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Chapter 12 Sections 12.6 to 12.10 Wavelength

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Light The study of light led to the development of the quantum mechanical model. The study of light led to the development of the quantum mechanical model. Light is a kind of electromagnetic radiation. Light is a kind of electromagnetic radiation. In Wave Model, Light is considered to consist of electromagnetic waves that travel in a vacuum @ speed of 3.00 x 10 8 m/s In Wave Model, Light is considered to consist of electromagnetic waves that travel in a vacuum @ speed of 3.00 x 10 8 m/s Electromagnetic radiation includes many kinds of waves Electromagnetic radiation includes many kinds of waves All move at 3.00 x 10 8 m/s ( c) All move at 3.00 x 10 8 m/s ( c)

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ER Electromagnetic Radiation – forms of energy that exhibits wavelight behavior as it travels thru spaceElectromagnetic Radiation – forms of energy that exhibits wavelight behavior as it travels thru space Examples of Electromagnetic Radiation:Examples of Electromagnetic Radiation: 1.Radio Wvaes 2.Microwaves 3.Visible Light 4.Infrared 5.Ultraviolet 6.X-Rays 7.Gamma Rays ER has measurable wave properties of wavelength and frequencyER has measurable wave properties of wavelength and frequency

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Parts of a wave Wavelength Amplitude Orgin Crest Trough

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Parts of Wave Orgin - the base line of the energy. Orgin - the base line of the energy. Crest - high point on a wave Crest - high point on a wave Trough - Low point on a wave Trough - Low point on a wave Amplitude - distance from origin to crest Amplitude - distance from origin to crest Wavelength - distance from crest to crest Wavelength - distance from crest to crest Wavelength - is abbreviated Greek letter lambda. Wavelength - is abbreviated Greek letter lambda.

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Frequency The number of waves that pass a given point per second. The number of waves that pass a given point per second. Units are cycles/sec or hertz (hz) Units are cycles/sec or hertz (hz) Abbreviated the Greek letter nu Abbreviated the Greek letter nu c = c =

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Frequency and wavelength Are inversely related Are inversely related As one goes up the other goes down. As one goes up the other goes down. Different frequencies of light is different colors of light. Different frequencies of light is different colors of light. There is a wide variety of frequencies There is a wide variety of frequencies The whole range is called a spectrum The whole range is called a spectrum

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Frequency and Wavelength are mathematically related, they are inversely related Frequency and Wavelength are mathematically related, they are inversely related The relationship is shown by the following equation: The relationship is shown by the following equation: c = c = c= speed of light c= speed of light Wavelength

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Long Wavelength Long Wavelength = Low Energy Low Frequency Short Wavelength Short Wavelength = High Energy High Frequency

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Radio waves Micro waves Infrared. Ultra- violet X- Rays Gamma Rays Low energy High energy Low Frequency High Frequency Long Wavelength Short Wavelength Visible Light

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Calculating Light What is the wavelength if light with a frequency of 5.89 x 10 5 Hz? What is the wavelength if light with a frequency of 5.89 x 10 5 Hz? What is the frequency of blue light with a wavelength of 484 nm? What is the frequency of blue light with a wavelength of 484 nm?

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H.W. Questions 1. List 5 examples of E.R. 2. What is the speed of all forms of E.R. in a vacuum 3. Relate Frequency and Wavelength 4. The speed of light is 3.00 x 10 8 m/s and the frequency is 7.500 x 10 12 Hz. Calculate the Wavelength of E.R. 5. Determine the frequency of light w/ a wavelength of 4.257 x 10 -7 cm.

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Atomic Spectrum How color tells us about atoms

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Spectrum Spectrum- Range of wavelengths of E.R., wavelengths of visible light are separated when a beam of white light passes thru a prism Spectrum- Range of wavelengths of E.R., wavelengths of visible light are separated when a beam of white light passes thru a prism Example of Spectrum Example of Spectrum Rainbow (also a phenomenon) Rainbow (also a phenomenon) Each droplet of water acts as a prism to produce a spectrum Each droplet of water acts as a prism to produce a spectrum Each color blends into the next color. Each color blends into the next color.

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Colors of the Spectrum Colors of the Spectrum: Colors of the Spectrum: 1. Red (Longest Wavelength & Lowest Frequency) 2. Orange 3. Yellow 4. Green 5. Blue 6. Indigo 7. Violet (Shortest Wavelength & Highest Frequency) These colors are known as the visible part of the spectrum These colors are known as the visible part of the spectrum

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Prism White light is made up of all the colors of the visible spectrum. White light is made up of all the colors of the visible spectrum. Passing it through a prism separates it. Passing it through a prism separates it.

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Diffraction When light passes through, or reflects off, a series of thinly spaced line, it creates a rainbow effect When light passes through, or reflects off, a series of thinly spaced line, it creates a rainbow effect because the waves interfere with each other. because the waves interfere with each other.

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A wave moves toward a slit.

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Comes out as a curve

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with two holes

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Two Curves

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with two holes Interfere with each other

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Two Curves with two holes Interfere with each other crests add up

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Several waves

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Several Curves

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Several waves Interference Pattern Several Curves

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Spectroscopic analysis of the visible spectrum… …produces all of the colors in a continuous spectrum

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If the light is not white By heating a gas with electricity we can get it to give off colors. By heating a gas with electricity we can get it to give off colors. Passing this light through a prism does something different. Passing this light through a prism does something different. More on that Later More on that Later

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Quantum Concept Laws of Physics state no limits on how much or how little energy can be gained or lost. Laws of Physics state no limits on how much or how little energy can be gained or lost. Classic physics assumed atoms and molecules could emit any arbitrary amount of radiant energy. Classic physics assumed atoms and molecules could emit any arbitrary amount of radiant energy. Does not explain the Emission Spectrum of Atoms Does not explain the Emission Spectrum of Atoms

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Max Plank Tried to explain why the body changed colors as it heated. Tried to explain why the body changed colors as it heated. He could only explain the change if assumed energy of the body changes in small discrete units (brick by brick). He could only explain the change if assumed energy of the body changes in small discrete units (brick by brick). Plank showed mathematically that the amount of radiant energy, absorbed or emitted by a body is proportional to the frequency of radiation Plank showed mathematically that the amount of radiant energy, absorbed or emitted by a body is proportional to the frequency of radiation

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Plank’s Quantum Concept Plank went against classic physics Plank went against classic physics Stated: atoms and molecules could emit energy only is discrete quantities, like small packages or bundles Stated: atoms and molecules could emit energy only is discrete quantities, like small packages or bundles Quantum- smallest quantity of energy that can be emitted in the form of E.R. Quantum- smallest quantity of energy that can be emitted in the form of E.R. The energy of a single quantum is given by E = hν The energy of a single quantum is given by E = hν

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Planck’s Quantum Theory Cont. According to theory, energy is always emitted in multiples of hν. According to theory, energy is always emitted in multiples of hν. Example: 2hv, 3hv, ect….. Example: 2hv, 3hv, ect….. Never in 1.67hv and so on Never in 1.67hv and so on Could not explain why energies are fixed but explained the emission of solids over the entire range or wavelengths. Could not explain why energies are fixed but explained the emission of solids over the entire range or wavelengths.

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Energy and frequency E = h x n E = h x n E is the energy of the photon E is the energy of the photon n is the frequency n is the frequency h is Planck’s constant h is Planck’s constant h = 6.6262 x 10 -34 Joules sec. h = 6.6262 x 10 -34 Joules sec. joule is the metric unit of Energy joule is the metric unit of Energy

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Examples What is the wavelength of blue light with a frequency of 8.3 x 10 15 hz? What is the wavelength of blue light with a frequency of 8.3 x 10 15 hz? What is the frequency of red light with a wavelength of 4.2 x 10 -5 m? What is the frequency of red light with a wavelength of 4.2 x 10 -5 m? What is the energy of a photon of each of the above? What is the energy of a photon of each of the above?

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Solving for photons Calculate the energy of: Calculate the energy of: A) photon with a wavelength 5.00 x 10 4 nm (infrared region) A) photon with a wavelength 5.00 x 10 4 nm (infrared region) B) photon with a wavelength of 5.00 x 10 2 nm (X ray region) B) photon with a wavelength of 5.00 x 10 2 nm (X ray region)

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Einstein and Photoelectric Effect 5 years later Einstein used Planck’s theory to derive the Photoelectric Effect 5 years later Einstein used Planck’s theory to derive the Photoelectric Effect Photoelectric Effect- a phenomenon in which electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency Photoelectric Effect- a phenomenon in which electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency Threshold Frequency Threshold Frequency

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Photoelectric Effect Number of electrons ejected was proportional to the intensity (brightness) of the light, but the energies of the electrons were not. Number of electrons ejected was proportional to the intensity (brightness) of the light, but the energies of the electrons were not. Below the threshold frequency no electrons were ejected no matter how intense the light. Below the threshold frequency no electrons were ejected no matter how intense the light. Could not be explained by the wave theory of light. Could not be explained by the wave theory of light.

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Photoelectric cont. Einstein proposed: Einstein proposed: That a beam of light is really a stream of particles. That a beam of light is really a stream of particles. Particles of light are now called Photons. Particles of light are now called Photons. Used Planck’s equation to determine: Used Planck’s equation to determine: Electrons are held in a metal surface by attractive forces, and removing them from the metal requires light of a sufficiently high frequency ( which corresponds to sufficiently high energy) to break them free. Electrons are held in a metal surface by attractive forces, and removing them from the metal requires light of a sufficiently high frequency ( which corresponds to sufficiently high energy) to break them free.

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Shining a beam of light onto a metal surface can be though as shooting a beam of particles/photons at the metal atoms. Shining a beam of light onto a metal surface can be though as shooting a beam of particles/photons at the metal atoms. Frequency of photons = binding energy, then light will have just enough energy to knock them free Frequency of photons = binding energy, then light will have just enough energy to knock them free What if the frequency is higher? What if the frequency is higher?

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Photoelectric cont. If frequency is stronger they will acquire some K.E. and be knocked loose. If frequency is stronger they will acquire some K.E. and be knocked loose. KE = hv – BE KE = hv – BE Shows more energetic the photon, greater the K.E. of the ejected electron. Shows more energetic the photon, greater the K.E. of the ejected electron.

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Wave-Particle Duality JJ Thomson won the Nobel prize for describing the electron as a particle. His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron. The electron is a particle! The electron is an energy wave!

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Light is a Particle Energy is quantized. Energy is quantized. Light is energy Light is energy Light must be quantized Light must be quantized These smallest pieces of light are called photons. These smallest pieces of light are called photons. Energy and frequency are directly related. Energy and frequency are directly related.

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Energy Change The size of an emitted or absorbed Quantum depends on the size of the energy change. The size of an emitted or absorbed Quantum depends on the size of the energy change. Ex. Ex. A. Small energy change involves emission or absorption of low frequency radiation. B. Large energy change involves emission or absorption of high frequency radiation.

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The Math in Chapter 12 Only 2 equations Only 2 equations c = ln c = ln E = hn E = hn Plug and chug. Plug and chug.

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An explanation of Atomic Spectra

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Atomic Spectrum Each element gives off its own characteristic colors. Each element gives off its own characteristic colors. Can be used to identify the atom. Can be used to identify the atom. How we know what stars are made of. How we know what stars are made of.

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Atomic Emission Spectrum Atomic Emission Spectrum- it passes light emitted by an element thru a prism Atomic Emission Spectrum- it passes light emitted by an element thru a prism Atoms first absorb energy and then lose energy as they emit light Atoms first absorb energy and then lose energy as they emit light Each line in the emission spectrum corresponds to one exact frequency of light being given off or emitted by an atom. Each line in the emission spectrum corresponds to one exact frequency of light being given off or emitted by an atom. The light emitted by an electron moving from a higher to lower energy level has a frequency directly proportional to the energy change of the electron The light emitted by an electron moving from a higher to lower energy level has a frequency directly proportional to the energy change of the electron Therefore each line corresponds to one exact amount of energy being emitted. Therefore each line corresponds to one exact amount of energy being emitted. Emission Spectrum of each element is unique to that element. Emission Spectrum of each element is unique to that element. The emission spectrum is obtained by an instrument called Emission Spectrograph The emission spectrum is obtained by an instrument called Emission Spectrograph

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These are called discontinuous spectra Or line spectra unique to each element. These are emission spectra The light is emitted given off.

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Where the electron starts When we write electron configurations we are writing the lowest energy. When we write electron configurations we are writing the lowest energy. The energy level and electron starts from is called its ground state. The energy level and electron starts from is called its ground state. If the energy levels are quantized, it takes Quantum Energy ( E = h n) to raise an electron from ground state to excited state. If the energy levels are quantized, it takes Quantum Energy ( E = h n) to raise an electron from ground state to excited state. Same amount of energy is emitted as a photon when the electron drops from the excited state to the ground state. Same amount of energy is emitted as a photon when the electron drops from the excited state to the ground state. Only electrons in transition from higher to lower energy levels lose energy and emit light. Only electrons in transition from higher to lower energy levels lose energy and emit light.

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Electron transitions involve jumps of definite amounts of energy. Electron transitions involve jumps of definite amounts of energy. This produces bands of light with definite wavelenghts This produces bands of light with definite wavelenghts

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Emission Spectrum of Hydrogen Transition Wavelength l (nm) Transition Wavelength l (nm) n = ¥ to n = 2 361 n = 7 to n = 2 396 n = 6 to n = 2 409 n = 5 to n = 2 433 n = ¥ to n = 2 361 n = 7 to n = 2 396 n = 6 to n = 2 409 n = 5 to n = 2 433 n = 4 to n = 2 485 n = 3 to n = 2 655 n = 4 to n = 2 485 n = 3 to n = 2 655

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Changing the energy Let’s look at a hydrogen atom Let’s look at a hydrogen atom

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Changing the energy Heat or electricity or light can move the electron up energy levels Heat or electricity or light can move the electron up energy levels

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Changing the energy As the electron falls back to ground state it gives the energy back as light As the electron falls back to ground state it gives the energy back as light

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May fall down in steps May fall down in steps Each with a different energy Each with a different energy Changing the energy

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{ { {

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Further they fall, more energy, higher frequency. Further they fall, more energy, higher frequency. This is simplified This is simplified the orbitals also have different energies inside energy levels the orbitals also have different energies inside energy levels All the electrons can move around. All the electrons can move around. Ultraviolet Visible Infrared

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We are worried about the change When the electron moves from one energy level to another. When the electron moves from one energy level to another. E = E final - E initial E = -2.178 x 10 -18 J Z 2 (1/ n f 2 - 1/ n i 2 ) Rydberg’s constant and it allowed the calculation of the wavelengths of all the spectral lines of hydrogen. Rydberg’s constant and it allowed the calculation of the wavelengths of all the spectral lines of hydrogen.

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Calculating Energy Problems What is the energy of the photon emitted when the electron in a hydrogen atom drops from the energy level n=5 to following: What is the energy of the photon emitted when the electron in a hydrogen atom drops from the energy level n=5 to following: A) n=2 A) n=2 B) n=3 B) n=3

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More Energy Problems How much energy must a hydrogen atom absorb to raise its electron from the energy level n=1 to the following: How much energy must a hydrogen atom absorb to raise its electron from the energy level n=1 to the following: A) n=2 A) n=2 B) n=4 B) n=4

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Positive or Negative When raising an electron the amount of energy is always positive. Why? When raising an electron the amount of energy is always positive. Why? When an electron drops the amount of energy is always negative. Why? When an electron drops the amount of energy is always negative. Why?

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Calculating Wavelength of Photon First determine ∆E First determine ∆E Then plug into: Then plug into: λ= c h / ∆E λ= c h / ∆E What is the wavelength (in nm) of a photon emitted during a transition from n i = 6 to n f = 4 What is the wavelength (in nm) of a photon emitted during a transition from n i = 6 to n f = 4

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What is light Light is a particle - it comes in chunks. Light is a particle - it comes in chunks. Light is a wave- we can measure its wave length and it behaves as a wave Light is a wave- we can measure its wave length and it behaves as a wave If we combine E=mc 2, c= ln, E = 1/2 mv 2 and E = h n If we combine E=mc 2, c= ln, E = 1/2 mv 2 and E = h n We can get l = h/mv We can get l = h/mv The wavelength of a particle. The wavelength of a particle.

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Matter is a Wave Does not apply to large objects Does not apply to large objects Things bigger that an atom Things bigger that an atom A baseball has a wavelength of about 10 - 32 m when moving 30 m/s A baseball has a wavelength of about 10 - 32 m when moving 30 m/s An electron at the same speed has a wavelength of 10 - 3 cm An electron at the same speed has a wavelength of 10 - 3 cm Big enough to measure. Big enough to measure.

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Calculating Wavelength of a Particle 1) Calculate the wavelength of a particle in: 1) Calculate the wavelength of a particle in: A) The fastest serve in tennis is about 140 miles per hour, or 63 m/s. Calculate the wavelength associated with a 6.0 x 10 -2 kg tennis ball traveling at this speed. What color would be produced? A) The fastest serve in tennis is about 140 miles per hour, or 63 m/s. Calculate the wavelength associated with a 6.0 x 10 -2 kg tennis ball traveling at this speed. What color would be produced?

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B) Calculate the wavelength associated with an electron (9.1094 x 10 -31 kg) moving at 63 m/s B) Calculate the wavelength associated with an electron (9.1094 x 10 -31 kg) moving at 63 m/s Which color would be produced? Which color would be produced?

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The Wave-like Electron Louis deBroglie The electron propagates through space as an energy wave. To understand the atom, one must understand the behavior of electromagnetic waves.

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The physics of the very small Quantum mechanics explains how the very small behaves. Quantum mechanics explains how the very small behaves. Classic physics is what you get when you add up the effects of millions of packages. Classic physics is what you get when you add up the effects of millions of packages. Quantum mechanics is based on probability because Quantum mechanics is based on probability because

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More obvious with the very small To measure where a electron is, we use light. To measure where a electron is, we use light. But the light moves the electron But the light moves the electron And hitting the electron changes the frequency of the light. And hitting the electron changes the frequency of the light.

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Moving Electron Photon Before Electron Changes velocity Photon changes wavelength After

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“One cannot simultaneously determine both the position and momentum of an electron.” “One cannot simultaneously determine both the position and momentum of an electron.”

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Heisenberg Uncertainty Principle It is impossible to know exactly the position and velocity (momentum) of a particle. It is impossible to know exactly the position and velocity (momentum) of a particle. The better we know one, the less we know the other. The better we know one, the less we know the other. The act of measuring changes the properties. The act of measuring changes the properties. More precisely the velocity is measured, less precise is the position (vice versa). More precisely the velocity is measured, less precise is the position (vice versa).

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