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1、IntroductionAlthough the Greek philosopher Democritus had postulated the existence of atoms in the first century BC and Daltons atomic theory of 1807 laid the basis for the existence of atoms before the turn of the twentieth century. Indeed, at that time an influential school of German physicists le

2、d by Ernst Mach considered the atomic model to be merely a useful picture with no basis in reality.1.1 THE EXISTENCE OF ATOMSThe situation was dramatically changed by an explosion of experimental investigation over the fifteen years between 1897 and 1912. in the 1870s, technical improvements in the

3、construction of vacuum pumps had made possible the investigation of electrical phenomenon in evacuated tubes and the discovery of invisible rays which traveled between an electrically negative electrode (cathode) and an electrically positive electrode (anode) in such a tube.These rays came to be kno

4、wn as cathode rays. At first there was considerable controversy over their nature, but a series of experiments carried out by J.J. Thomson in 1897 demonstrated conclusively that the cathode rays consisted of a stream of negatively charged particles, presumably emitted by atoms in the cathode (Fig. 1

5、.1).Thomsons measurements of the deflection of the rays by electric and magnetic fields enabled the speed of the particles to be measured and also the ratio of the charge of a particle to its mass. By the turn of the century, the charge-mass radio of these particles, which came to be called electron

6、s, could be measured to quite high precision.However, to give absolute values of the charge and mass, experiments of a different type were required. The most successful were investigations where macroscopic particles such as oil droplets were charged in some way and their motion in electric fields o

7、bserved. A relatively straightforward measurement of the mass of the oil droplets enabled the charge of the charge of the electron to be measured. The famous experiments carried out by Millikan between 1909 and 1916 gave a value for this charge as 1.592±.002×10-19 coulomb, less than 1 perc

8、ent lower than that accepted today. This, combined with Thomsons results, gave a value for the electrons mass of approximately 9×10-31 kg.Fig. 1.1 Schematic diagram of J.J. Thomsons cathode ray tube Electrons emitted by the cathode are accelerated through the anode. The beam of electrons hits t

9、he phosphorescent screen, producing a luminous spot.The measurement of electric charge made possible a direct measurement of atomic masses. Back in 1830, Faraday had carried out experiments on electrolysis. He had used his results to suggest that if matter were atomic, then electricity should also b

10、e atomic, but the converse is also true. The flow of electric current between two metallic plates in an electrolyte results in a measurable in increase in the mass of one electrode. The mass of metal deposited per unit charge flowing can be measured. Assuming that the motion of atoms between electro

11、des in due to the fact that each atom in the electrolyte carries a specified number of excess electrons, the mass of a single atom can be calculated.The investigation of cathode ray tubes produced another important line of experimentation. In 1895 Röntgen had discovered that cathode rays imping

12、ing on glass or metal produced a new type of ray the X-ray. These rays were shown to have wave-like properties and in 1899 their wavelength was estimated by the Dutch physicists Haga and Wind to be of the order of 10-10m, using diffraction at a v-shaped slit. In 1906 Marx demonstrated that the speed

13、 of the waves was equal to that of light to within experimental error, and it became generally accepted that X-rays were electromagnetic radiation like light, but with much shorter wavelengths.In 1912 Laue in Germany and Bragg in England demonstrated the diffraction of X-rays by the regular pattern

14、of atoms in a crystal lattice. These diffraction patterns gave the first direct evidence of the existence of atoms and of their sizes. An example is shown in Fig. 1.2.Fig. 1.2 Laue diffraction pattern caused by the diffraction of X-rays by the regular lattice of atoms in rock salt.In 1897, Rutherfor

15、d had found that pieces of the naturally occurring element uranium emitted two types of ray which were termed rays and rays. Both could be deflected by electric and magnetic fields and were therefore presumed to consist of charge particles. The particles were found to have the same charge and mass a

16、s cathode ray electrons, so were assumed to be electrons. The rays, on the other hand, were considerably more massive. Measurements of their charge and mass suggested that they consisted of helium atoms from which two electrons had been removed. This was confirmed by Rutherford and Royds in 1909, wh

17、o fired rays into a sealed and evacuated vessel and showed that helium accumulated in it. The evidence was conclusive that an particle consisted of a helium atom from which two electrons had been removed.This experiment also confirmed suggestions about the physical meaning of the atomic number Z. Th

18、is number had been introduced to define the order of elements in the periodic table. Hydrogen had Z=1, helium Z=2and so on. The identification of particles with helium atoms suggested that Z defined the number of electrons in a particular atom.By 1912, therefore, direct evidence existed on the mass

19、of individual atoms and the size of these atoms. Even more interestingly, the electron appeared to be a constituent of atom, suggesting some internal structure.1.2 THE SIZE OF ATOMSTurning from the historical development of the subject, it is worthwhile to sum up the measurement of atomic masses and

20、 dimensions.As mentioned above, direct measurement of atomic masses can be made using electrolysis. A typical electrolysis cell might consist of two copper electrodes immersed in a bath of copper sulphate (Fig. 1.3). A potential difference between the electrodes causes a current to flow an the depos

21、ition of copper on the cathode.Fig. 1.3 Electrolytic cell. The anode and cathode are immersed in an electrolyte such as copper sulphate solution. Positively charged copper ions are attracted to the cathode and are deposited there.Several assumptions have to be made. First, it is assumed that in solu

22、tion the copper sulphate crystals split up, giving free atoms of copper and that these free atoms have an excess positive charge. Second, using chemical knowledge that copper is reasonable extrapolation from the chemical valence theory, if it is assumed that chemical bonds result from the exchange o

23、f electrons, and that the lightest atom, hydrogen, has only a single electron to exchange. A copper atom in this state is referred to as being doubly ionized, Cu+. A final assumption is that all copper ions attracted to the cathode stick to it and gain further electrons to become electrically neutra

24、l again. The experiment then consists of driving a known quantity of electricity through the cell and measuring the increase in mass of the cathode.Experiments can be carried out with different elements and results confirm the atomic theory and the theory of valence. Most interesting for our discuss

25、 is the calculation of the mass of an atom of hydrogen, the lightest element. This turns out to be 1.67×10-27 kg, approximately 1800 times that of an electron.Knowing atomic masses, and the density of materials, it is straightforward to obtain values for atomic dimensions. The only problem is t

26、hat unless the atoms in a sample of material are arranged in a regular pattern, the answer is not very meaningful. For crystalline substances, X-ray diffraction enable the arrangement of atoms to be discovered. The dimensions of the crystal structure can then be calculated.Fig. 1.4 A single cell of

27、the simple cubic lattice of sodium chloride. The lattice is held together by the attraction between the positively charged sodium ion and the negatively charged chlorine ion.For example, crystals of rock salt (sodium chloride, NaCl) are found to have a cubic structure, with sodium and chlorine ions

28、on alternate corners (Fig. 1.4). If M is the kilogram molecular weight of NaCl and the density of the crystal, the volume of one kg-molecule is There are 2N atoms is one kg-molecule, where N is Avogadros number. Therefore the distance between the centres of atoms, d is given by:For sodium chloride,

29、this works out as 2.8×10-10m and similar results are obtained for other crystals.Of course, such calculations only tell us the distance between the centres of the atoms and hence the maximum possible size for an atom. To go further, it is necessary to investigate the structure of the atom itsel

30、f.2.3 THE NUCLEAR MODEL OF THE ATOMFig. 2.2 Classical models of the atom. (a) Thomsons model. Small, negatively charged electrons are held in a dense, positively charged body. (b) Rutherfords model. The vast majority of the mass and all the positive charge are concentrated in a relatively tiny nucle

31、us, surrounded by electrons. In both pictures the size of the electrons and of the nucleus are exaggerated. The nucleus should be at least 1000 times smaller and the electrons many times smaller again.In order to explain the result, Rutherford proposed a new model in which all the positive charge an

32、d most of the mass of the atom resided in a central nucleus, surrounded by electrons orbiting in free space. The size of the nucleus would be small compared with the size of the atom (Fig. 2.2(b). This model would give a qualitative explanation for Geiger and Marsdens results as most of the particle

33、s would pass through the atom without encountering any matter, but a very few would collide with the massive nucleus. However, much more importantly, this model gives a precise quantitative agreement between theory and experiment.Because of the seminal nature of this model, it is worthwhile looking

34、at Rutherfords analysis in detail. Only classical of physics is required .Fig 2.3 Path of particle (charge +2e) in the field of the nucleus (charge +Ze). The nucleus is at the origin and is very much more massive than the particle. The force F is due to electrostatic repulsion.The analysis of the sc

35、attering experiment falls into two parts. First, it it necessary to obtain an expression for the deflection of a single particle as a function of its kinetic energy and its trajectory relative to the nucleus. The particle and the nucleus are assumed to be very small, and the nucleus is assumed to ha

36、ve a positive charge Ze where e is the electronic charge and Z the atomic number. The particle has a charge of +2e and the force between it and the nucleus is given by Coulombs law. Figure 2.3 shows through situation, with the nucleus situated at the origin. The particle starts far enough away from

37、the nucleus for the interaction force to be negligible and travels parallel to the -axis. An important parameter of the motion is the impact parameter, b, which defines the minimum distance between the nucleus and the particle if the particle were mot deflected. Electrostatic repulsion means that th

38、e particle is deflected through an angle and it is obvious that the smaller the value of b, the greater is the value of . It is now possible to work out a value for in terms of b and the kinetic energy of the particle T. Since the mass of the nucleus is much greater than that of the particle, the ki

39、netic energy and hence the speed of the particle before and after deflection remains the same. However the particles direction of motion has changed and the law of conservation of momentum gives an expression for the absolute value of the change in momentum (Fig.2.4) (2.1)Where m is the mass of the

40、particle, and its speed.From Newtons second law,this change of momentum must be equal to the force acting on the particle, integrated over the whole time that the particle is in the field of the nucleus. Therefore, (2.2)Figure 2.3shows the direction of F a particular position of the particle, define

41、d by through angle , as shown, by symmetry, it can be seen that the integral in (2.2) is given by (since the integral of the component parallel to the -axis, F sin, must be zero, by symmetry ).Fig 2.4 Change in momentum of an particle during interaction with through nucleus.A change of variables for

42、 integration enables (2.2) to be rewritten: (2.3)(see Fig 2.3 for the changed limits of integration).Finally, (dt/d) is equal to 1/ where is the angular speed of the particle about the origin. Since the force acting on the particle is radial, the angular momentum of the particle is the same for any

43、value of , and must be given by the equation Therefore Coulombs law gives so that substituting in (2.3) and integrating through right hand side gives an expression for in terms of and b (2.4)or, in terms of the kinetic energy T of the particle (2.5)This gives an equation for the scattering angle in

44、terms of the kinetic energy and impact parameter of the particle and of the charge on the nucleus, Ze.介绍 虽然希腊哲学家德谟克利特曾推测了在公元前一世纪原子的存在和道尔顿的原子理论1807年奠定了原子的存在,在20世纪之交以前。事实上,当时一所有影响力的学校的领导德国物理学家马赫认为原子模型仅仅是一个没有现实的基础上有用的图片。 1.1原子的存在 这种情况戏剧性的改变由超过1897年和1912年之间15年的实验研究。在19世纪70年代,在真空泵施工技术的改进已使制造电极管和无形射线的发现成为

45、可能,电极管是一电负电极(阴极)和电正极(阳极)组成的。 这些射线后来被称为阴极射线。起初,曾经有过很大的争议的性质,而由汤姆孙在1897年一系列实验得出结论表明,该阴极射线是一个大概在阴极(图1.1)原子发射带负电荷的粒子流组成。 汤姆森对由电场和磁场的阴极射线偏转的测量由粒子的速度来衡量,也是一个粒子的电荷比质量。到了世纪之交,这些粒子,被称为电子,可以测量到相当高的精度。 然而,在不同的实验需要我们的荷质比绝对的值。实验最成功的是,油滴被控以某种方式及其在电力领域的宏观粒子的运动情况。油滴质量相对简单的测量启用了电子电荷来衡量。著名的实验由密立根在1909年和1916年间被做出,并且发表

46、了测量结果为1.592 ± 0.002×10-19库仑,和今天接受的实验结果相比不到百分之一的误差。这与汤姆逊的结果相结合,给出了一个电子的约9 × 10-31千克。电荷的测量使得成为可能原子电荷直接测量成为可能。早在1830年,法拉第进行了电解实验。他用自己的结果表明,如果电流是由于原子,那么带电也应原子,但反过来也是如此。电流在两个金属板之间的电解质中流动产生一个可衡量电极质量增加的结果。单位大规模的金属沉积量可以测量的。假设原子在电极之间的原因在于电解液中的每个原子带有指定数量的的电量,那么单个原子质量可以计算出来的。图 1.1 汤姆逊电子发射阴极射线管的示

47、意图阴极是通过阳极加速的示意图。对电子束打荧光屏,产生光点。阴极射线管的衍生了另一个重要实验。 1895年伦琴发现了阴极射线撞击在玻璃或金属产生了一个新型的射线 - X射线。这些射线波被证明具有波浪般的性质和他们的波长是在1899年由荷兰物理学家估计Haga和风能使用V形缝衍射测量出来的为10 - 10米。 1906年马克思证明,波速度等同于光实验误差之内,成为普遍接受了X -射线像光电磁辐射,但具有更短的波长。 在1912年,德国劳厄和英国布拉格证明了原子晶格X -射线衍射。这些衍射图给出了第一个原子的存在和它们的大小直接证据。一个例子如图 1.2。 图 1.2在盐原子晶格由X射线衍射造成的

48、劳厄衍射图案。1897年,卢瑟福发现,在天然铀元素释放两件射线其中称为射线和射线类型。双方可以通过偏转电场和磁场,因此推定为带电粒子组成。 粒子的发现具有相同电荷的阴极射线和电子的质量,因此被认为是电子。在另一方面,射线有相当多的巨大的质量。他们的电荷和质量表明,他们是氦的被拆掉两个电子组成。这在1909年卢瑟福和罗伊兹被证实了,是由开成一个密封的容器并表明它积累的氦。证据是确凿的,一个粒子由一个氦原子被拆掉两个电子组成。这个实验也证实有关的原子序数Z的物理意义,这个数字已经提出来定义周期表中元素的顺序。氢有Z=1和氦Z=2等等。对粒子与氦原子的鉴定表明,Z也表示一个特定原子的电子数。到191

49、2年,对个别原子的质量存在的直接证据以及这些原子大小。更有趣的是,电子似乎是一个原子的组成部分,这表明原子存在一些内部结构。1.2原子的大小转到历史发展的主体,值得总结的原子质量和尺寸测量。如上所述,原子质量的直接测量,可使用电解。一个典型的电解槽包括两个铜在硫酸铜(图1.3)浴浸泡电极。电极之间的电位差会导致电流,流在阴极上的一些铜的沉积。图 1.3 电解槽。阳极和阴极浸泡在电解液中如硫酸铜溶液。带正电的铜离子被吸引到阴极,并都沉积在这里。几种假设要作出。首先,这是假设在溶液中硫酸铜晶体的分裂铜原子,这些自由原子有一个多余的正电荷。第二,利用化学知识,铜的化学价是从理论的合理推断,如果假定,从化学键的电子交换的

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