Slide 1 of 38 chemistry. Slide 2 of 38 © Copyright Pearson Prentice Hall Physics and the Quantum Mechanical Model > Light The amplitude of a wave is the

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chemistry

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© Copyright Pearson Prentice Hall

Physics and the Quantum Mechanical Model

> Light

• The amplitude of a wave is the wave’s height from zero to the crest.

• The wavelength, represented by (the Greek letter lambda), is the distance between the crests.

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> Light

• The frequency, represented by (the Greek letter nu), is the number of wave cycles to pass a given point per unit of time.

• The SI unit of cycles per second is called a hertz (Hz). Mathematically the unit that works best for frequency is sec-1.

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> Light

The wavelength and frequency of light are inversely proportional to each other.

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> Light

The product of the frequency and wavelength always equals a constant (c), the speed of light.

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> Light

According to the wave model, light consists of electromagnetic waves.

• Electromagnetic radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays.

• All electromagnetic waves travel in a vacuum at a speed of 3.0 108 m/s.

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> Light

Sunlight consists of light with a continuous range of wavelengths and frequencies.

• When sunlight passes through a prism, the different frequencies separate into a spectrum of colors.

• In the visible spectrum, red light has the longest wavelength and the lowest frequency.

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> Light

The electromagnetic spectrum consists of radiation over a broad band of wavelengths.

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SAMPLE PROBLEM

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Practice Problems for Sample Problem 5.1

Problem-Solving 5.15 Solve Problem 15 with the help of an interactive guided tutorial.


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>

In the Rutherford model, there was no limitation on the distance from the nucleus to an electron.

The model was a major advance, but it did not explain all properties of the atom

• Proton-electron attraction• Why didn’t atom collapse?

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> The Photoelectric Effect

•Early 1900’s

•Only certain colors of light would cause the Photoelectric Effect

•If wave this not the case

•Explained by Max Planck

•Planck studied emission of light from hot objects

•Said light emitted in small packets called quanta

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> Max Planck

•Planck determined the Energy emitted and carried in the quanta was related to the frequency of light emitted.

•ν α E

•E=hν•E – energy in Joules •H – Planck’s Constant (6.626 x 10-34 J∙sec)•ν – frequency (sec-1)

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> Quantum Mechanics

In 1905, Albert Einstein successfully explained the Photoelectric Effect by proposing that light could be described as quanta of energy.

• The quanta behave as if they were particles.

• Light quanta are called photons.

• Therefore the frequency of the photons was directly related to the Energy of the photons by Planck’s equation.

• Different colors of light have different energy.

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> Einstein’s Contribution

•Einstein said electromagnetic radiation has a Dual Wave-Particle nature

•Light can act both like a wave and like a stream of particles

•Particles called photons.

•Photon – particle of electromagnetic radiation with zero mass and carrying a quantum (packet) of energy

•Photoelectric effect – electromagnetic radiation only absorbed in whole numbers of photons. The energy of the photon is related to its frequency

•Eject an electron by hitting it with a photon with enough energy to free electron

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> Atomic Spectra

A prism separates light into the colors it contains. When white light passes through a prism, it produces a rainbow of colors aka a continuous spectrum.

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> Atomic Spectra

•According to the Rutherford Model, there was no limitation on the location of electrons relative to the nucleus.

•Therefore, the electron could exist at any distance and therefore any energy

•Thus it was expected that when excited, an atom would give off a continuous spectrum.


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> Atomic Spectra

When atoms absorb energy, electrons move into higher energy levels. These electrons then lose energy by emitting light when they return to lower energy levels.

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> Emission and Absorption of Energy as Electrons Change Energy Level

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> Atomic Spectra

When light from a helium lamp passes through a prism, discrete lines are produced. Obviously this was unexpected. This led to the development of the Bohr Model of the atom.

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> An Explanation of Atomic Spectra

In the Bohr model, the lone electron in the hydrogen atom can have only certain specific energies.

• When the electron has its lowest possible energy, the atom is in its ground state.

• Excitation of the electron by absorbing energy raises the atom from the ground state to an excited state.

• A quantum of energy in the form of light is emitted when the electron drops back to a lower energy level.

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The light emitted by an electron moving from a higher to a lower energy level has a frequency directly proportional to the energy change of the electron.

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> Hydrogen’s Emission Spectrum

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The three groups of lines in the hydrogen spectrum correspond to the transition of electrons from higher energy levels to lower energy levels.

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> The Bohr Model

Unfortunately Bohr could only work out his model, and apply it to Hydrogen.

Cannot explain spectra of multi-electron atoms

Cannot explain chemical behavior of atoms

What is next????


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> Quantum Mechanics

Classical mechanics adequately describes the motions of bodies much larger than atoms, while quantum mechanics describes the motions of subatomic particles and atoms as waves.

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> Quantum Mechanics

•In 1924, De Broglie developed an equation that predicts that all moving objects have wavelike behavior.

•Postulated electrons also have a dual wave-particle nature

•Electrons act like waves confined around the nucleus (standing waves) and therefore could only have certain frequencies

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Tacoma Narrows

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> De Broglie

•These correspond to the energy of Bohr’s orbits.

•Investigation showed that electrons can be diffracted and can interfere with each other

•These are wave properties

•Electrons have a dual wave-particle nature.

Electron Motion

http://www.youtube.com/watch?v=ofp-OHIq6Wo

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> Quantum Mechanics

The Heisenberg uncertainty principle states that it is impossible to know exactly both the velocity and the position of a particle at the same time.

• This limitation is critical in dealing with small particles such as electrons.

• This limitation does not matter for ordinary-sized object such as cars or airplanes.

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> Quantum Mechanics

The Heisenberg Uncertainty Principle

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Slide 1 of 38 chemistry. Slide 2 of 38 © Copyright Pearson Prentice Hall Physics and the Quantum Mechanical Model > Light The amplitude of a wave is the