Chapter 7Chapter 7The Quantum-Mechanical The Quantum-Mechanical Model of the AtomModel of the Atom

A Theory that Explains Electron A Theory that Explains Electron BehaviorBehavior the quantum-mechanical model explains the manner

electrons exist and behave in atoms helps us understand and predict the properties of

atoms that are directly related to the behavior of the electrons◦ why some elements are metals while others are

nonmetals◦ why some elements gain 1 electron when forming an

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

are practically inert◦ and other Periodic patterns we see in the properties

of the elements

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One of the ways that energy travels through space: – Light from sun; microwave oven; radiowaves for MRI

mapping

• Exhibit the same type of wavelike behavior and travel at the speed of light in a vacuum

• It has electric and magnetic fields that simultaneously oscillate in planes mutually perpendicular to each other and to the direction of propagation through space.Electromagnetic radiation has oscillating electric (E) and magnetic (H) fields in planes

The Nature of Light its Wave The Nature of Light its Wave NatureNature light 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 speed◦ 3.00 x 108 m/s in a vacuum = the speed of light, c

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Characterizing WavesCharacterizing Waves Waves are characterized by wavelength, frequency,

and speed.

– wavelength (λ) is the distance between two consecutive peaks or troughs in a wave. – frequency (ν) is defined as the number of waves

(cycles) per second - is a measure of the distance covered by the wave

◦ the distance from one crest to the next ◦ the number of waves = number of cycles◦ units are hertz, (Hz) or cycles/s = s-1

1 Hz = 1 s-1

the 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

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Amplitude & WavelengthAmplitude & Wavelength

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Dim light

Bright light

InterferenceInterference the interaction between

waves is called interference

when waves interact so that they add to make a larger wave it is called constructive interference◦ waves are in-phase

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

phase

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DiffractionDiffraction when 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 diffraction◦ traveling 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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2-Slit Interference2-Slit Interference

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The Relationship Between The Relationship Between Wavelength and FrequencyWavelength 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 proportional◦ since the speed of light is constant, if we know

wavelength we can find the frequency, and visa versa

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cCalculate the wavelength of red light with a frequency of 4.62 x 1014 s-1

A laser dazzels the audience in a rock concert by emitting green light with a wave length of 515 nm. Calculate the frequency of the light

ColorColor the color of light is determined

by its wavelength◦ or frequency

white light is a mixture of all the colors of visible light◦ a spectrum◦ RedOrangeYellowGreenBlue

Violet when an object absorbs some

of the wavelengths of white light while reflecting others, it appears colored◦ the observed color is

predominantly the colors reflected

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The Electromagnetic The Electromagnetic SpectrumSpectrum visible light comprises only a small fraction of all the

wavelengths of light – called the electromagnetic spectrum

short wavelength (high frequency) light has high energy◦ radiowave light has the lowest energy◦ gamma ray light has the highest energy

high energy electromagnetic radiation can potentially damage biological molecules◦ ionizing radiation

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The Photoelectric EffectThe Photoelectric Effect it was observed that many

metals emit electrons when a light shines on their surface◦ this 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

in experiments with the photoelectric effect, it was observed that there was a maximum wavelength for electrons to be emitted◦ called the threshold

frequency◦ regardless 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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Particlelike Properties of Particlelike Properties of Electromagnetic EnergyElectromagnetic Energy

Refers to the phenomenon in which electrons are emitted from the surface of a metal when light strikes it:

– No electrons are emitted by a given metal below a specific threshold frequency νo.

– For light with frequency lower than the threshold frequency, no electrons are emitted regardless of the intensity of the light.

– For light with frequency greater than the threshold frequency, the number of electrons emitted increases with the intensity of the light.

– For light with frequency greater than the threshold frequency, the kinetic energy of the emitted electrons increases linearly with the frequency of the light.

Einstein’s ExplanationEinstein’s Explanation Energy is in fact quantized and can be transferred only

in discrete units of size hν. A system can transfer energy only in whole quanta Einstein 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 frequency◦ inversely proportional to it wavelength◦ the proportionality constant is called Planck’s

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

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chhEphoton

Ejected ElectronsEjected Electrons 1 photon at the threshold frequency has just enough

energy for an electron to escape the atom◦ binding 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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ExamplesExamples he blue color in fireworks is often achieved by heating

copper(I) chloride (CuCl) to about 1200°C. The hot compound emits blue light having a wave-length of 450 nm. What is the increment of energy (the quantum) tha is emitted at 450 nm by CuCl?

What is the energy (in kJ/mol) of photons of radar waves with ν = 3.35 x 108 Hz?

Calculate 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?

SpectraSpectra when atoms or molecules absorb energy, that energy is

often released as light energy◦ fireworks, 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 spectrum◦ non-continuous◦ can 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

However, his equation gave little information into why atomic spectra were discrete, why atoms are stable, or why his equation worked

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Examples of SpectraExamples of Spectra

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Oxygen spectrum

Neon spectrum

Emission vs. Absorption Emission vs. Absorption SpectraSpectra

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Spectra of Mercury

Bohr’s ModelBohr’s Model Neils Bohr proposed that the

electrons could only have very specific amounts of energy◦ fixed amounts = quantized

the electrons traveled in orbits that were a fixed distance from the nucleus◦ stationary states◦ therefore 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 energy◦ the distance between the

orbits determined the energy of the photon of light produced

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Bohr Model of H AtomsBohr Model of H Atoms

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Wavelike Properties of MatterWavelike Properties of Matter

mvh =

Energy is really a form of matter, and all matter exhibits both particulate and wave properties. –Large “pieces” of matter, such as base balls, exhibit predominantly particulate properties –Very small “pieces” of matter, such as photon, while showing some particulate properties through relativistic effects, exhibit dominantly wave properties –“Pieces” of intermediate mass, such as electrons, show both the particulate and wave properties of matterLouis de Broglie in 1924 suggested that, if light can behave in some respects like matter, then perhaps matter can behave in some respects like light.In other words, perhaps matter is wavelike as well as particlelike.

examplesexamples What velocity would an electron (mass = 9.11 x 10-31kg)

need for its de Broglie wavelength to be that of red light (750 nm)?

What is the velocity of an electron having a de Broglie wavelength that is approximately the length of a chemical bond? Assume this length to be 1.2 x 10-10 m

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

Quantum Mechanics and the Quantum Mechanics and the Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle

Heisenberg Uncertainty Principle – both the position (Δx) and the momentum (Δmv) of an electron cannot be known beyond a certain level of precision

1. (Δx) (Δmv) > h 4π

2. Cannot know both the position and the momentum of an electron with a high degree of certainty

3. If the momentum is known with a high degree of certaintyi. Δmv is smallii. Δ x (position of the electron) is large

4. If the exact position of the electron is knowni. Δmv is largeii. Δ x (position of the electron) is small

Determinacy vs. Determinacy vs. IndeterminacyIndeterminacy

according to classical physics, particles move in a path determined by the particle’s velocity, position, and forces acting on it◦ determinacy = definite, predictable future

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

probability

the best we can do is to describe the probability an electron will be found in a particular region using statistical functions

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