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Chapter 7 ELECTRONS IN ATOMS AND PERIODIC

PROPERTIES

- Problems 7.1-7.16, 7.18-7.27, 7.31-7.56,

7.61-7.107, 7.109-7.119, 7.124-7.125, 7.128-7.134

Electromagnetic Radiation

- Electromagnetic (EM) Spectrum a continuum of the

different forms of electromagnetic radiation or

radiant energy

Radar Radio Waves

Weather systems

A galaxy imaged in the visible spectrum.

Radio telescopes. This is the Very Large Array

(VLA) in NM.

The same galaxy imaged in the radio spectrum at

the VLA.

Thermal Imaging Detecting IR radiation

Much of a persons energy is radiated away from

the body in the form of infrared (IR) energy. You

can produce more IR energy to warm yourself by

moving aroundthis is why you shiver when you go

outside in the cold with no coat on. This process

is called thermogenesis.

Why does your mother insist you wear a hat in the

winter?

IR Photography

Image obtained with IR film, which is really

film that is activated by light at 700-900 nm.

Electromagnetic Radiation

- Electromagnetic radiation or light is a form of

energy.

- Has both electric (E) and magnetic (H) components.

- Characterized by
- Wavelength (?)
- Amplitude (A)

Electromagnetic Radiation (cont.)

- Wavelength (l) The distance between two

consecutive peaks in the wave.

Increasing Wavelength

l1 gt l2 gt l3

Unit length (m)

Electromagnetic Radiation (cont.)

- Frequency (n) The number of waves (or cycles)

that pass a given point in space per second.

Decreasing Frequency

n1 lt n2 lt n3

Units 1/time (1/sec) or, Hertz (Hz)

Electromagnetic Radiation (cont.)

- The product of wavelength (l) and frequency (n)

is a constant.

(?)(?) c

Speed of light

c 3 x 108 m/s

c is a constant, independent of ?

Properties of Waves

- Wavelength (?) is the distance from peak-to-peak

in a wave. - Frequency (?) is the number of waves in a

specific time frame (usually per second Hz) - As wavelength goes up, frequency goes down (and

vice versa) - Electromagnetic waves travel at the speed of

light - ? ? c
- c speed of light 3 x 108 m/s

What statement is true when comparing red light

to blue light?

A. Red light travels at a greater speed than

blue light.

B. Blue light travels at greater speed than red

light.

C. The wavelength of blue light is longer.

D. The wavelength of red light is longer.

Behavior of Waves

- Waves refract, diffract and interact
- Refraction The bending of light as it passes

from one medium to another of different density

Light is also bent by liquids, causing the straw

to appear disconnected.

Refraction throught a prism separates white light

into its separate components (light of different

wavelengths) without changing the light itself.

Behavior of Waves

- Diffraction The bending of electromagnetic

radiation as it passes around an edge of an

object or through a narrow opening.

What causes the bright and dark spots?

Behavior of Waves

- Waves interact by adding together or cancelling

each other out

Light is a Wave, Right?

- Back in the old days
- It was generally agreed that matter and light

were distinct. - Matter was particulate in nature, light could be

described using waves. - Physicists circa 1900 had it all figured out
- One famous physicist asserted that within ten

years or so all the major problems in physics

would be solved. - The only thing left, really, was this niggling

little problem with black-body radiation

The State of Physics Before 1900

- Newton discovered light could be separated by a

prism in 170 - Heat, electricity and phlogiston were weightless,

imponderable fluids responsible for most

observed processes - It wasnt until the early 1800s that the

following, revolutionary ideas were put forth

light was a wave, atoms existed, and air could

trap heat (the greenhouse effect).

Physics in the early 1900s

- The end of the 1800s saw an explosion of real

scientific progress. - Thermodynamics, electromagnetism and the kinetic

molecular theory were well-developed. - There were still some problems, though, that

needed explaining - Blackbody radiation, new particle discoveries,

what was the ether?, radioactivity, the

instability of the atom, the photoelectric

effect. - There had to be one theory to explain them all

The big problem

- Black body radiation When a metal object is

heated, it begins to glow. If it is heated hot

enough, it glows white hot, emitting all the

wavelengths of visible light but little to none

in the UV range or higher. - Current (at the time) theories by Maxwell could

not explain this common phenomenon. - Max Planck proposed a new theory of light that

it behaved as a wave, but with particle-like

properties. - Light traveled in particle-like packets he called

quanta (a single one is called a quantum). - Each quantum was the smallest amount of energy

found in nature.

Light as Energy

- Planck found that in order to model this

behavior, one has to envision that energy (in the

form of light) is lost in integer values

according to

DE nhn

frequency

Energy Change

n 1, 2, 3 (integers)

h Plancks constant 6.626 x 10-34 Js

Light as Energy (cont.)

- In general the relationship between frequency and

photon energy is

h 6.636 x 10-34 Js c 2.9979 x 108 m/s 1 Hz

1 s-1

Ephoton h?

Example What is the energy of a 500 nm

photon?

? c/? (3x108 m/s)/(5.0 x 10-7 m)

? 6 x 1014 1/s

E h? (6.626 x 10-34 Js)(6 x 1014 1/s) 4 x

10-19 J

Energy Quantization

The student can stop only at certain points on a

flight of stairs. Her distance from the ground is

quantized.

The student can stop at any point on the ramp.

Her distance from the ground changes continuously.

Similarly, atomic energy levels are like

stepsthe energies available to an atom do not

form a continuum, they are quantized.

Evidence of Quantization

- Black-body Radiation (Planck)
- A system can transfer energy in packets of size

hn. - These packets are called quanta
- Prior to this discovery it was thought that

systems could absorb or emit any amount of

energy. - Other observations supported this quantum view

- Atomic Emission spectra (Balmer, Rydberg, Bohr)
- Light emitted from excited atoms occurs in

discrete lines rather than a continuum. - Photoelectric Effect (Einstein)
- Energy itself is actually quantized into packets

called photons. - This means energy has a particle-like nature as

well as a wave-like nature. - Electron Diffraction Patterns (Davisson Germer)
- Matter also has a wave-like nature!!

Atomic Emission

- When we heat a sample of an element, the atoms

become excited. When the atom relaxes it emits

visible light. The color of the light depends on

the element.

When the light emitted from excited atoms is

passed through a prism, we see discrete bands of

color at specific wavelengths.

Photon Emission

An excited atom relaxes from high E to low E by

emitting a photon. We can determine the energy

difference (?E) between levels by measuring the

wavelength of the emitted photon.

Emission of photon

?E hc/? ? ? hc/?E If ? 410 nm, ?E

4.52 x 10-19 J

The Photoelectric Effect

- Observed by Albert Einstein in 1905 Light

shining on a clean metal surface causes the

emission of electrons but only when the light has

a minimum threshold frequency (?0) - When ?lt?0 ? no electrons are emitted
- When ?gt?0 ? electrons are emitted, more e

emitted with greater intensity of light

? lt ?0

? gt ?0

Einstein applied Planck's quantum theory to

light light exists as a stream of "particles"

called photons.

The Photoelectric Effect (cont)

Frequency determines whether e- are ejected, and

their KE (velocity).

Intensity determines the number of e- that are

ejectedbut they will all have the same velocity!!

The Photoelectric Effect (cont.)

As frequency of incident light is increased,

kinetic energy of emitted e- increases linearly.

- hn0
- Workfunction energy needed to release e-

Light apparently behaves as a particle.

The Photoelectric Effect (cont.)

For Na with F 4.4 x 10-19 J, what wavelength

corresponds to ?o?

0

h? F 4.4 x 10-19 J

hc/? 4.4 x 10-19 J

? 4.52 x 10-7 m 452 nm

Electron Diffraction Patterns

- Light is shined through a crystal, and its

waveforms are scattered. When they come out the

other side, they create interference patterns on

a detector plate.

Diffraction can only be explained by treating

light as a wave instead of a particle.

Diffraction of Particles?

- Turns out we can get similar interference

patterns by bombarding crystals with beams of

high energy electrons also - This can only be explained by treating matter as

a wave.

de Broglie Wavelength

- If matter exhibits wave-like properties, we

should be able to determine the wavelength of a

particle. - Recall the energy of a photon, and the definition

of the speed of light - Substituting, E hc/?
- Using Einsteins relationship, E mc2,

Ephoton h? c ?? ? ? c/?

de Broglie Wavelength

- We can generalize this relationship to any

velocity (v) - What is the de Broglie wavelength of an electron

traveling at the speed of light? (melectron

9.31 x 10-31 kg) - What is the de Broglie wavelength of a 80 kg

student walking across campus at 3 m/s?

? (6.626 x 10-34 Js)/(9.31x10-31 kg)(3x108

m/s) 2.37 x 10-12 m

? (6.626 x 10-34 Js)/(80 kg)(3 m/s) 2.76 x

10-36 m

You are a wave, too, but you have a VERY small

wavelength!!

What does all this mean for matter?

- Scientists needed to find a way to explain how

light, usually thought of as a wave, could behave

like a particle AND how matter, which was usually

thought of as a particle, could behave as a wave. - They started with the hydrogen emission spectrum
- Balmer and Rydberg developed equations that

predicted where these lines should appear (even

before anyone had observed them).

The Bohr Model

- Balmer and Rydberg didnt know why their

equations worked. - Niels Bohr used their equations and observations

to develop a quantum model for H. - Central idea electron circles the nucleus in

only certain allowed circular orbitals. - Bohr postulated that there is Coulombic

attraction between e- and nucleus. However,

classical physics is unable to explain why an H

atom doesnt simply collapse. Why doesnt the

electron just spiral into the nucleus?

The Bohr Model of the atom

Principle Quantum number n An index of the

energy levels available to the electron.

656

486

434

410

The Bohr Model (cont.)

- Bohr model for the H atom is capable of

reproducing the energy levels given by the

empirical formulas of Balmer and Rydberg.

Z atomic number (1 for H)

n integer (1, 2, .)

Ry x h -2.178 x 10-18 J

The Bohr Model (cont.)

Energy levels get closer together as n

increases At n infinity, E 0 ? the electron

is free (not a part of the atom)

The Bohr Model (cont.)

We can use the Bohr model to predict what DE is

for any two energy levels

The Bohr Model (cont.)

Example At what wavelength will emission from n

4 to n 1 for the H atom be observed?

1

4

The Bohr Model (cont.)

Example What is the longest wavelength of light

that will result in removal of the e- from H?

?

1

Extension to Higher Z

The Bohr model can be extended to any single

electron system.must keep track of Z (atomic

number).

Z atomic number

n integer (1, 2, .)

Examples He (Z 2), Li2 (Z 3), etc.

Extension to Higher Z (cont.)

Example At what wavelength will emission from n

4 to n 1 for the He atom be observed?

2

1

4

So what happened to the Bohr Model?

- Although it successfully described the line

spectrum of hydrogen and other one-electron

systems, it failed to accurately describe the

spectra of multi-electron atoms. - The Bohr model was soon scrapped in favor of the

Quantum Mechanical model, although the vocabulary

of the Bohr model persists. - However, Bohr pioneered the idea of quantized

electronic energy levels in atoms, so we owe him

big.

Thanks Niels Bohr!

Quantum Concepts

- The Bohr model was capable of describing the

discrete or quantized emission spectrum of H. - But the failure of the model for multielectron

systems combined with other issues (the

ultraviolet catastrophe, workfunctions of metals,

etc.) suggested that a new description of atomic

matter was needed.

Quantum Concepts (cont.)

- This new description was known as wave mechanics

or quantum mechanics.

- Recall, photons and electrons readily demonstrate

wave-particle duality.

- The idea behind wave mechanics was that the

existence of the electron in fixed energy levels

could be though of as a standing wave.

Quantum Concepts (cont.)

- What is a standing wave?

A standing wave is a motion in which

translation of the wave does not occur.

In the guitar string analogy

(illustrated), note that standing waves

involve nodes in which no motion of the

string occurs.

Note also that integer and half- integer

values of the wavelength correspond to

standing waves.

Quantum Concepts (cont.)

- Louis de Broglie suggested that for the e- orbits

envisioned by Bohr, only certain orbits are

allowed since they satisfy the standing wave

condition.

not allowed

Quantum Concepts (cont.)

- Erwin Schrodinger developed a mathematical

formalism that incorporates the wave nature of

matter - H, the Hamiltonian, is a special kind of

function that gives the energy of a quantum

state, which is described by the wavefunction, Y.

Quantum Concepts (cont.)

- What is a wavefunction?

a probability amplitude

- Probability of finding a particle in space

The probability distribution for the hydrogen 1s

orbital in three-dimensional space

Probability

With the wavefunction, we can describe spatial

distributions.

The probability of finding the electron at points

along a line drawn from the nucleus outward in

any direction for the hydrogen 1s orbital.

Hydrogens Electron

Cross section of the hydrogen 1s orbital

probability distribution divided into successive

thin spherical shells (b) The radial probability

distribution

The surface contains 90 of the total electron

probability (the size of the orbital, by

definition)

Quantum Concepts (cont.)

- Another limitation of the Bohr model was that it

assumed we could know both the position and

momentum of an electron exactly.

- Werner Heisenberg observed that there is a

fundamental limit to how well one can know both

the position and momentum of a particle.

where

Uncertainty in position

Uncertainty in momentum

Quantum Concepts (cont.)

- Example
- What is the uncertainty in velocity for an

electron in a 1 Å radius orbital in which the

positional uncertainty is 1 of the radius. (1 Å

10-10 m)

?x (1 Å)(0.01) 1 x 10-12 m

HUGE!

Quantum Concepts (cont.)

- Example (youre quantum as well)
- What is the uncertainty in position for a 80

kg student walking across campus at 1.3 m/s with

an uncertainty in velocity of 1.

?p m?v (80kg)(0.013 m/s) 1.04 kg.m/s

Very smallwe know where you are.