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  • Physics

    414

    12.1 INTRODUCTIONBy the nineteenth century, enough evidence had accumulated in favour ofatomic hypothesis of matter. In 1897, the experiments on electric dischargethrough gases carried out by the English physicist J. J. Thomson (1856 1940) revealed that atoms of different elements contain negatively chargedconstituents (electrons) that are identical for all atoms. However, atoms on awhole are electrically neutral. Therefore, an atom must also contain somepositive charge to neutralise the negative charge of the electrons. But whatis the arrangement of the positive charge and the electrons inside the atom?In other words, what is the structure of an atom?

    The first model of atom was proposed by J. J. Thomson in 1898.According to this model, the positive charge of the atom is uniformlydistributed throughout the volume of the atom and the negatively chargedelectrons are embedded in it like seeds in a watermelon. This model waspicturesquely called plum pudding model of the atom. Howeversubsequent studies on atoms, as described in this chapter, showed thatthe distribution of the electrons and positive charges are very differentfrom that proposed in this model.

    We know that condensed matter (solids and liquids) and dense gases atall temperatures emit electromagnetic radiation in which a continuousdistribution of several wavelengths is present, though with differentintensities. This radiation is considered to be due to oscillations of atoms

    Chapter Twelve

    ATOMS

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    Atoms

    and molecules, governed by the interaction of each atom ormolecule with its neighbours. In contrast, light emitted fromrarefied gases heated in a flame, or excited electrically in aglow tube such as the familiar neon sign or mercury vapourlight has only certain discrete wavelengths. The spectrumappears as a series of bright lines. In such gases, theaverage spacing between atoms is large. Hence, theradiation emitted can be considered due to individual atomsrather than because of interactions between atoms ormolecules.

    In the early nineteenth century it was also establishedthat each element is associated with a characteristicspectrum of radiation, for example, hydrogen always givesa set of lines with fixed relative position between the lines.This fact suggested an intimate relationship between theinternal structure of an atom and the spectrum ofradiation emitted by it. In 1885, Johann Jakob Balmer(1825 1898) obtained a simple empirical formula whichgave the wavelengths of a group of lines emitted by atomichydrogen. Since hydrogen is simplest of the elementsknown, we shall consider its spectrum in detail in thischapter.

    Ernst Rutherford (18711937), a former researchstudent of J. J. Thomson, was engaged in experiments on-particles emitted by some radioactive elements. In 1906,he proposed a classic experiment of scattering of these-particles by atoms to investigate the atomic structure.This experiment was later performed around 1911 by HansGeiger (18821945) and Ernst Marsden (18891970, whowas 20 year-old student and had not yet earned hisbachelors degree). The details are discussed in Section12.2. The explanation of the results led to the birth ofRutherfords planetary model of atom (also called thenuclear model of the atom). According to this the entirepositive charge and most of the mass of the atom is concentrated in a smallvolume called the nucleus with electrons revolving around the nucleus justas planets revolve around the sun.

    Rutherfords nuclear model was a major step towards how we seethe atom today. However, it could not explain why atoms emit light ofonly discrete wavelengths. How could an atom as simple as hydrogen,consisting of a single electron and a single proton, emit a complexspectrum of specific wavelengths? In the classical picture of an atom, theelectron revolves round the nucleus much like the way a planet revolvesround the sun. However, we shall see that there are some seriousdifficulties in accepting such a model.

    12.2 ALPHA-PARTICLE SCATTERING ANDRUTHERFORDS NUCLEAR MODEL OF ATOM

    At the suggestion of Ernst Rutherford, in 1911, H. Geiger and E. Marsdenperformed some experiments. In one of their experiments, as shown in

    Ernst Rutherford (1871 1937) British physicistwho did pioneering work onradioactive radiation. Hediscovered alpha-rays andbeta-rays. Along withFederick Soddy, he createdthe modern theory ofradioactivity. He studiedthe emanation of thoriumand discovered a new noblegas, an isotope of radon,now known as thoron. Byscattering alpha-rays fromthe metal foils, hediscovered the atomicnucleus and proposed theplenatery model of theatom. He also estimated theapproximate size of thenucleus.

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    Fig. 12.1, they directed a beam of5.5 MeV -particles emitted from a21483Bi radioactive source at a thin metal

    foil made of gold. Figure 12.2 shows aschematic diagram of this experiment.Alpha-particles emitted by a 21483Biradioactive source were collimated intoa narrow beam by their passagethrough lead bricks. The beam wasallowed to fall on a thin foil of gold ofthickness 2.1 107 m. The scatteredalpha-particles were observed througha rotatable detector consisting of zincsulphide screen and a microscope. Thescattered alpha-particles on strikingthe screen produced brief light flashesor scintillations. These flashes may beviewed through a microscope and thedistribution of the number of scatteredparticles may be studied as a functionof angle of scattering.

    FIGURE 12.2 Schematic arrangement of the Geiger-Marsden experiment.

    A typical graph of the total number of -particles scattered at differentangles, in a given interval of time, is shown in Fig. 12.3. The dots in thisfigure represent the data points and the solid curve is the theoreticalprediction based on the assumption that the target atom has a small,dense, positively charged nucleus. Many of the -particles pass throughthe foil. It means that they do not suffer any collisions. Only about 0.14%of the incident -particles scatter by more than 1; and about 1 in 8000deflect by more than 90. Rutherford argued that, to deflect the -particlebackwards, it must experience a large repulsive force. This force could

    FIGURE 12.1 Geiger-Marsden scattering experiment.The entire apparatus is placed in a vacuum chamber

    (not shown in this figure).

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    be provided if the greater part of themass of the atom and its positive chargewere concentrated tightly at its centre.Then the incoming -particle could getvery close to the positive charge withoutpenetrating it, and such a closeencounter would result in a largedeflection. This agreement supportedthe hypothesis of the nuclear atom. Thisis why Rutherford is credited with thediscovery of the nucleus.

    In Rutherfords nuclear model ofthe atom, the entire positive charge andmost of the mass of the atom areconcentrated in the nucleus with theelectrons some distance away. Theelectrons would be moving in orbitsabout the nucleus just as the planetsdo around the sun. Rutherfordsexperiments suggested the size ofthe nucleus to be about 1015 m to1014 m. From kinetic theory, the sizeof an atom was known to be 1010 m,about 10,000 to 100,000 times largerthan the size of the nucleus (see Chapter 11, Section 11.6 in Class XIPhysics textbook). Thus, the electrons would seem to be at a distancefrom the nucleus of about 10,000 to 100,000 times the size of the nucleusitself. Thus, most of an atom is empty space. With the atom being largelyempty space, it is easy to see why most -particles go right through athin metal foil. However, when -particle happens to come near a nucleus,the intense electric field there scatters it through a large angle. The atomicelectrons, being so light, do not appreciably affect the -particles.

    The scattering data shown in Fig. 12.3 can be analysed by employingRutherfords nuclear model of the atom. As the gold foil is very thin, itcan be assumed that -particles will suffer not more than one scatteringduring their passage through it. Therefore, computation of the trajectoryof an alpha-particle scattered by a single nucleus is enough. Alpha-particles are nuclei of helium atoms and, therefore, carry two units, 2e,of positive charge and have the mass of the helium atom. The charge ofthe gold nucleus is Ze, where Z is the atomic number of the atom; forgold Z = 79. Since the nucleus of gold is about 50 times heavier than an-particle, it is reasonable to assume that it remains stationarythroughout the scattering process. Under these assumptions, thetrajectory of an alpha-particle can be computed employing Newtonssecond law of motion and the Coulombs law for electrostaticforce of repulsion between the alpha-particle and the positivelycharged nucleus.

    FIGURE 12.3 Experimental data points (shown bydots) on scattering of -particles by a thin foil atdifferent angles obtained by Geiger and Marsden

    using the setup shown in Figs. 12.1 and12.2. Rutherfords nuclear model predicts the solidcurve which is seen to be in good agreement with

    experiment.

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    The magnitude of this force is

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    r= (12.1)where r is the distance between the -particle and the nucleus. The forceis directed along the line joining the -particle and the nucleus. Themagnitude and direction of the force on an -particle continuouslychanges as it approaches the nucleus and recedes away from it.

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