Structure of the Atom

1. Structure of the Atom

2. CHAPTER 4Structure of the Atom • The Atomic Models of Thomson and Rutherford • Rutherford Scattering • The Classic Atomic Model • The Bohr Model of the Hydrogen Atom • Successes & Failures of the BohrModel • Characteristic X-Ray Spectra and Atomic Number • Atomic Excitation by Electrons Niels Bohr (1885-1962) The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth. An expert is a person who has made all the mistakes that can be made in a very narrow field. Never express yourself more clearly than you are able to think. Prediction is very difficult, especially about the future. - Niels Bohr

3. History • 450 BC, Democritus – The idea that matter is composed of tiny particles, or atoms. • XVII-th century, Pierre Cassendi, Robert Hook – explained states of matter and transactions between them with a model of tiny indestructible solid objects. • 1811 – Avogadro’s hypothesis that all gases at given temperature contain the same number of molecules per unit volume. • 1900 – Kinetic theory of gases. Consequence – Great three quantization discoveries of XX century: (1) electric charge: (2) light energy; (3) energy of oscillating mechanical systems.

4. Historical Developments in Modern Physics • 1895 – Discovery of x-rays by Wilhelm Röntgen. • 1896 – Discovery of radioactivity of uranium by Henri Becquerel • 1897 – Discovery of electron by J.J.Thomson • 1900 – Derivation of black-body radiation formula by Max Plank. • 1905 – Development of special relativity by Albert Einstein, and interpretation of the photoelectric effect. • 1911 – Determination of electron charge by Robert Millikan. • 1911 – Proposal of the atomic nucleus by Ernest Rutherford. • 1913 – Development of atomic theory by Niels Bohr. • 1915 – Development of general relativity by Albert Einstein. • 1924+ - Development of Quantum Mechanics by deBroglie, Pauli, Schrödinger, Born, Heisenberg, Dirac,….

5. The Structure of Atoms There are 112 chemical elements that have been discovered, and there are a couple of additional chemical elements that recently have been reported. Fleroviumis the radioactive chemical element with the symbol Fl and atomic number 114. The element is named after Russian physicist GeorgyFlerov, the founder of the Joint Institute for Nuclear Research in Dubna, Russia, where the element was discovered. GeorgiFlerov (1913-1990) The name was adopted by IUPAC on May 30, 2012.About 80 decays of atoms of flerovium have been observed to date. All decays have been assigned to the five neighbouring isotopes with mass numbers 285–289. The longest-lived isotope currently known is 289Fl with a half-life of ~2.6 s, although there is evidence for a nuclear isomer, 289bFl, with a half-life of ~66 s, that would be one of the longest-lived nuclei in the superheavy element region.

6. The Structure of Atoms Each element is characterized by atom that contains a number of protonsZ, and equal number of electrons, and a number of neutronsN. The number of protonsZis called theatomic number. The lightest atom, hydrogen (H), hasZ=1; the next lightest atom, helium (He), hasZ=2; the third lightest, lithium (Li), hasZ=3and so forth.

7. The Nuclear Atoms Nearly all the mass of the atom is concentrated in a tiny nucleus which contains the protons and neutrons. Typically, the nuclear radius is approximately from 1 fm to 10 fm(1fm = 10-15m). The distance between the nucleus and the electrons is approximately0.1 nm=100,000fm. This distance determines the size of the atom.

8. Nuclear Structure An atom consists of an extremely small, positively charged nucleus surrounded by a cloud of negatively charged electrons. Although typically the nucleus is less than one ten-thousandth the size of the atom, the nucleus contains more than 99.9% of the mass of the atom!

9.  The number of protons in the nucleus,Z, is called the atomic number. This determines what chemical element the atom is. The number of neutrons in the nucleus is denoted by N. The atomic mass of the nucleus, A, is equal to Z + N. A given element can have many different isotopes, which differ from one another by the number of neutrons contained in the nuclei. In a neutral atom, the number of electrons orbiting the nucleus equals the number of protons in the nucleus.

10. There seemed to be too many kinds of atoms, each belonging to a distinct chemical element (way more than earth, air, water, and fire!). • Atoms and electromagnetic phenomena were intimately related (magnetic materials; insulators vs. conductors; different emission spectra). • Elements combine with some elements but not with others, a characteristic that hinted at an internal atomic structure (valence). • The discoveries of radioactivity, x-rays, and the electron (all seemed to involve atoms breaking apart in some way). Structure of the Atom Evidence in 1900 indicated that the atom wasnota fundamental unit:

11. The Nuclear Atoms We will begin our study of atoms by discussing some early models, developed in beginning of 20 century to explain the spectra emitted by hydrogen atoms.

12. Atomic Spectra By the beginning of the 20th century a large body of data has been collected on the emission of light by atoms of individual elements in a flame or in a gas exited by electrical discharge. • Diagram of the spectrometer

13. Atomic Spectra Light from the source passed through a narrow slit before falling on the prism. The purpose of this slit is to ensure that all the incident light strikes the prism face at the same angle so that the dispersion by the prism caused the various frequencies that may be present to strike the screen at different places with minimum overlap.

14. The source emits only two wavelengths, λ2>λ1. The source is located at the focal point of the lens so that parallel light passes through the narrow slit, projecting a narrow line onto the face of the prism. Ordinary dispersion in the prism bends the shorter wavelength through the lager total angel, separating the two wavelength at the screen.

15. In this arrangement each wavelength appears as a narrow line, which is the image of the slit. Such a spectrum was dubbed a line spectrum for that reason. Prisms have been almost entirely replaced in modern spectroscopes by diffraction gratings, which have much higher resolving power.

16. When viewed through the spectroscope, the characteristic radiation, emitted by atoms of individual elements in flame or in gas exited by electrical charge, appears as a set of discrete lines, each of a particular color or wavelength. The positions and intensities of the lines are a characteristic of the element. The wavelength of these lines could be determined with great precision.

17. Emission line spectrum of hydrogen in the visible and near ultraviolet. The lines appear dark because the spectrum was photographed. The names of the first five lines are shown. As is the point beyond which no lines appear,H∞called thelimits of the series.

18. Atomic Spectra In 1885 a Swiss schoolteacher, Johann Balmer, found that the wavelengths of the lines in the visible spectrum of hydrogen can be represented by formula Balmer suggested that this might be a special case of more general expression that would be applicable to the spectra of other elements.

19. Atomic Spectra Such an expression, found by J.R.Rydberg and W. Ritz and known as the Rydberg-Ritz formula, gives the reciprocal wavelengths as: where m and n are integers with n>m, and Ris the Rydberg constant.

20. Atomic Spectra The Rydberg constant is the same for all spectral series. For hydrogen the RH = 1.096776 x 107m-1. For very heavy elements Rapproaches the value R∞ = 1.097373 x 107m-1. Such empirical expressions were successful in predicting other spectra, such as other hydrogen lines outside the visible spectrum.

21. Atomic Spectra So, the hydrogen Balmer series wavelength are those given by Rydberg equation with m=2 and n=3,4,5,… Other series of hydrogen spectral lines were found for m=1 (by Lyman) and m=3(by Paschen).

22. Hydrogen Spectral Series Compute the wavelengths of the first lines of the Lyman, Balmer, and Paschen series.

23. Emission line spectrum of hydrogen in the visible and near ultraviolet. The lines appear dark because the spectrum was photographed. The names of the first five lines are shown, as is the point beyond which no lines appear,H∞called thelimits of the series.

24. The Limits of Series Find the predicted by Rydberg-Ritz formula for Lyman, Balmer, and Paschen series.

25. A portion of the emission spectrum of sodium. The two very close bright lines at589 nmare theD1 andD2lines. They are the principal radiation from sodium streetlighting.

26. A portion of emission spectrum of mercury.

27. Part of the dark line (absorption) spectrum of sodium. White light shining through sodium vapor is absorbed at certain wavelength, resulting in no exposure of the film at those points. Note that frequency increases toward the right , wavelength toward the left in the spectra shown.

28. Nuclear Models Many attempts were made to construct a model of the atom that yielded the Balmer and Rydberg-Ritz formulas. It was known that an atom was about10-10min diameter, that it contained electrons much lighter than the atom, and that it was electrically neutral. The most popular model was that of J.J.Thomson, already quite successful in explaining chemical reactions.

29. Electrons (discovered in 1897) carried the negative charge. Electrons were very light, even compared to the atom. Protons had not yet been discovered, but clearly positive charge had to be present to achieve charge neutrality. Knowledge of atoms in 1900

30. Thomson’s “plum-pudding” model of the atom had the positive charges spread uniformly throughout a sphere the size of the atom, with electrons embedded in the uniform background. Thomson’s Atomic Model In Thomson’s view, when the atom was heated, the electrons could vibrate about their equilibrium positions, thus producing electromagnetic radiation. Unfortunately, Thomson couldn’t explain spectra with this model.

31. The difficulty with all such models was that electrostatic forces alone cannot produce stable equilibrium. Thus the charges were required to move and, if they stayed within the atom, to accelerate. However, the acceleration would result in continuous radiation, which is not observed. Thomson was unable to obtain from his model a set of frequencies that corresponded with the frequencies of observed spectra. The Thomson model of the atom was replaced by one based on results of a set of experiments conducted by Ernest Rutherford and his student H.W.Geiger.

32. Experiments of Geiger and Marsden Rutherford, Geiger, and Marsden conceived a new technique for investigating the structure of matter by scattering aparticles from atoms.

33. Rutherford was investigating radioactivity and had shown that the radiations from uranium consist of at least two types, which he labeledαandβ. He showed, by an experiment similar to that of Thompson, thatq /mfor theα - particleswas half that of the proton. Suspecting that theαparticles were double ionized helium, Rutherford in his classical experiment let a radioactive substance decay and then, by spectroscopy, detected the spectra line of ordinary helium.

34. Beta decay Beta decay occurs when the neutron to proton ratio is too great in the nucleus and causes instability. In basic beta decay, a neutron is turned into a proton and an electron. The electron is then emitted. Here's a diagram of beta decay with hydrogen-3: Beta Decay of Hydrogen-3 to Helium-3.

35. Alpha Decay The reason alpha decay occurs is because the nucleus has too many protons which cause excessive repulsion. In an attempt to reduce the repulsion, a Helium nucleus is emitted. The way it works is that the Helium nuclei are in constant collision with the walls of the nucleus and because of its energy and mass, there exists a nonzero probability of transmission. That is, an alpha particle (Helium nucleus) will tunnel out of the nucleus. Here is an example of alpha emission with americium-241: Alpha Decay of Americium-241 to Neptunium-237

36. Gamma Decay Gamma decay occurs because the nucleus is at too high an energy. The nucleus falls down to a lower energy state and, in the process, emits a high energy photon known as a gamma particle. Here's a diagram of gamma decay with helium-3: Gamma Decay of Helium-3

37. Rutherford was investigating radioactivity and had shown that the radiations from uranium consist of at least two types, which he labeledαandβ. He showed, by an experiment similar to that of Thompson, thatq /mfor theα - particleswas half that of the proton. Suspecting that theαparticles were double ionized helium, Rutherford in his classical experiment let a radioactive substance decay and then, by spectroscopy, detected the spectra line of ordinary helium.

38. Schematic diagram of the Rutherford apparatus. The beam ofα- particles is defined by the small holeDin the shield surrounding the radioactive source Rof214Bi. Theαbeam strikes an ultra thin gold foil F, and α particles are individually scattered through various angelsθ. The experiment consisted of counting the number of scintillations on the screenSas a function ofθ.

39. A diagram of the original apparatus as it appear in Geiger’s paper describing the results.

40. An α-particle by such an atom (Thompson model) would have a scattering angle θ much smaller than 10. In the Rutherford’s scattering experiment most of the α-particles were either undeflected, or deflected through very small angles of the order 10, however, a few α-particles were deflected through angles of 900and more.

41. An α-particle by such an atom (Thompson model) would have a scattering angle θ much smaller than 10. In the Rutherford’s scattering experiment a few α-particles were deflected through angles of 900and more.

42. Experiments of Geiger and Marsden Geiger showed that many a particles were scattered from thin gold-leaf targets at backward angles greater than 90°.

43. Before After Electrons can’t back-scatter a particles. Calculate the maximum scattering angle - corresponding to the maximum momentum change. It can be shown that the maximum momentum transfer to the a particle is: Determine qmax by letting Dpmaxbe perpendicular to the direction of motion: too small!

44. Try multiple scattering from electrons N= the number of atoms across the thin gold layer, t = 6 × 10−7 m: If an aparticle is scattered by N electrons: n = The distance between atoms, d = n-1/3, is: N = t / d still too small!

45. If the atom consisted of a positively charged sphere of radius10-10 m, containing electrons as in the Thomson model, only a very small scattering deflection angle could be observed. Such model could not possibly account for the large angles scattering. The unexpected large anglesα-particles scattering was described by Rutherford with these words: It was quite incredible event that ever happened to me in my life. It was as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.

46. Rutherford’s Atomic Model even if the αparticle is scattered from all 79 electrons in each atom of gold. Experimental results were not consistent with Thomson’s atomic model. Rutherford proposed that an atom has a positively charged core (nucleus!) surrounded by the negative electrons. Geiger and Marsden confirmed the idea in 1913. Ernest Rutherford (1871-1937)

47. Rutherford concluded that the large angle scattering could result only from a single encounter of theαparticle with a massive charge with volume much smaller than the whole atom. Assuming this“nucleus”to be a point charge, he calculated the expected angular distribution for the scatteredαparticles. His predictions on the dependence of scattering probability on angle, nuclear charge and kinetic energy were completely verified in experiments.

48. Rutherford Scattering geometry. The nucleus is assumed to be a point chargeQat the originO. At any distance rtheαparticle experiences a repulsive forcekqαQ/r2. The αparticle travel along a hyperbolic path that is initially parallel to line OAa distancebfrom it and finally parallel toOB, which makes an angleθwith OA.

49. Force on a point charge versus distancerfrom the center of a uniformly charged sphere of radiusR. Outside the sphere the force is proportional toQ/r2, inside the sphere the force is proportional toqI/r2= Qr/R3, whereqI = Q(r/R)3 is the charge within a sphere of radius r. The maximum force occurs atr =R

50. Twoαparticles with equal kinetic energies approach the positive chargeQ = +Zewith impact parametersb1andb2, whereb1<b2. According to equation for impact parameter in this caseθ1 > θ2.