Download CHEM 121

F 24 Aug 2012
Chapters 8-11 aim to explain differing reactivities of elements and to understand bonding.
Why are the alkali metals so reactive, while Au is unreactive?
To answer this question, chemists look at the nature of the atom.
Ch. 8 takes a historical view, develops Quantum Mechanics, and applies the concepts to discuss
electron configurations.
Ch. 9-11 uses electron configurations to discuss bonding between atoms.
Chapter 8: Atomic Theory and Quantum Mechanics
§8-1 Electromagnetic radiation is a wavelike form of energy that travels at the speed of light [p278 in
textbook is more detailed]
Figures 8-1 through 8-3
Visible light: 700 - 400 nm (red to violet)
just a small part of the electromagnetic spectrum
wavelength λ: distance between successive peaks
units of m or nm typically
frequency ν: # of waves passing a fixed point in one second
units of s-1 ≡ Hz
λν = c where c ≡ 2.99792458 x 108 m s-1
in vacuum
Interference (p281, Figure 8-4) and diffraction from a grooved surface (p282) are wave phenomena
Figure 8-5 shows interference
§8-3 But electromagnetic radiation also has particle properties:
1. Blackbody radiation and ultraviolet catastrophe
Figure 8-11 Radiation intensity vs. wavelength
Max Planck
ΔE = nhν
Quantized energy
h = Planck's constant = 6.626 x 10-34 J s
In a collection of atoms radiating energy, as in the sun or a heated iron rod, only certain energies are possible.
2. Photoelectric effect ==> photons
Albert Einstein
The energy of a photon = E = hν
Figure 8-12, K&P OVERHEAD15
No matter how many pennies you have, you can't buy time at a parking meter. Similarly, no matter
how intense nonlaser light is, if the frequency (or energy) of the light is less than the threshold frequency (or
energy), no electrons can be ejected.
A quarter buys more time than a nickel at one parking spot, but you can only get one parking spot.
Similarly, if you have photons with sufficient energy to eject an electron, each photon can only eject one
electron, and you need more photons (more intense light) to eject more electrons. The greater the photon
energy is beyond the threshold energy, the more kinetic energy an ejected electron can have.
Arrange visible colors ROYGBIV in order of increasing energy.
Electromagnetic radiation behaves as both waves and particles (photons).
2
3
§8-2
White light consists of all wavelengths ==> continuous spectrum
Figure 8-7
But atomic spectra are line spectra since electrons in atoms may only exist at certain energy levels.
Figures 8-8, 8-9, 8-10; U&B Figure 7.22
§8-4 Bohr model for H atom is like miniature solar system
Figures 8-13, 8-14
En = -Rhc/n2
Eq (8.5) En = -RH/n2
U:\_SC Student File Area\Pultz\EnergyLevel_H-atom.pdf
ground state vs. excited state
Bohr explanation for line spectrum of H atom
R is Rydberg constant, not gas constant
2
2
Balmer-Rydberg formula
1/λ = R[(1/nl) - (1/nu) ]
Rationalize Bohr model by fitting electron waves on orbit.
==> only certain allowed orbits; corresponds to quantized energy levels
Typical electrons have the same wavelength as X-rays;
used in electron microscopes.
§8-5 de Broglie: matter has wave properties as well as particle properties
Derive equation using E=mc2 & E = hc/λ
==>
mc = h/λ
Identify mc as momentum or mv=p ==>
λ = h/p
or λ = h/(mv)
Figure 8-19
where v = velocity
Calculate de Broglie wavelength of 100-g object moving at 1 m/s.
λ = 6.6 x 10-34 J s = 7 x 10-33 kg m2 s-2 s = 7 x 10-33 m
(0.1 kg)(1 m/s)
kg m s-1
which is too small to be measureable!
What is the de Broglie wavelength of an electron moving at 1 m/s?
λ = 6.6 x 10-34 J s
= 7 x 10-4 m
-31
(9 x 10 kg)(1 m/s)
0.7 mm is measureable!
Davisson & Germer showed that a crystal could diffract electrons.
The wavelength associated with macroscopic objects such as an eraser is too small to observe.
4
Heisenberg Uncertainty Principle
Δx⋅Δpx ≥ h/4π
Δ stands for uncertainty, not change
♦ The more precisely you know the position of an object, the less precisely you know its momentum, and
vice versa.
♦ This is a fundamental uncertainty, unlike the uncertainty in lab where you can develop more accurate
methods/instruments.
♦ Follows from wave nature of matter.
♦ Or photon has momentum & energy, so sending in light to determine x & px of an e- changes e- position &
mvx
Like the de Broglie relation, the Heisenberg Uncertainty Principle is important only for very small masses
such as e-s, n0s, etc.
§8-6 Quantum Mechanics & Schrödinger equation: Bohr model only applies to atoms with one eMotivated by classical wave equation for violin string
Fig 8-18
Builds in de Broglie relation
1-D, time-independent, non-relativistic:
-(h2/8π2m)(d2ψ/dx2) + Vψ = Eψ
m = mass of particle, V = potential energy
For atoms with more than one electron, we must approximate V.
Usually we must use numerical methods to obtain a solution.
Find wave function ψ (psi) & energy E
Only some ψ & E are possible, just as only certain vibrations are possible in a vibrating string.
ψ has no physical meaning
ψ2 gives probability of finding e- or other particle of interest at a particular point in space
Particle in Box is one case where the Schrödinger equation can be solved exactly
ψn(x) ~ sin(nπx/L)
Figures 8-20, 8-21 (slides 26,27)
Two points to know:
1. Shows that there is a minimum energy for quantized particles ==> zero-point energy
2. E = n2h2/(8mL2) shows that as system gets larger, spacing between energy levels shrinks
§8-7 Quantum numbers & orbitals (modification of "orbit," or ψ)
Quantum numbers arise from solution of Schrödinger equation for H atom!
3-D world ==> 3 quantum #s; Einstein's special relativity (x,y,z,t) ==> 4 quantum #s
Quantum # Name
Significance
Values
n
principal quantum #
size & energy 1,2,3,...
l
angular momentum QN
shape
0,1,...,n-1
ml
magnetic quantum #
orientation
-l,...,+l
electron spin QN
±½
ms
Spin QN is important for diamagnetism & paramagnetism.
see §9-6
Spin QN is also important in sets of quantum numbers!
Pauli
Value of l
Letter for Atomic Orbital
0
s
1
p
2
d
3
f
5
Figure 8-23 shows energy levels for hydrogen atom and ions with one electron; not to scale
§8-8 different views of H 1s orbital
Figure 8-24, slide 32
2
2 2
probability distribution ψ vs radial distribution function 4πr ψ
Zumdahl Chem Prin 4th Fig 12.16-17
6
1s, 2s, & 3s orbitals (note size & nodes)
p orbitals
3d orbitals
3p and 4dxy in Figure 8-31
§8-9 Electron spin
Figure 8-25; in book only
Figures 8-26, 8-27 (PowerPoint is correct), 8-28
Figures 8-29, 8-30