If classical physics is wrong, why do we still use it?

Transcription

1 If classical physics is wrong, why do we still use it? Introduction The word quantum came from the Latin word which means "how great" or "how much." In quantum mechanics, it refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest. The discovery that waves have discrete energy packets (called quanta) that behave in a manner similar to particles led to the branch of physics that deals with atomic and subatomic systems which we today call quantum mechanics. The foundations of quantum mechanics were established during the first half of the twentieth century by Werner Heisenburg, Max Planck, Louis de Broglie, Albert Einstein, Niels Bohr, Erwin Schrodinger, Max Born, Neumann, Paul Dirac, Wolfgang Pauli and others. Some fundamental aspects of the theory are still actively studied. Quantum mechanics is essential to understand the behavior of systems at atomic length scales and smaller. For example, if Newtonian mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus, making stable atoms impossible. However, in the natural world the electrons normally remain in an unknown orbital path around the nucleus, defying classical electromagnetism. Quantum theory provides us with the rules and regulations of the miniature world. The conceptual foundation of quantum theory is mysterious. It led to intense debates among scientists, and confused many. Niels Bohr, one of the most prominent scientists in this domain, once remarked, 'You have not studied quantum mechanics well if you aren't confused by it.' Albert Einstein, the greatest physicist of the 20th century, never approved of this theory. Bizarre though it may seem, quantum physics has led physicists step by step to a deeper view of the reality, and has answered many fundamental questions. Material prepared by: < Physics faculty > Topic No: < 1 > Page 1 of 10

2 Over three hundred years ago, Sir Isaac Newton revolutionised the study of the natural world by putting forth laws of nature that were stated in mathematical form for the first time. Newton's book, The Mathematical Principles of Natural Philosophy forever changed how scholars would study the physical world. Newton's formulation of physical laws was so powerful that his equations are still in use today. By the start of the 20th century, physicists had worked with Newton's laws so thoroughly that some of them thought that they were coming to the end of physics. In their opinion, not much was left to do to make physics a complete system. Little did they know that the world they described was soon to be understood in a completely different way. The quantum revolution was about to happen. This revolution was begun by a very unlikely person, a physicist named Max Planck, who was very conservative in all his views. It speaks well of Planck's intellectual honesty that he was able to accept the reality of what he discovered, even though he found the consequences of his discoveries distasteful and unpleasant for the rest of his life. Learning Objectives On completion of this session you will be able to: 1. Understand the dual nature of electromagnetic radiation. 2. Understand Planck s quantum theory of black body radiation. 3. Derive Wien s radiation law and Rayleigh-Jean s law from Planck s law. The wave-particle duality of light and matter In 1690 Christiaan Huygens theorized that light was composed of waves, while in 1704 Isaac Newton explained that light was made of tiny particles. Experiments supported each of their theories. However, neither a completely-particle theory nor a completely-wave theory could explain all of the phenomena associated with light! So scientists began to think of light as both a particle and a wave. In 1923 Louis de Broglie hypothesized that a material particle could also exhibit wavelike properties, Material prepared by: < Physics faculty > Topic No: < 1 > Page 2 of 10

3 and in 1927 it was shown (by Davisson and Germer) that electrons can indeed behave like waves. How can something be both a particle and a wave at the same time? For one thing, it is incorrect to think of light as a stream of particles moving up and down in a wavelike manner. Actually, light and matter exist as particles; what behaves like a wave is the probability of where that particle will be. The reason light sometimes appears to act as a wave is because we are noticing the accumulation of many of the light particles distributed over the probabilities of where each particle could be. Planck s quantum theory of black body radiation Planck was investigating the properties of heat and light-emitting bodies. Classical physics had theories which predicted that the brightness of a body increases continuously as the frequency of its electromagnetic radiation is increased. Unfortunately, experiments revealed a totally different picture. The brightness did increase initially, but only upto a limit. Then, actually, it began to fall. We thus get a bell-shaped curve if we plot frequency against brightness. Intensity vs. Frequency Plot Material prepared by: < Physics faculty > Topic No: < 1 > Page 3 of 10

4 Besides, another observation was made: as bodies become hotter, their maximum brightness shifts towards higher frequencies. This is why an object, heated to C, emits mostly infra-red or heat waves. As the temperature is increased, the object appears to be red, then orange, and finally white or even blue. Classical theories totally failed to explain this discrepancy between the known facts and the observations. Then, in the winter of 1900, Max Planck found a solution to this problem. Planck ushered in the quantum era by making a bizarre assumption: Emission and absorption of energy can occur only in discrete amounts This might seem totally unsurprising to you, but believe me, it shook the scientists of that period. Planck himself did not know he would end up with this statement! It was a completely unexpected discovery, and yet it was only the beginning of what would come later. Planck called these discrete lumps as quanta. This was against the entire world-view that had been built from the beginning. And so the quantum revolution began. Black body At a particular temperature the black body would emit the maximum amount of energy possible for that temperature. It would emit at every wavelength of light as it must be able to absorb every wavelength to be sure of absorbing all incoming radiation. The maximum wavelength emitted by a black body radiator is infinite. It also emits a definite amount of energy at each wavelength for a particular temperature, so standard black body radiation curves can be drawn for each temperature, showing the energy radiated at each wavelength. Material prepared by: < Physics faculty > Topic No: < 1 > Page 4 of 10

5 Black body radiation curves showing peak wavelengths at various temperatures This graph shows how the black body radiation curves change at various temperatures. These all have their peak wavelengths in the infra-red part of the spectrum. At a given temperature, the energy is not uniformly distributed in the spectrum. At a given temperature, the intensity of radiation is maximum at a particular wavelength λ m. As temperature increases, λ m decreases. For all wavelengths, increase in temperature causes an increase in the energy emission. Material prepared by: < Physics faculty > Topic No: < 1 > Page 5 of 10

6 As temperature increases, the total energy emitted increases, because the total area under the curve increases. Deduction of Wien s radiation law and Rayleigh-Jean s law from Planck s law. WIEN'S LAW λ m T = constant (1) λ m = Peak Wavelength (m) T = Surface Temperature (K) Constant = x 10-3 mk This rearranges to λ m = x 10-3 / T This rearranged equation shows why the peak wavelength decreases as temperature increases. This decrease in wavelength explains why objects glow first red, then orange-red, then yellow, then even blue. These colours are successive decreases in wavelength. STEFAN'S LAW (2) P = Power radiated in W (J/s) σ = Stefan's Constant 5.67 x 10-8 W m -2 K -4 A = Surface area of body (m²) T = Temperature of body (K) Therefore the power radiated is proportional to T 4 for an identical body which explains why the area under the black body curves (the total energy) increases so much for a relatively small increase in temperature. RAYLEIGH-JEANS LAW The energy distribution in the thermal spectrum is given by Material prepared by: < Physics faculty > Topic No: < 1 > Page 6 of 10

7 E λ = 8πkT / λ 4 where k is the Boltzmann Constant. This law holds good in the region of longer wavelengths. PLANCK ENERGY DISTRIBUTION FORMULA E λ = 8πhc / λ 5 [exp (hע/kt) - 1]. (3) E λ = energy distribution in the spectrum. h = Planck's constant (6.626 x Js) c = Speed of Light (3 x 10 8 m/s) λ = Wavelength (m) k = Boltzmann Constant (1.38 x J/K) T = Temperature (K) This complex looking formula is used to plot the black body curves for each temperature by working out the power emitted at each wavelength. (a) For shorter wavelengths exp (hע/kt) is greater than or equal to 1. Equation (3) reduces to E λ = 8πhcλ -5 exp (-hע/kt). (4) This represents the Wien s radiation law. (b) For longer wavelengths, hע/kt is small. Equation (3) reduces to E λ = 8πkT / λ 4 This represents Rayleigh-Jeans law. Material prepared by: < Physics faculty > Topic No: < 1 > Page 7 of 10

8 Comparison of the classical Rayleigh-Jeans Law and the quantum Planck formula Thus Planck s formula for the energy distribution is in agreement for the entire wavelength region. Check your understanding 1. Choose the right answer from the options given below: Who proposed in his 1923 doctoral thesis that all matter and radiation have both particle-and wavelike characteristics. a. Louis-Victor de Broglie b. Werner Heisenburg c. Albert Einstein 2. State if the following statement is true or false? Material prepared by: < Physics faculty > Topic No: < 1 > Page 8 of 10

9 Emission and absorption of energy can occur only in discrete amounts. a) True b) False 3. Fill in the blank with the right answer. As bodies become hotter, their maximum brightness shifts towards frequencies. Check the correct answers on page _10_. Summary On completion of this chapter you have learned: Quantum mechanics is important for understanding how individual atoms combine covalently to form chemicals or molecules. The dual nature (wave and particle nature) of electromagnetic radiation. Planck s quantum theory of black body radiation and its success over the classical theories. To derive Wien s radiation law and Rayleigh-Jean s law from Planck s law. Activity 1. After studying the topic, derive Planck s law of black body radiation. Material prepared by: < Physics faculty > Topic No: < 1 > Page 9 of 10

10 Suggested Reading 1. Engineering Physics by P.K. Palanisamy. 2. Quantum Physics by Jim Branson. Answers to CYU. 1. a 2. a 3. Higher Material prepared by: < Physics faculty > Topic No: < 1 > Page 10 of 10