the angular wave function.


8-7 Quantum Numbers and Electron Orbitals

• Principle electronic shell, n = 1, 2, 3…• Angular momentum quantum number,

l = 0, 1, 2…(n-1)

l = 0, sl = 1, pl = 2, dl = 3, f

• Magnetic quantum number, ml= - l …-2, -1, 0, 1, 2…+l


Orbital Energies


8-8 Interpreting and Representing the Orbitals of the Hydrogen Atom.

Simplified wave functions (Z=1, a0=1)

Slide 41 of 60

n l m Rnl(r) Y( ,f )real

Complex

1 0 0 1s 2e-r -

2 0 0 2s -

2 1 0 2pz-

2 1 (±1) 2px,yYes

e±if

Rn,0(r) for s orbitals for Z=1

Slide 42 of 60

Radial part of the 3s orbital Radial part of the 4s orbital

Radial part of the 1s orbital Radial part of the 2s orbital

Rn,1(r) for p orbitals for Z=1

Slide 43 of 60

Radial part of the 2p orbital

Radial part of the 3p orbital

of 60

8-8 Interpreting and Representing Orbitals of the Hydrogen Atom

0 in the yz plane 0 in the xz plane 0 in the xy plane

of 60

d orbitals

The shape of the atomic orbitals

Slide 46 of 60

/61

The electron density of s orbitals

s orbitals

22s 2

3sπ

e 221

r

s

r (distance)

of 60

The electron density of p orbitals

22 xp

of 60

Radial electron density r(r) = 4p r2 y2(r)

The probability of finding electrons on the surface of a sphere with radius r. The surface area = 4p r2


8-8 Electron Spin: A Fourth Quantum Number


8-10 Multi-electron Atoms

• Schrödinger equation was for only one e-.• Electron-electron repulsion in multi-

electron atoms.• Hydrogen-like orbitals (by approximation).

Általános Kémia, Periódikus tulajdonságok

Slide 52 of 60

Shielding

Zeff = Z – S

En = - RH n2

Zeff2


Shielding

Slater rules: For a 1s electron, S = 0.3.

For electrons in an s or p orbital with n > 1, the screening constant is given by

S = 1.00·N2 + 0.85·N1 + 0.35·N0N0 represents the number of other electrons in the same shell, N1 represents the number of electrons in the next smaller shell (n-1), and N2 is the number of electrons in other smaller shells

(n-2 and smaller).

The effective nuclear charge is

Zeff = Z - S


8-11 Electron Configurations

• Aufbau principle.– Build up and minimize energy.

• Pauli exclusion principle.– No two electrons can have all four quantum

numbers alike (n, l, ml, s).

• Hund’s rule.– Degenerate orbitals are occupied singly first,

and the spins of the electrons are parallel.


Orbital Energies


Orbital Filling

Dia 57/61

Aufbau Process and Hunds Rule

C

E(1s) < E(2s) < E(2p)

B


Filling p Orbitals

Electron configuration

• Short notation. For example:• B: 1s2 2s2 2p1

• C: 1s2 2s2 2p2

• N: 1s2 2s2 2p3

• O: 1s2 2s2 2p4

• F: 1s2 2s2 2p5

• Ne: 1s2 2s2 2p6 is: [Ne] (10 electrons)

Dia 59/61


Filling the d Orbitals


Electon Configurations of Some Groups of Elements


8-12 Electron Configurations and the Periodic Table


Focus on He-Ne Lasers


Chapter 9 Questions

1, 2, 3, 4, 12, 15, 17, 19, 22, 25, 34, 35, 41, 67, 69, 71, 83, 85, 93, 98

prentice-hall © 2002general chemistry: chapter 9slide 1 of 50 general chemistry principles and...

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