2007, Prentice Hall

Chemistry: A Molecular Approach, 1st Ed.

Nivaldo Tro

Roy KennedyMassachusetts Bay Community College

Wellesley Hills, MA

The Behavior of the Very Small

electrons are incredibly smalla single speck of dust has more electrons than

the number of people who have ever lived on earth

electron behavior determines much of the behavior of atoms

directly observing electrons in the atom is impossible, the electron is so small that observing it changes its behavior

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A Theory that Explains Electron Behaviorthe quantum-mechanical model explains the

manner electrons exist and behave in atomshelps us understand and predict the properties

of atoms that are directly related to the behavior of the electronswhy some elements are metals while others are

nonmetalswhy some elements gain 1 electron when forming an

anion, while others gain 2why some elements are very reactive while others are

practically inertand other Periodic patterns we see in the properties of

the elements

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The Nature of Lightits Wave Naturelight is a form of electromagnetic radiation

composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field an electric field is a region where an electrically charged

particle experiences a force a magnetic field is a region where an magnetized particle

experiences a force

all electromagnetic waves move through space at the same, constant speed3.00 x 108 m/s in a vacuum = the speed of light, c

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Characterizing Wavesthe amplitude is the height of the wave

the distance from node to crest or node to trough

the amplitude is a measure of how intense the light is – the larger the amplitude, the brighter the light

the wavelength, () is a measure of the distance covered by the wavethe distance from one crest to the next

or the distance from one trough to the next, or the distance between alternate nodes

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Characterizing Wavesthe frequency, () is the number of waves

that pass a point in a given period of timethe number of waves = number of cyclesunits are hertz, (Hz) or cycles/s = s-1

1 Hz = 1 s-1

the total energy is proportional to the amplitude and frequency of the wavesthe larger the wave amplitude, the more force it

hasthe more frequently the waves strike, the more

total force there is

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The Relationship Between Wavelength and Frequency

for waves traveling at the same speed, the shorter the wavelength, the more frequently they pass

this means that the wavelength and frequency of electromagnetic waves are inversely proportionalsince the speed of light is constant, if we know

wavelength we can find the frequency, and visa versa

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m

cs s

m1-

ExamplesCalculate the wavelength of red light with

a frequency of 4.62 x 1014 s-1

Calculate the wavelength of a radio signal with a frequency of 100.7 MHz

Colorthe color of light is determined by its wavelength

or frequencywhite light is a mixture of all the colors of visible

light a spectrumRedOrangeYellowGreenBlueViolet

when an object absorbs some of the wavelengths of white light while reflecting others, it appears coloredthe observed color is predominantly the colors

reflected

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12

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The Electromagnetic Spectrumvisible light comprises only a small fraction of

all the wavelengths of light – called the electromagnetic spectrum

short wavelength (high frequency) light has high energyradiowave light has the lowest energygamma ray light has the highest energy

high energy electromagnetic radiation can potentially damage biological moleculesionizing radiation

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Interferencethe interaction between waves is called

interferencewhen waves interact so that they add to make a

larger wave it is called constructive interferencewaves are in-phase

when waves interact so they cancel each other it is called destructive interferencewaves are out-of-phase

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Diffractionwhen traveling waves encounter an obstacle

or opening in a barrier that is about the same size as the wavelength, they bend around it – this is called diffractiontraveling particles do not diffract

the diffraction of light through two slits separated by a distance comparable to the wavelength results in an interference pattern of the diffracted waves

an interference pattern is a characteristic of all light waves

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The Photoelectric Effectit was observed that many metals emit

electrons when a light shines on their surfacethis is called the Photoelectric Effect

classic wave theory attributed this effect to the light energy being transferred to the electron

according to this theory, if the wavelength of light is made shorter, or the light waves intensity made brighter, more electrons should be ejected

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The Photoelectric EffectThe Problemin experiments with the photoelectric effect,

it was observed that there was a maximum wavelength for electrons to be emittedcalled the threshold frequencyregardless of the intensity

it was also observed that high frequency light with a dim source caused electron emission without any lag time

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Einstein’s ExplanationEinstein proposed that the light energy was

delivered to the atoms in packets, called quanta or photons

the energy of a photon of light was directly proportional to its frequencyinversely proportional to it wavelengththe proportionality constant is called Planck’s

Constant, (h) and has the value 6.626 x 10-34 J∙s

chhE

ExamplesCalculate the number of photons in a laser pulse

with wavelength 337 nm and total energy 3.83 mJ

What is the frequency of radiation required to supply 1.0 x 102 J of energy from 8.5 x 1027 photons?

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Ejected Electrons1 photon at the threshold frequency has just

enough energy for an electron to escape the atombinding energy,

for higher frequencies, the electron absorbs more energy than is necessary to escape

this excess energy becomes kinetic energy of the ejected electron

Kinetic Energy = Ephoton – Ebinding

KE = h -

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Spectrawhen atoms or molecules absorb energy, that

energy is often released as light energyfireworks, neon lights, etc.

when that light is passed through a prism, a pattern is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrumnon-continuouscan be used to identify the material

Rydberg analyzed the spectrum of hydrogen and found that it could be described with an equation that involved an inverse square of integers

22

21

1-7

n

1

n

1m 10097.1

1

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Na K Li Ba

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Spectra of Mercury

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Bohr’s ModelNeils Bohr proposed that the electrons could

only have very specific amounts of energyfixed amounts = quantized

the electrons traveled in orbits that were a fixed distance from the nucleusstationary statestherefore the energy of the electron was

proportional the distance the orbital was from the nucleus

electrons emitted radiation when they “jumped” from an orbit with higher energy down to an orbit with lower energythe distance between the orbits determined the

energy of the photon of light produced

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Wave Behavior of Electronsde Broglie proposed that particles could have

wave-like characterbecause it is so small, the wave character of

electrons is significantelectron beams shot at slits show an

interference patternthe electron interferes with its own wave

de Broglie predicted that the wavelength of a particle was inversely proportional to its momentum

)s(m(kg)

s

mkg

m1-

2

2

velocitymass

h

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however, electrons actually present an interference pattern, demonstrating the behave like waves

if electrons behave like particles, there should only be two bright spots on the target

examplesCalculate the wavelength of an electron traveling

at 2.65 x 106 m/s

Determine the wavelength of a neutron traveling at 1.00 x 102 m/s(Massneutron = 1.675 x 10-24 g)

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Uncertainty PrincipleHeisenberg stated that the product of the

uncertainties in both the position and speed of a particle was inversely proportional to its massx = position, x = uncertainty in positionv = velocity, v = uncertainty in velocitym = mass

the means that the more accurately you know the position of a small particle, like an electron, the less you know about its speedand visa-versa

m

1

4

hv

x

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any experiment designed to observe the electron results in detection of a single electron particle and no interference pattern

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Determinacy vs. Indeterminacyaccording to classical physics, particles move

in a path determined by the particle’s velocity, position, and forces acting on itdeterminacy = definite, predictable future

because we cannot know both the position and velocity of an electron, we cannot predict the path it will followindeterminacy = indefinite future, can only predict

probabilitythe best we can do is to describe the

probability an electron will be found in a particular region using statistical functions