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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.介紹 雖然希臘哲學(xué)家德謨克利特曾推測(cè)了在公元前一世紀(jì)原子的存在和道爾頓的原子理論1807年奠定了原子的存在,在20世紀(jì)之交以前。事實(shí)上,當(dāng)時(shí)一所有影響力的學(xué)校的領(lǐng)導(dǎo)德國(guó)物理學(xué)家馬赫認(rèn)為原子模型僅僅是一個(gè)沒(méi)有現(xiàn)實(shí)的基礎(chǔ)上有用的圖片。 1.1原子的存在 這種情況戲劇性的改變由超過(guò)1897年和1912年之間15年的實(shí)驗(yàn)研究。在19世紀(jì)70年代,在真空泵施工技術(shù)的改進(jìn)已使制造電極管和無(wú)形射線的發(fā)現(xiàn)成為

45、可能,電極管是一電負(fù)電極(陰極)和電正極(陽(yáng)極)組成的。 這些射線后來(lái)被稱為陰極射線。起初,曾經(jīng)有過(guò)很大的爭(zhēng)議的性質(zhì),而由湯姆孫在1897年一系列實(shí)驗(yàn)得出結(jié)論表明,該陰極射線是一個(gè)大概在陰極(圖1.1)原子發(fā)射帶負(fù)電荷的粒子流組成。 湯姆森對(duì)由電場(chǎng)和磁場(chǎng)的陰極射線偏轉(zhuǎn)的測(cè)量由粒子的速度來(lái)衡量,也是一個(gè)粒子的電荷比質(zhì)量。到了世紀(jì)之交,這些粒子,被稱為電子,可以測(cè)量到相當(dāng)高的精度。 然而,在不同的實(shí)驗(yàn)需要我們的荷質(zhì)比絕對(duì)的值。實(shí)驗(yàn)最成功的是,油滴被控以某種方式及其在電力領(lǐng)域的宏觀粒子的運(yùn)動(dòng)情況。油滴質(zhì)量相對(duì)簡(jiǎn)單的測(cè)量啟用了電子電荷來(lái)衡量。著名的實(shí)驗(yàn)由密立根在1909年和1916年間被做出,并且發(fā)表

46、了測(cè)量結(jié)果為1.592 ± 0.002×10-19庫(kù)侖,和今天接受的實(shí)驗(yàn)結(jié)果相比不到百分之一的誤差。這與湯姆遜的結(jié)果相結(jié)合,給出了一個(gè)電子的約9 × 10-31千克。電荷的測(cè)量使得成為可能原子電荷直接測(cè)量成為可能。早在1830年,法拉第進(jìn)行了電解實(shí)驗(yàn)。他用自己的結(jié)果表明,如果電流是由于原子,那么帶電也應(yīng)原子,但反過(guò)來(lái)也是如此。電流在兩個(gè)金屬板之間的電解質(zhì)中流動(dòng)產(chǎn)生一個(gè)可衡量電極質(zhì)量增加的結(jié)果。單位大規(guī)模的金屬沉積量可以測(cè)量的。假設(shè)原子在電極之間的原因在于電解液中的每個(gè)原子帶有指定數(shù)量的的電量,那么單個(gè)原子質(zhì)量可以計(jì)算出來(lái)的。圖 1.1 湯姆遜電子發(fā)射陰極射線管的示

47、意圖陰極是通過(guò)陽(yáng)極加速的示意圖。對(duì)電子束打熒光屏,產(chǎn)生光點(diǎn)。陰極射線管的衍生了另一個(gè)重要實(shí)驗(yàn)。 1895年倫琴發(fā)現(xiàn)了陰極射線撞擊在玻璃或金屬產(chǎn)生了一個(gè)新型的射線 - X射線。這些射線波被證明具有波浪般的性質(zhì)和他們的波長(zhǎng)是在1899年由荷蘭物理學(xué)家估計(jì)Haga和風(fēng)能使用V形縫衍射測(cè)量出來(lái)的為10 - 10米。 1906年馬克思證明,波速度等同于光實(shí)驗(yàn)誤差之內(nèi),成為普遍接受了X -射線像光電磁輻射,但具有更短的波長(zhǎng)。 在1912年,德國(guó)勞厄和英國(guó)布拉格證明了原子晶格X -射線衍射。這些衍射圖給出了第一個(gè)原子的存在和它們的大小直接證據(jù)。一個(gè)例子如圖 1.2。 圖 1.2在鹽原子晶格由X射線衍射造成的

48、勞厄衍射圖案。1897年,盧瑟福發(fā)現(xiàn),在天然鈾元素釋放兩件射線其中稱為射線和射線類型。雙方可以通過(guò)偏轉(zhuǎn)電場(chǎng)和磁場(chǎng),因此推定為帶電粒子組成。 粒子的發(fā)現(xiàn)具有相同電荷的陰極射線和電子的質(zhì)量,因此被認(rèn)為是電子。在另一方面,射線有相當(dāng)多的巨大的質(zhì)量。他們的電荷和質(zhì)量表明,他們是氦的被拆掉兩個(gè)電子組成。這在1909年盧瑟福和羅伊茲被證實(shí)了,是由開(kāi)成一個(gè)密封的容器并表明它積累的氦。證據(jù)是確鑿的,一個(gè)粒子由一個(gè)氦原子被拆掉兩個(gè)電子組成。這個(gè)實(shí)驗(yàn)也證實(shí)有關(guān)的原子序數(shù)Z的物理意義,這個(gè)數(shù)字已經(jīng)提出來(lái)定義周期表中元素的順序。氫有Z=1和氦Z=2等等。對(duì)粒子與氦原子的鑒定表明,Z也表示一個(gè)特定原子的電子數(shù)。到191

49、2年,對(duì)個(gè)別原子的質(zhì)量存在的直接證據(jù)以及這些原子大小。更有趣的是,電子似乎是一個(gè)原子的組成部分,這表明原子存在一些內(nèi)部結(jié)構(gòu)。1.2原子的大小轉(zhuǎn)到歷史發(fā)展的主體,值得總結(jié)的原子質(zhì)量和尺寸測(cè)量。如上所述,原子質(zhì)量的直接測(cè)量,可使用電解。一個(gè)典型的電解槽包括兩個(gè)銅在硫酸銅(圖1.3)浴浸泡電極。電極之間的電位差會(huì)導(dǎo)致電流,流在陰極上的一些銅的沉積。圖 1.3 電解槽。陽(yáng)極和陰極浸泡在電解液中如硫酸銅溶液。帶正電的銅離子被吸引到陰極,并都沉積在這里。幾種假設(shè)要作出。首先,這是假設(shè)在溶液中硫酸銅晶體的分裂銅原子,這些自由原子有一個(gè)多余的正電荷。第二,利用化學(xué)知識(shí),銅的化學(xué)價(jià)是從理論的合理推斷,如果假定,從化學(xué)鍵的電子交換的

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