Unit 3 Part 1: Quantum Physics. introduce the idea of quanta as a new way of looking at light and sub atomic physical behaviour

Transcription

1 In this lesson you will Unit 3 Part 1: Quantum Physics consider and list some of the properties of light and sub atomic particles that were at odds with the classical wave theory of electromagnetic radiation introduce the idea of quanta as a new way of looking at light and sub atomic physical behaviour define photon write Planck's equation and describe the terms in it use Planck's equation to do numerical exercises May 10 10:14 PM 1

2 Section 1: Light and the Electromagnetic Spectrum (Read Chapter 10) A: What is light? In what ways can light be produced? Sources of Light 1. Incandescent If something is hot enough it will glow. For example, the filament of the screw in light bulb in the ceiling and the element on your electric stove when the control button is on maximum. In both of these cases electrical energy makes the material so hot that light is given off. We say that the electrons of the material become so "excited" that they give off some of their energy as light. The proper name for this type of light that is caused by high temperature is incandescent light. Two other obvious ones are fire and the sun. 2. Fluorescent Have you seen the pinkish red glow from a neon light? In this case, one type of radiation (moving electrons ) is causing the material (the neon gas) to give off another type of radiation. The electricity passing through the neon gas excites the gas atoms to give off the characteristic red glow. The gas emits light only as long as it is being stimulated by the original energy source (the electricity). Light produced in this way is called fluorescent light. The neon gas is called a fluorescent source. The most common fluorescent source is the long, white fluorescent light bulbs that you see in school and in office buildings. These operate by a two step process: mercury vapour in the tube gives off ultra violet rays when electricity passes through it. This ultra violet radiation strikes a special coating on the inside of the tube, causing the coating to fluoresce with its characteristic "white" light. When the switch is turned off, the fluorescing stops. May 10 10:19 PM 2

3 3. Phosphorescent Some materials continue to give off light even after the stimulating radiation stops. The most common example of such material is on the luminous hands of some watches and clocks. This material absorbs ordinary light during the day time and gives off a characteristic green glow afterwards. Such materials which continue to remain luminous, even alter the stimulating radiation has been turned off are called phosphorescent light sources. 4. Chemiluminescent Certain chemicals when mixed together produce a glow. Such chemicals are called chemiluminescent light sources. Some safety lamps use this feature. Sometimes chemical reactions within the bodies of living organisms produce a glow. Fireflies and certain fish produce light in this way. These are called bioluminescent light sources. B The Electromagnetic Spectrum Light can be thought of as travelling as electromagnetic waves. An electromagnetic wave is a transverse wave that has both electric and magnetic properties, hence the name. It is assumed that the electric part is vibrating at right angles to the magnetic part. Visible Light Spectrum With light waves, each different colour of visible light can be thought of as an electromagnetic wave with a certain frequency and wavelength. All of the colours of visible light together make up a continuous band of colours called the visible spectrum. Each colour has its own frequency and wavelength. Higher Wavelength Lower Wavelength (Longer waves) (shorter waves) Lower Frequency Higher Frequency Electromagnetic Spectrum The electromagnetic spectrum includes: radio waves produced and used by radio equipment microwaves used in cooking and radar visible light infrared responsible for much of the heating effects of the sun ultraviolet light responsible for sunburns x rays produced when high speed electrons are suddenly stopped gamma rays May 10 10:26 PM 3

4 Each type of radiation has its own frequency and wavelength. The Electromagnetic Spectrum includes all of the above forms of radiation. In the diagram that follows, note that: On the left of the spectrum, the wavelengths are very large (long waves) and thus the frequencies are very small. On the right of the spectrum, the wavelength are very small (short waves) and the frequencies are now very large. Even though the various components of the electromagnetic spectrum have different frequencies and wavelengths, they have one thing in common: They all travel at the same speed. We use "c" for the speed of light, or electromagnetic radiation in general: c = 3.00 x 10 8 m/s. Electromagnetic waves can travel through a vacuum such as space. May 10 10:37 PM 4

5 C Properties of Light (Read Chapter 10) We can never be really absolutely sure about the science of our times. At any time new discoveries may be made which will force us to re think certain theories to the point where they are modified or discarded altogether. The study of light is a very good example of this feature of the nature of science. Light is a form of energy. But how does light travel, and how is the energy of light carried from a source of energy, such as the sun. Energy can be carried from one place to another as energy of moving objects or particles (Kinetic Energy) and the energy of waves. In order for objects (particles) to have kinetic energy (and then be able to transfer it) they had to have a mass and velocity. Energy can also be conveyed over long distances in waves even though individual particles do not travel these distances. Newton and his supporters believed in the particle nature of light. Huygens and others proposed a wave nature. Some properties of light are listed below. For each property of light listed you must ask yourself these questions: Can the particle model explain this property? Can the wave model explain this property? Are both models equally good in explaining the properties? May 10 10:42 PM 5

6 Ask yourself the 3 questions above to determine which models they support: 1. Rectilinear propagation light travels in straight lines. (can be supported by the wave and particle theory of light) 2. Law of Reflection the angle made by the reflected beam equals the angle made by the incident beam. (can be supported by the wave and particle theory of light) 3. The inverse square law of intensity like sound, if the distance from a point source doubles, the intensity of light becomes one fourth of its original value. (supported by the wave theory) 4. Refraction the speed and direction of light change in materials of different optical density. When compared to the speed in air, the speed of light is smaller in transparent substances. (supported by wave theory. The particle theory gave a satisfactory explanation but it was later shown to be inaccurate.) 5. Beams of light can criss cross each other and not affect each other. (wave theory) 6. Dispersion the separation of white light into a band of colors. (wave and particle) 7. Partial reflection and partial refraction this may not be clear to you, so a ray box and glass block setup is shown below. Don't forget, in all light demonstrations it helps to have a darkened room. 8. Diffraction the bending of light around sharp obstacles or through tiny slits. (wave theory) May 10 10:45 PM 6

7 9. Interference resulting in alternating bright and dark lines, and also resulting in beautiful colored patterns when a film of oil or gasoline is viewed on the pavement or on water. Sometimes you see colors in the bubbles as you do the dishes. (wave theory) 10. The photoelectric effect when light of certain frequencies strikes certain metals, the electrons are "bounced" off the metal sort of like the cue ball striking the other balls on the pool table. The photoelectric effect is the most recently discovered property of all the properties listed on this page. Read about this discovery and the affect it had on our views of the nature of light. (particle theory) The Wave Particle Duality of Light Light is not a wave and it is not a particle; it is some kind of combination of the two that we cannot model or visualize. Physicists have come to the conclusion that this duality of light is a fact of life. It is referred to as the wave particle duality. This leads us to the modern quantum theory of light that sees light travel as an electromagnetic wave composed of particles called photons. May 10 10:51 PM 7

8 Section 2: Problems with the Classical Theory of Light The Quantum Idea to the Rescue Thus far, our study of physics has kept the ideas of matter and energy separate. We have learned that neither matter nor energy can be created or destroyed. We have also learned that they are very different phenomena. However, we need to consider what happen when matter and energy interact and if they are ever distinguishable. Quantum theory (quantum or wave mechanics) is the theory of how atoms, matter and energy interact. Introduction the problems In the late 1800's and early 1900's science was in a bit of turmoil as far energy at the molecular and atomic levels were concerned. There was no problem in dealing with energy of large objects, such as boulders falling, water waves crashing, and trains speeding along. But when it came to dealing with light energy and energy at the atomic and subatomic levels, all was not well. 1 According to the wave theory of light, the energy of a system can be of any value, but this phenomenon is not observed; the spectra of atoms and electrons have very specific and consistent energy values. (Sections 17.2 and 17.6 of text Blackbody Radiation and the Bohr Atom) For example, since a water wave with a large amplitude can do more damage than a water wave with a small amplitude, it seemed reasonable to apply this analogy to light and state that the energy of light depends on the amplitude of its wave, or its brightness. But, as you shall see later, this common sense extension did not work for light. May 10 10:59 PM 8

9 2 In some experiments, light exhibits particle like properties, such as momentum, a phenomenon that can t be explained in terms of the wave theory of light alone because a wave does not have mass. (Section and 17.4 of text Photoelectric Effect and Photon Momentum) The actual nature of light also became as issue. Because of the interference characteristic of light it seemed a certainty that light traveled in waves. But then around the turn of the 20th century, it was discovered that, in certain situations, when light hit certain materials, electrons were bounced out (something like a cue ball hitting a bunch of pool balls). In this situation light seemed to be acting as tiny balls or particles. So, here we have the particle wave controversy once again. 3 Electrons, protons, and neutrons are particles and therefore should not exhibit wave characteristics. Yet diffraction of all three types of particles was observed in laboratory experiments. (Section 17.5 and 17.7 of text DeBroglie and Matter Waves and Probability Waves) During this time of uncertainty an even weirder phenomenon was observed. Not only was light behaving like particles, but also streams of particles such as electrons, protons and neutrons were causing interference patterns. That is, these particles were observed to have wave characteristics! 4 If moving charged particles produce electromagnetic radiation, then electrons orbiting an atom should lose energy as they emit this radiation and fall into the nucleus, which does not occur. (Section 17.6 of text Bohr Atom.) Another puzzling event centered on the emission of light. The view was that light is emitted because electrons lose energy and fall back to lower orbits around the nucleus. That is, the lost energy comes out as light. This was bothersome because it seemed that electrons should therefore finally spiral into the nucleus. Everyone knew that this was not happening, but there was no theory to explain what was going on in the atom as light was emitted. May 10 11:03 PM 9

10 A way out In 1900 a few smart people like Max Planck and Albert Einstein said that maybe we were looking at energy the wrong way where atomic maers are concerned. A simple way to present their idea is shown in the picture below. On the ramp the box can have any amount of potential energy because it is everywhere on the ramp as it slides down. However, on the steps the box can have only 4 specific amounts of energy (if you count the very top and very bottom). In fact, it is possible for the box to become stuck at one energy level and stay there. In this analogy the box represents an electron orbiting the nucleus. As the electron "falls from one step to the another", a fixed or discrete amount of energy is lost (that is, emitted as light). Planck named these discrete amounts quanta. You should be able to see that Max Planck's idea of quanta satisfies very well the idea that sometimes the behaviour of light is more like traveling particles than traveling waves. Each quantum of energy that is emitted can be viewed as a tiny packet or particle of light. The scientific name for each tiny packet is photon. May 12 2:52 PM 10

11 A mathematical expression for a photon of energy Plank abandoned the idea that the amount of energy depends on the amplitude of the wave (as in water waves), and instead went with the revolutionary idea that the energy depends on the frequency of the wave! In fact, he stated that the emitted energy of one photon of light is directly proportional to the frequency associated with the wavelength of that light ( E α f). In that one sentence "Rev." Planck "married" the particle and wave nature of electromagnetic radiation. We can now say light has a dual nature: wave particle. Back to the mathematics: for one photon of light E α f. Insertion of a constant permits the writing of an equation: E = h f. You have probably guessed that h is called Planck's constant. Empirical (experimental) evidence tells us that h = 6.63 x J s. Sometimes the Greek letter gamma (γ) is used to represent one photon of energy: E γ = hf. Recall the general wave equation: v = f λ Solving for gives f = v/ λ, which for light becomes f = c/λ, where c is the speed of light. All of this means that E γ = hf can be written as E γ = h(c/λ). 1 electron volt or 1eV is the amount of energy an electron has after it has been accelerated through a potential difference of 1 V. 1eV = 1.6 x J. May 12 2:57 PM 11

12 Examples 1 Calculate the energy of a photon of blue light, λ = 450 nm. 2 What is the energy of a single photon of electromagnetic radiation from an FM station that is broadcasting at 99.1 MHz on your radio dial? 3 An FM station is broadcasting at 99.1 MHz with a power of 10,000 W. How many photons of electromagnetic energy are emitted in one second? May 12 3:01 PM 12

13 Practice: 1. Calculate the energy of a photon of violet light, λ = 410 nm. Express your answer in J and in ev. 2. Compare your answer in #1 with the answer for blue light in Practice exercise 1. What is the relationship between energy and wave length? 3. Calculate the number of photons emitted in 1 s by a 7.0 W red Christmas bulb, λ = 656 nm. 4. What is the energy range (in J and ev) of photons in the visible spectrum of wavelength 400 nm to 700 nm? May 12 3:02 PM 13

14 5. What is the wavelength and frequency of a photon that has energy of 2.9 ev? In your textbook: on p. 731 do #1 #5 on p. 732 do #25 May 12 3:04 PM 14

15 May 12 3:06 PM 15

16 May 12 3:06 PM 16