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近代科學發展 近代物理學發展 To understand a science it is necessary to know its history. ----AUGUST COMTE Content Class I: 歷史 & 相對性原理 Class II: Quantum Theory(量子論) Class III: Statistic Physics(統計物理) Class IV: Semiconductor Theory(半導體) Class V: Atomic Physics(原子物理) Class VI: Elementary Particles and Modern Cosmology(基本粒子與近代天文 學) History -1 1895為古典物理與近代物理分界點. 1895以前, 人們以為: 重力, 電, 磁等已被 全然了解. 1895以後, 其他的作用力如核力與若作用 力陸續被發現. Classical Physics of the 1890s Scientists could easily access political leader. Basic research was recognized helpful. Scientists felt that given enough time and resources, they could explain just about anything. They didn’t clearly understand the structure of matter. Classical Physics of the 1890s Classical ideas of physics: Conservation of Energy Conservation of Linear Momentum Conservation of Angular Momentum Conservation of Charge These conservation laws are reflected in the laws of mechanics, electromagnetism, and thermodynamics. Classical Physics of the 1890s Electricity and magnetism had been combined by the great James Clerk Maxwell (1831-1879) in his four equations. Optics had been shown by Maxwell, among others, to be a special case of electromagnetism. Waves were believed an important component of nature. Mechanics The laws of mechanics were developed over hundreds of years by many researchers, most astronomers. Galileo (1564-1642) may be called the first great experimenter. His experiments ad observations laid the groundwork for the important discoveries to follow during the next two hundred years. Mechanics Isaac Newton (1642-1727) was certainly the greatest scientist of his name and one the best the world has ever seen. His discoveries were in the fields of mathematics, astronomy, and physics and include gravitation, optics, motion, and forces. He also spent considerable time on alchemy and theology. Mechanics He clearly understood the relationships among position, displacement, velocity, and acceleration. He understood how motion was possible and that a body at rest was just a special case of a body having constant velocity. Newton was able to carefully elucidate the relationship between forces and acceleration. Mechanics -Newton’s laws Newton’s first law An object in motion with a constant velocity will continue in motion unless acted upon by some net external forces. Mechanics -Newton’s laws Newton’s second law The acceleration of a body is proportional to the net external force and inversely propostional to the mass of the body. F ma or dp F dt Mechanics -Newton’s laws Newton’s third law The force exerted by body 1 on body 2 is equal to and opposite to thehat body 2 exerts on body 1. F21 F12 Electromagnetism Electromagnetism developed over a period of several hundred years. Important contributions were made by Coulomb(1736-1806), Oersted(17771851), Young(1773-1829), Ampere(17751836), Faraday (1791-1867), Henry (1797-1878), Maxwell (1831-1879), and Hertz (1857-1894). Electromagnetism Maxwell showed that electricity and magnetism were intimately connected and were related by a change in the inertial frame of reference. His work also led to the understanding of electromagnetic radiation, of which light and optics are special cases. Maxwell’s four equation, together with the Lorentz force law, explain much of electromagnetism. James Clerk Maxwell 1831 – 1879 Developed the electromagnetic theory of light Developed the kinetic theory of gases Explained the nature of color vision Explained the nature of Saturn’s rings Died of cancer Electromagnetism Gauss’s law for electricity Gauss’s law for magnetism Faraday’s law Generalized Ampere’s law q E d A 0 B d A 0 d B E d s dt d E B d s 0 0 dt 0 I F qE qv B Conduction Current, cont. Ampère’s Law in this form is valid only if the conduction current is continuous in space In the example, the conduction current passes through only S1 This leads to a contradiction in Ampère’s Law which needs to be resolved Ampère’s Law, General – Example The electric flux through S2 is EA S2 is the gray circle A is the area of the capacitor plates E is the electric field between the plates If q is the charge on the plates, then Id = dq/dt This is equal to the conduction current through S1 Plane em Waves We will assume that the vectors for the electric and magnetic fields in an em wave have a specific space-time behavior that is consistent with Maxwell’s equations Assume an em wave that travels in the x direction with the electric field in the y direction and the magnetic field in the z direction Thermodynamics Thermodynamics deals with temperature T, heat Q, work W, and the internal energy of systems U. The understanding of the concepts used in thermodynamics: pressure P, volume V, temperature T, thermal equilibrium, heat, entropy, and energy, was slow in coming. Important contributions to thermodynamics were made by Benjamin Thompson (17531814), Carnot (1796-1832), Joule (18181889), Clausius (1822-1888), and Lord Kelvin (1824-1907). The Laws of Thermodynamics First law of thermodynamics: The change in the internal energy of a system U is equal to the heat Q added to the system minus the work W done by the system. U Q W The Laws of Thermodynamics Second law of thermodynamics: It is not possible to convert heat completely into work without some other change taking place. ( 要將熱完全轉變成功而沒有任 何損耗是不可能的) The Laws of Thermodynamics Zeroth law of thermodynamics: 如果有兩個熱力學系統分別與第三個熱力學系 統進行熱接觸而達到熱平衡,則此兩個熱力學 系統必定達成熱平衡。 Zeroth Law of Thermodynamics, Example Object C (thermometer) is placed in contact with A until it they achieve thermal equilibrium Object C is then placed in contact with object B until they achieve thermal equilibrium The reading on C is recorded The reading on C is recorded again If the two readings are the same, A and B are also in thermal equilibrium Temperature 溫度可視為物質的一種性質可用來決 定它是否與其他物體已達成熱平衡 兩物體若達成熱平衡必定具有相同的 溫度 The Laws of Thermodynamics Third law of thermodynamics: 要達到絕對零度是不可能的 Energy at Absolute Zero 根據古典物理分子的動能在絕對零度時必定為 零 因此分子必定都躺在箱子底部 量子論指出在絕對零度時仍有殘餘的能量– 此 能量稱為零點能量 The kinetic Theory of Gases 分子動力論以粒子觀點來探討熱力學現象. Irist chemist Robert Boyle (1627-1681) : (the Boyle’s law) 定溫時氣體的體積與壓 力的乘積保持定值 PV constant The kinetic Theory of Gases The French physicist Charles (17461823) (the Charle’s law) 在定壓下氣體的 體積與溫度的比值保持定值: V / T constant Idea Gas Equation Combining the Boyle’s law and the Charle’s law: PV nRT Ideal Gas – Details A collection of atoms or molecules that Move randomly Exert no long-range forces on one another Are so small that they occupy a negligible fraction of the volume of their container Ideal Gas Law The equation of state for an ideal gas combines and summarizes the other gas laws PV = n R T This is known as the ideal gas law R is a constant, called the Universal Gas Constant R = 8.314 J/ mol K = 0.08214 L atm/mol K From this, you can determine that 1 mole of any gas at atmospheric pressure and at 0o C is 22.4 L Avogadro law In 1811 the Italian physicist Avogadro (1776-1856) proposed that equal volume of gases at the same temperature and pressure contained equal numbers of molecules. This hypothesis was so far ahead of its time that it was not accepted for many years. Bernoulli Daniel Bernoulli (1700-1782) apparently originated the kinetic theory of gases in 1738, but his result was generally ignored. Development Many scientists, including Newton, Laplace, Davy, Herapath, and Waterston, had contributed to the development of kinetic theory by 1850. By 1895, the kinetic theory of gases was widely accepted. The statistical interpretation of thermodynamics was made in the latter half of the nineteenth century by the great Scottish mathematical physicist Maxwell, the Austrian physicist Ludwig Boltzmann (1844-1906), and the american physicist Williard Gibbs (1839-1903). Ludwid Boltzmann 1844 – 1906 Contributions to Kinetic theory of gases Electromagnetism Thermodynamics Work in kinetic theory led to the branch of physics called statistical mechanics Ideal Gas Notes An ideal gas is often pictured as consisting of single atoms However, the behavior of molecular gases approximate that of ideal gases quite well Molecular rotations and vibrations have no effect, on average, on the motions considered Pressure and Kinetic Energy Assume a container is a cube Edges are length d Look at the motion of the molecule in terms of its velocity components Look at its momentum and the average force Pressure and Kinetic Energy, 2 Assume perfectly elastic collisions with the walls of the container The relationship between the pressure and the molecular kinetic energy comes from momentum and Newton’s Laws Pressure and Kinetic Energy, 3 The relationship is 2 N 1 ___2 P mv 3 V 2 This tells us that pressure is proportional to the number of molecules per unit volume (N/V) and to the average translational kinetic energy of the molecules A Molecular Interpretation of Temperature We can take the pressure as it relates to the kinetic energy and compare it to the pressure from the equation of state for an idea gas 2 N 1 ___2 P mv NkBT 3 V 2 Therefore, the temperature is a direct measure of the average translational molecular kinetic energy A Microscopic Description of Temperature, cont Simplifying the equation relating temperature and kinetic energy gives 1 ___2 3 mv kBT 2 2 This can be applied to each direction, 1 ___2 1 mv x kBT 2 2 with similar expressions for vy and vz A Microscopic Description of Temperature, final Each translational degree of freedom contributes an equal amount to the energy of the gas In general, a degree of freedom refers to an independent means by which a molecule can possess energy A generalization of this result is called the theorem of equipartition of energy (能量均分原理) Theorem of Equipartition of Energy The theorem states that the energy of a system in thermal equilibrium is equally divided among all degrees of freedom Each degree of freedom contributes ½ kBT per molecule to the energy of the system Total Kinetic Energy The total translational kinetic energy is just N times the kinetic energy of each molecule Etotal 1 ___2 3 3 N mv NkBT nRT 2 2 2 This tells us that the total translational kinetic energy of a system of molecules is proportional to the absolute temperature of the system Monatomic Gas For a monatomic gas, translational kinetic energy is the only type of energy the particles of the gas can have Therefore, the total energy is the internal energy: 3 Eint n RT 2 For polyatomic molecules, additional forms of energy storage are available, but the proportionality between Eint and T remains Distribution of Molecular Speeds The observed speed distribution of gas molecules in thermal equilibrium is shown NV is called the Maxwell-Boltzmann distribution function Distribution Function The fundamental expression that describes the distribution of speeds in N gas molecules is 3 mo 2 2 mv 2 2kBT NV 4 N v e 2 kBT mo is the mass of a gas molecule, kB is Boltzmann’s constant and T is the absolute temperature Average and Most Probable Speeds The average speed is somewhat lower than the rms speed 8kBT kBT v 1.60 mo mo The most probable speed, vmp is the speed at which the distribution curve reaches a peak 2k T kT v mp B mo 1.41 B mo Root Mean Square Speed The root mean square (rms) speed is the square root of the average of the squares of the speeds Square, average, take the square root Solving for vrms we find v rms ___ 2 3 kBT 3 RT v m M M is the molar mass in kg/mole Some Example vrms Values At a given temperature, lighter molecules move faster, on the average, than heavier molecules Speed Distribution The peak shifts to the right as T increases This shows that the average speed increases with increasing temperature The width of the curve increases with temperature The asymmetric shape occurs because the lowest possible Waves and Particles Many aspects of physics can be treated as if the bodies are simply particles, without internal structure. Many natural phenomena can be explained only in terms of waves, which are traveling disturbances that carry energy. Waves and particles were the subject of disagreement as early as the seventeenth century, where there were two competing theories of the nature of light. Waves and Particles Newton supported the idea that light consisted of corpuscles (particles). He performed extensive experiments on light for many years, and finally published his book Opticks in 1704. Geometrical optics uses straight-line, particlelike trajectories called rays to explain familiar phenomena like reflection and refraction. Geometrical optics was also able to explain the apparent observation of sharp shadows. Waves and Particles Dutch physicist Christiaan Huygens (1629-1695) presented his theory in 1678 befroe publishing in 1690. The wave theory could also explain reflection and refraction, but it could not explain the sharp shadows. Diffraction Pattern, Penny The shadow of a penny displays bright and dark rings of a diffraction pattern The bright center spot is called the Arago bright spot Named for its discoverer, Dominque Arago Diffraction Pattern, Penny, cont The Arago bright spot is explained by the wave theory of light Waves that diffract on the edges of the penny all travel the same distance to the center The center is a point of constructive interference and therefore a bright spot Geometric optics does not predict the presence of the bright spot The penny should screen the center of the pattern The Nature of Light Before the beginning of the nineteenth century, light was considered to be a stream of particles The particles were emitted by the object being viewed, Newton was the chief architect of the particle theory of light He believed the particles left the object and stimulated the sense of sight upon entering the eyes Nature of Light – Alternative View Christian Huygens argued the light might be some sort of a wave motion Thomas Young (1801) provided the first clear demonstration of the wave nature of light He showed that light rays interfere with each other Such behavior could not be explained by particles More Confirmation of Wave Nature During the nineteenth century, other developments led to the general acceptance of the wave theory of light Maxwell asserted that light was a form of high-frequency electromagnetic wave Hertz confirmed Maxwell’s predictions Heinrich Rudolf Hertz 1857 – 1894 Greatest discovery was radio waves 1887 Showed the radio waves obeyed wave phenomena Died of blood poisoning Hertz’s Experiment An induction coil is connected to a transmitter The transmitter consists of two spherical electrodes separated by a narrow gap Particle Nature Some experiments could not be explained by the wave nature of light The photoelectric effect was a major phenomenon not explained by waves When light strikes a metal surface, electrons are sometimes ejected from the surface The kinetic energy of the ejected electron is independent of the frequency of the light Dual Nature of Light In view of these developments, light must be regarded as having a dual nature In some cases, light acts like a wave, and in others, it acts like a particle Properties of EM Waves The solutions of Maxwell’s are wave-like, with both E and B satisfying a wave equation Electromagnetic waves travel at the 1 speed of light c oo This comes from the solution of Maxwell’s equations Two Clouds on the Horizon Blackbody Radiation Electromagnetic Medium Two Clouds on the Horizon Blackbody Radiation An object at any temperature is known to emit thermal radiation Characteristics depend on the temperature and surface properties The thermal radiation consists of a continuous distribution of wavelengths from all portions of the em spectrum Blackbody Radiation, cont At room temperature, the wavelengths of the thermal radiation are mainly in the infrared region As the surface temperature increases, the wavelength changes It will glow red and eventually white The basic problem was in understanding the observed distribution in the radiation emitted by a black body Classical physics didn’t adequately describe the observed distribution Blackbody Radiation, final A black body is an ideal system that absorbs all radiation incident on it The electromagnetic radiation emitted by a black body is called blackbody radiation Blackbody Approximation A good approximation of a black body is a small hole leading to the inside of a hollow object The nature of the radiation leaving the cavity through the hole depends only on the temperature of the cavity walls Blackbody Experiment Results The total power of the emitted radiation increases with temperature Stefan’s Law P = s A e T4 For a blackbody, e = 1 The peak of the wavelength distribution shifts to shorter wavelengths as the temperature increases Wien’s displacement law lmax T = 2.898 x 10-3 m.K Stefan’s Law – Details P = s Ae T4 P is the power s is the Stefan-Boltzmann constant s = 5.670 x 10-8 W / m2 . K4 Was studied in Chapter 17 Wien’s Displacement Law lmax T = 2.898 x 10-3 m.K lmax is the wavelength at which the curve peaks T is the absolute temperature The wavelength is inversely proportional to the absolute temperature As the temperature increases, the peak is “displaced” to shorter wavelengths Intensity of Blackbody Radiation, Summary The intensity increases with increasing temperature The amount of radiation emitted increases with increasing temperature The area under the curve The peak wavelength decreases with increasing temperature Ultraviolet Catastrophe At short wavelengths, there was a major disagreement between classical theory and experimental results for black body radiation This mismatch became known as the ultraviolet catastrophe You would have infinite energy as the wavelength approaches zero Max Planck 1858 – 1947 He introduced the concept of “quantum of action” In 1918 he was awarded the Nobel Prize for the discovery of the quantized nature of energy Planck’s Theory of Blackbody Radiation In 1900, Planck developed a structural model for blackbody radiation that leads to an equation in agreement with the experimental results He assumed the cavity radiation came from atomic oscillations in the cavity walls Planck made two assumptions about the nature of the oscillators in the cavity walls Planck’s Assumption, 1 The energy of an oscillator can have only certain discrete values En En = n h ƒ n is a positive integer called the quantum number h is Planck’s constant ƒ is the frequency of oscillation This says the energy is quantized Each discrete energy value corresponds to a different quantum state Planck’s Assumption, 2 The oscillators emit or absorb energy only in discrete units They do this when making a transition from one quantum state to another The entire energy difference between the initial and final states in the transition is emitted or absorbed as a single quantum of radiation An oscillator emits or absorbs energy only when it changes quantum states Energy-Level Diagram An energy-level diagram shows the quantized energy levels and allowed transitions Energy is on the vertical axis Horizontal lines represent the allowed energy levels The double-headed arrows indicate allowed transitions More discoveries Discovery of X rays: Roentgen (1845-1923) in 1895 Discovery of radioactivity: Henri Becquerel (1852-1908) in 1896 Discovery of electron: Michael Faraday in 1833; J.J. Thomson (1856-1940) in 1897 Discovery of the Zeeman effect: Pieter Zeeman (1865-1943) in 1896 found that spectra lines were separated into two or three lines when placed in magnetic field. Problems bring the beginning of modern physics The problems existing in 1895 and the important doscoveries of 1895-1897 bring us to the subject: modern physics. In 1900 Max Palnck completed his radiation law, which solved the blackbody problem bu required that energy be quantized. In 1905 Einstein presented his three important papers on Brownian motion, the photoelectric effect, and special relativity.