1、Chapter 33 To 35 Quantum Physics,Plancks Quantum Hypothesis The Photoelectric Effect Compton Effect Wave Nature of Matter Heisenberg Uncertainty Principle Schrdingers Equation Hydrogen Atom,33-1 Plancks Quantum Hypothesis (P763),Black-body Radiation:,One of the observations that was unexplained at t
2、he end of the 19th century was the spectrum of light emitted by hot objects.,A we known that all objects emit radiation whose total intensity is proportional to the fourth power of the Kelvin temperature.,The rate at which an object emits energy via electromagnetic radiation depends on the objects s
3、urface area A and the temperature T of that area in Kelvins and is given by,This is called the Stefan-Boltzmann equation, and is a universal (Stefan-Boltzmann)constant,The factor e, called the emissivity（发射率）of the objects surface, is a value between 0 and 1 that is characteristic of the material.,A
4、 surface the maximum emissivity of 1.0 is said to be a blackbody radiator.,A blackbody (绝对黑体) is a body that would absorb all the radiation falling on it (在任何温度下对任何入射辐射能都全部吸收而不反射的物体).,Two important theoretical curves on blackbody based on classical idears were those proposed by W.Wien (in 1896) and
5、by Rayleigh-Jeans (in 1900).,Neither Wiens nor Rayleigh-Jeans formulations were in accord with experiment.,Wiens was accurate at short wavelenths but deviated from exp. At longer ones, whereas the reverse was true for the Rayleigh-Jeans theory.,A cloud covered in fair skies of physics (物理学晴朗天空中的一朵乌云
6、)!,“紫外灾难”,The break came in late 1900 when Max Planck (1858-1947) proposed an empirical formula (经验式) that nicely fit the date:,- Planck constant,Rubens proved by experiments that it fit with experimental curve in whole wavelength region.,M. Planck Germany (18581947),Planck then sought a theoredical
7、 basis for the formula by making a new and radical assumption:,The energy of any molecular vibration could be only some whole number multiple of hf,-quantum of energy 能量子,Energy would not be a continuous quantity as had been believed for centuries; rather it is quantized it exists only in discrete a
8、mount.,h = 6.6310-34 Js,Plancks Quantum Hypothesis (P765),E=n n=1,2,3., = h f,“Quantum” means “discrete amount” as opposed to “continuous”.,This is the first time that the quantum concept was proposed in physics history. Later, the day of December 14, 1900 was called the birthday of quantum theory.,
9、Planck got the first Nobel Physics Prize in 1918 for his radical innovation (根本的改革, 创新).,普朗克量子假设与经典理论不相容，是一个革命性的概念，打破几百年来人们奉行的自然界连续变化的看法，圆满地解释了热辐射现象，并成为现代量子理论的开端，带来物理学的一次巨大变革。,33-2 The Photoelectric Effect 光电效应 (P765),The photoelectric effect:,1. Experimental apparatus,Henrich Hertz proposed in 1887
10、 first, the charged particles was proved as electrons later.,Photoelectric effect is the phenomenon that when light shines on a metal surface, electrons are emitted from the surface.,光照射某些金属时能从表面释放出电子的效应.这时逸出的电子称为光电子.,(1) The numbers of electrons in unit time emited from C proportional to the intens
11、ity of incident light (饱和光电流与入射光强成正比).,2. Experimental results,(2) Adjusting the V, there exists a stopping potential Vstop截止电压, at which the reading of meter “A” has just dropped to zero no electrons have sufficient kinetic energy to reach collector C.,Then Kmax, the maximum kinetic energy of the e
12、mitted electrons (光电子的最大初动能) can be determined using conservation of energy:,Measurements show that: the maximum kinetic energy of these electrons Kmax is linearly increased with the frequency of incident light.,For light of a given frequency, Kmax does not depend on the intensity of the light sourc
13、e (与入射光强无关).,(3) Varying the frequency f of the incident light and measure the associated stopping potential Vstop.,The cutoff wavelength:,There exist cutoff frequency f0 (红限频率,入射光频率大于f0) below which no photoelectric effect occur no matter how intense the incident light is.,(4) The electrons are eje
14、cted instantaneously (光子打出光电子是瞬时发生的).,l0 = c/f0,The Einsteins photoelectric equation:,If the electron is to escape from the target, it must pick up energy at least equal to W0. Any additional energy (hf W0) that the electron acquires from the photon appears as kinetic energy K of the electron.,Einst
15、ein summed up the experimental results as:,where W0 is the work function (逸出功).,电子吸收一个光子的能量 = 电子的最大初动能 + 逸出功,In 19131914, carefully experiments were carried out by R.A.Millikan. The results were fully in agreement with Einsteins particle theory.,If the frequency f is less than the cutoff frequency f
16、0, where hf0 = W0, no electrons will be ejected at all, no matter how great the intensity.,Look at examples 33-3 to 33-5 from P767 to 768.,One other aspect of the photoelectric also confirmed the photon theory.,Example:,Solution:,Show that, for light of wavelength in nanometers, the photon energy hf
17、 in electron-volts is 1240/ ,For blue light, = 450nm, as the example 33-3, the energy of photon is:,Example 33-5 of P768:,Solution:,What is the Kmax and speed of an electron ejected from a sodium surface whose W0=2.28eV when illuminated by light of wavelength: (a) 410nm; (b) 550nm.,(b),No electrons
18、are ejected.,Applications of the photoelectric effect:,Besides playing an important historical role in confirming the photo theory of light, it also has many practical applications.,光电控制的路灯系统,Optical sound track on movie film; automatic door opener making use of the photocell circuit,33-3 Photons an
19、d Compton Effect (P769),在散射X射线中除有与入射波长相同的射线外，还有波长比入射波长更长的射线,这种现象称为康普顿效应.,The scattered light had a slightly longer than did the incident light by an amount Dl, which is increase as the scattering angle increase Compton shift.,Compton scattered short wavelength light (X-rays) from various materials.,
20、The scattered light had a slightly longer than did the incident light by an amount Dl, which is increase as the scattering angle increase. It is called the Compton shift.,When light pass through materials, electrons in it will be forced vibration. The frequency of vibration should be same with incid
21、ent light, and radiate electromagnetic wave with the same frequency to all directions.,By colliding photon transfers “part” of energy to electron, then Epho , so the frequency of scattered X-rays, then wavelength .,Compton shift,incoming photon scattered photon+electron,The shift of wavelength is on
22、ly depends on the scattering angle of X-ray.,where c=h/(m0c),=2.4310-12 m=2.43 pm,is the Compton wavelength of electron (电子的Compton波长) which is accord well with Exp. m0 is rest mass of electron.,Look at example 33-7 in P770!,(1) The peak centered about the incident wave-length arises from interactio
23、ns between X-rays and the electrons that are tightly bound to the carbon atoms making up the target 波长不变的散射光来自光子与整个原子（内层电子）的碰撞.,Explanations:,(2) The peak centered about the longer wave-length arises from interactions between X-rays and the very loosely bound electrons in the target (波长变长的散射光来自光子与原子
24、外层电子的碰撞).,(3) Compton effect is pronounced enough to be observed if and c are comparable, so does X-ray (只有当入射波长与c可比拟时，康普顿效应才显著,因此要用X射线才能观察到)., = h f,p = E/c = h f / c = h/,Example:,Assume that photon in X-ray of wavelength =1.0010-10 m collide elastically with free electron. The scattering angle of
25、 X-ray =90. Find: what is (a) the compton shift =? (b) the kinetic energy gotten by recoiling (反冲) electron ?,(b) The kinetic energy gotten by electron K is what photon losses, so,=4.7110-17 J =295 eV,Different effect of photon interactions (P771):,1. The photon can be scattered from an electron ( o
26、r a nucleus) and in the process lose some energy and its f will be lower Compton effect (当光子与原子中的自由电子或弱束缚电子弹性碰撞时发生康普顿效应).,2. A photon may knock an electron out of an atom and in the process itself disappear (光子与原子中束缚电子发生完全非弹性碰撞时，光子被电子吸收) photo-electric effect.,4. A photon can actually create matter,
27、 such as the production of an electron and a position. This process is called pair production (正负电子偶).,光与物质的相互作用时可能会发生若干种不同的效应: 有光电效应、康普顿效应,还产生正负电子偶,它们是不同能量的光子与原子、电子、原子核相互作用的结果。,3. A photon may knock an atomic electron to a higher energy state in the atom in the process photon disappears, and all it
28、s energy is given to the atom. (Such an atom is in a excited state. ),Why cant we think of a moving electronor any other particle, for that matteras a matter wave that transfers energy and momentum to other matter at points?,In 1924 French physicist Louis de Broglie (18921986 extended the idea of th
29、e wave-particle duality of light and made following appeal to symmetry:,Light-wave have particle nature, then does matter has wave nature?,He suggested that a particle of matter with E and p has wave nature (能量为E,动量为p的实物粒子同时具有波动性).,matter wave (de Broglie wave), de Broglie wavelength,Let electron is
30、 accelerated by voltage of 100V(设电子动能由100V电压加速产生), then, A crystal can be used as a type of diffraction of grating as was done for X-ray (P773-4)!,How to proof it?,=1.225,It also showed that proton, neutral and other particles have wave properties.,Comparing with a bullet of m=0.01kg, v=300m/s:,Macr
31、oscopic particles has larger m, so 0，the wave-nature can not be shown (宏观物体表现不出波动性,只表现出粒子性).,De Broglies prediction of the existence of matter waves was first verified experimentally in 1927, by C. J. Davisson and L. H. Germer and by G. P. Thomson later.,The principle of complementarity（互补性 P772):,T
32、hese two aspects of light complement one another.,The great Danish physicist Niles Bohr(18851962) proposed his famous principle of complementarity.,It states that to understand any given experiment, we must use either the wave or photon theory, but not both.,微观粒子在某些条件下表现出粒子性，在另一些条件下表现出波动性，而两种性质虽寓于同一
33、体中，却不能同时明显地表现出来.,We cannot picture a combination of wave and particle. Instead, we must recognize that the two aspects of light are different “faces” that light shows to experiments.,The idea that electrons have wave properties led to the development of electron microscope (显微镜) by German physicist
34、E. Ruska (1906-) in 1932,A scanning electron microscope has been further developed later, which produces images with 3D quality.,which can produce images much greater magnification than a light microscope (resolution can reach 0.2nm).,De Broglie got the Norbel Prize of physics of 1929.,33-5 The Hydr
35、ogen Atom,The idea that matter is made up of atoms was accepted by most scientists by 1900. With the discovery of the electron in the 1890s, scientists began to think of the atom itself as having a structure and electrons as part of that structure.,Early models of the atom (P775):,J. J. Thomson, soo
36、n after his discovery of electrons in 1897, visualized a typical model of the atom in 1903 as a homogeneous sphere of positive charge inside of which there were tiny negative charged electrons.,Thomsons apparatus for measuring the ratio of mass to charge for the electron.,Around 1911, E. Rutherford
37、(18711937) and his colleagues performed experiments whose results contradicted Thomsons model of the atom., 粒子实验存在大角散射,The results based on the Rutherfords “planetary” model is accord well with the one from scattering of particle.,Two main difficulties of “planetary” model:,(2) It predicts that ligh
38、t of a continuous range of frequencies will be emitted, whereas experiment shows line spectra (原子光谱的谱线).,(1) It predicts that atoms are unstable electrons should quickly spiral into the nucleus but we know that atoms in general are stable, since the matter around us is stable;,Rutherfords “planetary
39、” model of the atom was a major step toward how we view the atom today. It wasnt a complete model and showed some major problems, as we shall see.,Atomic spectra key to the structure of atom:,Heated solids, liquids and dense gases emit light, due to oscillations of atoms and molecules.,A. J. ngstrm
40、(Swedish瑞典人) observed the red line of hydrogen line spectrum in the visible region in 1853.,The emission spectrum (发射光谱) is characteristic of the material and can serve as a type of “fingerprint” for identification of the gas.,In 1885, J. J. Balmer showed that the four visible lines in hydrogen spec
41、trum fit following formula:,R = 1.0974 107 m-1 Rydberg constant 里德伯常量,The radiation from excited gases showed that the spectrum was not continuous, but discrete.,This Balmer series of lines also extended into the UV region , ending at l =365nm corresponding to n=.,Later experiments on hydrogen showe
42、d that there were similar series of lines (谱线系) which had a pattern just like the Balmer series , but at different wavelength.,Lyman series 莱曼系:,(in the UV region),Paschen series帕邢系:,(in the IR region),Rutherfords model needs to be modified. It was Neils Bohr who provided it by adding an essential i
43、dea the quantum hypothesis.,The series limit for Balmer, Lyman and Paschen is different. Eg. The series limit for Balmer series represents a transition 2.,Bohrs theory of the Hydrogen atom (P778):,Electrons move about the nucleus in circular orbits, but only certain orbits (stationary state ) are al
44、lowed.,An electron in each orbit would have a definite energy and would move in the orbit without radiating energy 电子绕核作圆周运动，某些轨道有确定的能量（不辐射能量）称为定态 .,In heated solids, the energy of oscillating electric charges must change discontinuouslyfrom one discrete energy state to another, with the emission of
45、 a quantum of light.,The electrons angular momentum L is quantized and equal to an integer n times h/2.,n: quantum number of orbit.,When an electron jumps from state Eu to state El , a single photon of light (frequency f ) is imitted,Discussion:,(1) The circular orbit of radius of electron in a hydr
46、ogen atom (氢原子中电子的圆轨道半径):,The force between proton and electron:,Based on N-II law,From quantum condition:,The smallest orbit is for n=1 (第一玻尔轨道半径),An electron can exist only in the orbits above. There are no allowable orbits in between.,(2) The speed of electron on the circular orbit of radius rn,(
47、3) The energy-formular of hydrogen atom when electrons move on the orbit of quantum number n,Bohrs model of atom gave us a first picture of what an atom is like. It proposed an explanation for why there should be emission and absorption of light by atoms at discrete wavelength.,The electron in a hyd
48、rogen atom tends to be in the lowest energy level in its ground state.,We see that not only are the orbit radii quantized, but so is the energy. The quantum number n that labels the orbit radii also labels the energy levels.,For n = 1,由能级算出的光谱线频率和实验结果完全一致,Bohr theory predicts well ionization energy
49、13.6eV for hydrogen, but was not so successful for others.,Fig.33-25 of P782,According to de Broglie, a particle of mass m moving with a nonrelativistic speed v would have,He proposed: Each electron orbit in an atom is a standing wave. To form constructive interference, persist, the circumference of a Bohr orbit of radius rn should be 2 rn as Fig., so,This is the quantum condition proposed by Bohr.,This implies that the wave-particle duality is at the root of atomic structure.,
