Chapter 7 The Quantum Mechanical Model of the Atom

Quantum mechanics — microscopic particles Classical mechanics — macroscopic objects

Some properties of light

Light travels and carries energy

Speed of light c = 3.00 x 10 8 m/s

Light has many colors

Light can be invisible to human

Light is an electromagnetic radiation Light is a wave

Wavelength λ: distance between two consecutive peaks. Unit: m

Frequency ν : number of complete wavelengths, or cycles, that pass a given point each second. Unit: 1/s = s −1 = Hz Period T: time required for a complete wavelength or cycle to pass a given point. Unit: s ν = 1/T c = λ/T = λ ν

Demo on Sr salt λ = 6.50 x 10 2 nm, what is the frequency of the red light? What is the period of the light?

ν

1. Blackbody radiation Phenomena that could not be explained by classic mechanics

ρ(λ) (kJ/nm)

Energy can only be gained or lost in whole-number multiples of the quantity h v, a quantum. Planck’s constant: h = 6.63 x 10 −34 J·s

1. Blackbody radiation Phenomena that could not be explained by classic mechanics 2. Photoelectric effect

Photoelectric Effect Occurs only if ν > ν 0

Electromagnetic radiation can be viewed as a stream of particles called photons. Energy of one photon is E = h ν

What is the energy of one photon from the red light? What is the energy of one photon from a yellow light whose wavelength is 589 nm? 3.37 x 10 −19 J 3.06 x 10 −19 J4.61 x Hz 5.09 x Hz

ν

Electromagnetic Radiation Exhibits Wave Properties and Particulate Properties Is light a stream of particles or waves?

1. Blackbody radiation Phenomena that could not be explained by classic mechanics 2. Photoelectric effect 3. Atomic spectra

Pink Floyd: Dark Side of the Moon

λ Continuous spectrum

Ne gas in tube

HgHeH

Electrons in an atom can only occupy certain energy levels Neils Bohr

Unknown volatile liquid: methanol CH 3 OH

Schrödinger’s Equation Ĥ — an operator related to energy E — energy Ψ — wave function Ψ contains all the information of a system Ψ = Ψ(x,y,z) x,y,z: coordinates of electrons

H atom

│Ψ(x,y,z)│ 2 — probability density distribution of electrons Max Born Ψ — wave function Ψ contains all the information of a system What is the physical significance of Ψ?

A specific wave function Ψ is called an orbital. An atomic orbital is characterized by three quantum numbers.

Three Quantum Numbers Principle quantum number n. Only positive integers. n = 1, 2, 3, 4, · · ·shell Angular momentum quantum number l. l = 0, 1, 2, 3, 4, · · ·, (n − 1)subshell s p d f g

Magnetic quantum number m l m l = − l, − l +1, − l + 2, · · ·, 0, · · ·, l − 1, l Must remember the possible values for quantum numbers One set of n, l, and m l specify One atomic orbital.

The sets of quantum numbers are each supposed to specify an orbital. One set, however, is erroneous. Which one and why? (a) n = 3; l = 0; m l = 0(b) n = 2; l = 1; m l = – 1 (c) n = 1; l = 0; m l = 0(d) n = 4; l = 1; m l = – 2 EXAMPLE 7.6 Quantum Numbers II n = 1, 2, 3, 4, · · · l = 0, 1, 2, 3, 4, · · ·, (n − 1) m l = − l, − l +1, − l + 2, · · ·, 0, · · ·, l − 1, l

Which of the following names are incorrect: 1s, 1p, 7d, 9s, 3f, 4f, 2d n = 1, 2, 3, 4, · · · l = 0, 1, 2, 3, 4, · · ·, (n − 1) m l = − l, − l +1, − l + 2, · · ·, 0, · · ·, l − 1, l

What are the quantum numbers and names (for example, 2s, 2p) of the orbitals in the n = 4 principal level? How many n = 4 orbitals exist? n = 1, 2, 3, 4, · · · l = 0, 1, 2, 3, 4, · · ·, (n − 1) m l = − l, − l +1, − l + 2, · · ·, 0, · · ·, l − 1, l n = 4; therefore l = 0, 1, 2, and 3

Try “For practice 7.5 and 7.6” on page 299 and homework questions

1s orbital of H atom How to represent an orbital in 3D? 2) Contour surface 1) Probability distribution

1s orbital of H atom How to represent an orbital in 3D? 2) Contour surface 90 % 1) Probability distribution

Two Representations of the Hydrogen 1s, 2s, and 3s Orbitals (a) The Electron Probability Distribution (b) The Surface Contains 90% of the Total Electron Probability (the Size of the Oribital, by Definition) n↑ → size↑

Representation of the 2p Orbitals (a) The Electron Probability Distribution for a 2p Oribtal (b) The Boundary Surface Representations of all Three 2p Orbitals l is related to shape of orbitals

Representation of the 3d Orbitals (a) Electron Density Plots of Selected 3d Orbitals (b) The Boundary Surfaces of All of the 3d Orbitals

Chapter 7 Problems 5, 20, 28, 32, 59, 61, 63