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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 2 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 3 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 4 of 50

8-1 Electromagnetic Radiation

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

• A wave transmits energy.

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 5 of 50

EM Radiation

Low

High

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 6 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 7 of 50

Electromagnetic Spectrum

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 8 of 50

RedOrange

Yellow

Green

Blue

Indigo

Violet

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

ROYGBIV

700 nm 450 nm

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

Constructive and Destructive Interference

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 10 of 50

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 11 of 50

Refraction of Light

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 12 of 50

8-2 Atomic Spectra

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 13 of 50

Atomic Spectra

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 14 of 50

8-3 Quantum Theory

Blackbody Radiation:

Max Planck, 1900:

Energy, like matter, is discontinuous.

Energy quantum: є = h E = n h ν

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 15 of 50

The Photoelectric Effect

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

• > o threshold frequency

• e- ~ I• ek ~

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 16 of 50

The Photoelectric Effect

Vs stop voltage

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 17 of 50

The Photoelectric Effect

• 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)

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 18 of 50

The Photoelectric Effect

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

The Photoelectric Effect

General Chemistry: Chapter 9 Slide 19 of 50

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 20 of 50

8-4 The Bohr Atom (1913)

E = -RH

n2

RH = 2.179.10-18 J

General Chemistry: Chapter 9 Slide 21 of 50

Energy-Level Diagram

ΔE = Ef – Ei = -RH

nf2

-RH

ni2

–

= RH ( ni2

1

nf2

–1

) = h = hc/λ

H atom spectral series

General Chemistry: Chapter 9 Slide 22 of 50

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 23 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 24 of 50

Emission and Absorption Spectroscopy

General Chemistry: Chapter 9 Slide 25 of 50

Visible atomic emission spectra

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 26 of 50

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.

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 27 of 50

deBroglie and Matter Waves

E = mc2

h = mc2

h/c = mc = p

p = h/λ

λ = h/p = h/mu

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 28 of 50

X-Ray Diffraction

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 29 of 50

The Uncertainty Principle

Δx Δp ≥ h

4π

• Werner Heisenberg 1927

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 30 of 50

8-6 Wave Mechanics

2Ln

• Standing waves.– Nodes do not undergo displacement.

λ = , n = 1, 2, 3…

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 31 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 32 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 34 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 37 of 50

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.

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 38 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 39 of 50

Orbital Energies

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 40 of 50

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

Slide 44 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

Slide 45 of 60

d orbitals

The shape of the atomic orbitals

Slide 46 of 60

Slide 47/61

The electron density of s orbitals

s orbitals

22s 2

3sπ

e 221

r

s

r (distance)

Slide 48 of 60

The electron density of p orbitals

22 xp

Slide 49 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

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

8-8 Electron Spin: A Fourth Quantum Number

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 51 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 53 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 54 of 50

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.

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 55 of 50

Orbital Energies

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 56 of 50

Orbital Filling

Dia 57/61

Aufbau Process and Hunds Rule

C

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

B

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 58 of 50

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

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 60 of 50

Filling the d Orbitals

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 61 of 50

Electon Configurations of Some Groups of Elements

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 62 of 50

8-12 Electron Configurations and the Periodic Table

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 63 of 50

Focus on He-Ne Lasers

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 64 of 50

Chapter 9 Questions

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