1. 1 6/7/2016 THE ATOM Chapter 8

2. 2 The Concepts of Particle and Wave We regard objects such as a stone or electron as particles. We regard the ripples in a lake as waves. Classical physics, the physics of chapters 1-6, treats particles and waves as separate aspects of the reality we find in everyday life.

3. 3 The Concepts of Particle and Wave In the small scale world of atoms, molecules, electrons, and nuclei there are neither particles nor waves in our sense of these terms.  We think of electrons as particles (they have charge and mass) Evidence exists that a moving electron is a type of wave in some instances.  We think of em waves as waves (they exhibit wave behavior such as diffraction and interference) Em waves also behave as though they consist of streams of particles. Modern physics – refers to the physics in which wave- particle duality is central to an understanding. It is the physics of the atomic world.

4. 4 PHOTOELECTRIC EFFECT Can electrons be set free from atoms by light? Refers to electrons being emitted by a metal surface when light is directed onto it. Most metals need ultraviolet light for the photoelectric effect to occur, but not all.  Potassium and cesium respond to visible light. electron

5. 5 Everyday Examples of the Photoelectric Effect Photoelectric cells measure light intensity in a camera. Solar cells produce electric current when sunlight falls on them. Television camera tubes convert the image of a scene into an electric signal.

6. 6 Light The word “light” is defined here as “electromagnetic radiation of any wavelength”  X-rays, gamma rays, uv light, microwaves, radio waves, visible light

7. 7 The Photoelectric Effect No Simple Explanation The electrons are always emitted at once, even when a faint light is used.  According to the electromagnetic theory of light, the energy in an em wave is spread out across the wave; hence, a certain period of time should be needed for an individual electron to gather enough energy to leave the metal.

8. 8 The Photoelectric Effect No Simple Explanation A bright light causes more electrons to be emitted than a faint light, but the average KE of the electrons is the same.  The electromagnetic theory of light predicts that the stronger the light, the greater the KE of the electrons.

9. 9 The Photoelectric Effect No Simple Explanation The higher the frequency of light, the more KE the electrons have. (blue light yields faster electrons than red)  According to the electromagnetic theory of light, the frequency should NOT matter.

10. 10 The Photoelectric Effect The higher the frequency of light, the more KE the photoelectrons have. The brighter the light, the more photoelectrons are emitted.

11. 11 Quantum Theory of Light Until the discovery of the photoelectric effect, the electromagnetic theory of light completely explained the behavior of light. The Quantum Theory of Light arose from the discovery of the photoelectric effect. Created by Albert Einstein (1905) The same year saw the birth of the Theory of Relativity. All of modern physics has its roots in these two theories.

12. 12 Photons – Particles of Light The modern concept of the photon was developed gradually by Einstein (1905-17) to explain experimental observations that did not fit the classical wave (or electromagnetic) model of light. Particularly, the photon model accounted for the frequency dependence of light’s energy.

13. Photons Einstein proposed that light consists of tiny bursts of energy called photons. 13

14. 14 I want to know more about PHOTONS! The photon is an elementary particle responsible for all electromagnetic phenomena; they produce all electric and magnetic fields.  In other words, photons make up all forms of light on the em spectrum. A photon is a discrete bundle (quantum) of electromagnetic (or light) energy. Photons have zero mass, zero rest energy, and zero charge. Photons are always in motion and travel at the speed of light (c), in free space. Photons carry energy and momentum.  Can be slowed down or even absorbed, transferring energy and momentum proportional to its frequency

15. I want to know more about PHOTONS! Photons can be destroyed/created when radiation is absorbed/emitted. Photons have particle-like interactions (i.e. collision) with electrons and other particles. Photons are one of the rare particles that are identical to their antiparticle, the antiphoton. Photons act as both a wave and a particle all the time (even though it’s common, but basically incorrect, to say that it’s “sometimes a wave and sometimes a particle” depending upon which features are more obvious at a given time). Photons are emitted in many natural processes such as when a charge is accelerated, when an atom or nucleus jumps from a higher to lower energy level, or when a particle and its antiparticle are annihilated. 15

16. 16 Max Planck and Quanta Einstein’s proposal that light consists of photons came about from a hypothesis suggested 5 years earlier by Max Planck (1858-1947), a German physicist.  In order to explain variation of color with temperature (Figure 4-4) (i.e. red (hot) to yellow (hotter) to white(hottest) Planck said: The higher the temperature, the shorter the wavelength and higher the frequency. Planck hypothesized that warm bodies emit radiant energy in discrete bundles, what he called quanta.  Mass and electric charge are considered quantized, in that they consist of some whole number of fundamental units. Planck said the energy in each energy bundle is proportional to the frequency of radiation. All the quanta associated with a given frequency of light have the same energy: E=hf

17. 17 Quantum Energy E = hf E=quantum energy h = Plank’s constant = 6.63 x 10 -34 joule. Sec f = frequency of light

18. 18 Quanta A quantum is the smallest elemental unit of a quantity. Quanta are discrete bundles in which radiation and other forms of energy occur.  Light (or any form of radiant energy), is composed of many quanta, each of which is called a photon.

19. 19 Photoelectric Effect EINSTEIN’S HYPOTHESIS : if light is emitted in little packets, it should travel through space and be absorbed in the same little packets. Einstein proposed that some minimum energy, w, is needed to pull an electron away from a metal surface.

20. 20 Photoelectric Effect Einstein’s formula for the photoelectric effect can be summarized as: hf = KE + w where  w = minimum energy to pull an electron away from a metal surface  h = Planck’s constant  f = frequency  KE = kinetic energy

21. 21 Photoelectric Effect In summation, if the frequency of the light is too low, so that E (quantum energy = hf) is less than w, no electrons can come out.  The energy of the ejected electron is related only to the light’s frequency, not to its intensity.

22. 22 Photoelectric Effect When E is greater than w, a photon of light striking an electron can give the electron enough energy for it to leave the metal with a certain amount of kinetic energy (KE).

23. 23 Photon Example The average frequency of light emitted by a 100-W light bulb is 5.5 x 10 14 Hz. How many photons per second does the light bulb emit?? The energy of each photon can be calculated using: E=hf (6.63 x 10 -34 J*s)(5.5 x 10 14 Hz) = 3.6 x 10 -19 J Since 100 W = 100 J/s, the number of photons emitted per second is Such an enormous amount of photons makes it impossible for us to experience light as a stream of individual particles.

24. 24 What is Light?? Light traveling as a series of little packets of energy is directly opposed to the wave theory of light. But, in fact, Einstein suggested in 1905 that light travels through space in the form of distinct photons. LIGHT can be defined as having both wave and particle aspects.

25. 25 Light Wave Theory of Light – accounts for the diffraction and interference of light.  Light waves are spread out like waves traveling across water. Quantum Theory of Light – accounts for the photoelectric effect.  Light travels from a source as a series of tiny bursts of energy, each burst so small that it can be taken up by a single electron.

26. 26 tam8s6_3 The Wave and Quantum Theories of Light

27. 27 Light The wave theory of light and the quantum theory of light complement each other. Both theories are needed to account for a single physical phenomenon. Wave theory (em waves) provides the only explanation for some experiments involving light. Quantum theory (photons) provides the only explanation for other experiments involving light. In any particular event light exhibits either a wave nature or a particle nature, never both at the same time.

28. 28 X-Rays – High Energy Photons Wilhelm Roentgen (1845-1923) discovered x- rays. X-rays are given off whenever fast electrons are stopped suddenly. This is the inverse of the photoelectric effect.  The photoelectric effect shows that photons of light can give energy to electrons. X-rays are high frequency em waves. Electron KE is transformed into photon energy.

29. 29 tam8s6_4 An X-Ray Tube

30. 30 Matter Waves Is it possible for a particle, such as an electron, to have wave properties as well? Yes! Louis de Broglie (1892-1987) proposed that moving objects have wave properties that complement their particle properties. He suggested that a particle of mass m and speed v behaves as though it is a wave whose wavelength is: λ=de Broglie wavelength h=Planck’s constant mv=momentum

31. 31 Matter Waves The more momentum (mv) a particle has, the shorter its de Broglie wavelength λ. Matter waves are real but are only significant in the atomic world and are crucial to the understanding of atomic structure and behavior.

32. 32 Calculate the de Broglie wavelength of (a) a 46-g golf ball whose speed is 30 m/s, and (b) an electron whose speed is 10 7 m/s. Wavelength of golf ball is small compared with its dimensions and would not Expect to find any wave aspects in its behavior. Dimensions of atoms are comparable with wavelength (radius of hydrogen atom Is 5.3x10 -11 m) Therefore, the wave character of moving electrons is important In the world of the atom.

33. 33 Waves of Probability In water waves, the quantity that varies periodically is the height of the water surface; in sound waves, it is air pressure; in light waves, it is electric and magnetic fields. What varies in the case of matter waves?? The quantity whose variations make up matter waves is called the wave function, symbol  (the Greek letter psi). The value  2 at a given place and time for a given particle determines the probability of finding the particle there at that time. For this reason  2 is called the probability density of the particle.  A large value of  2 means the strong possibility of the particle’s presence.

34. 34 tam8s6_5 Particle and Wave Description of a Moving Object Particle description of moving object. Wave description of same moving object. The packet of matter waves that corresponds to a certain object moves with the same speed v as the object does. The waves are waves of probability.

35. 35 Heisenberg’s Uncertainty Principle To regard a moving particle as a wave packet suggests that there are limits to the accuracy with which we can measure “particle” properties such as position and speed. Werner Heisenberg 1901-1976  It is impossible to know both the exact position and the exact momentum of a particle at the same time.  The narrower its wave packet, the more precisely a particle’s position can be identified. However the wavelength of the waves is not well defined.  The wider its wave packet, the wavelength can be precisely identified. However the position cannot be determined.

36. 36 tam8s6_6 Narrow and Wide Wave Packets

37. 37 Atomic Spectra With the Rutherford model of the atom, the quantum theory of light, and the wave theory of moving particles, we have what is needed to make sense of atomic structures. When these concepts are linked together, they give rise to a theory of the atom that agrees with experiment. The starting point will be the hydrogen atom.

38. 38 Atomic Spectra A spectroscope is an instrument used to observe the color components of ANY light source. The spectroscope allows us to analyze the light emitted by elements when they are excited by various types of energy (current or heat, for example). When light from glowing atoms is viewed through a spectroscope, we see the light consists of a number of discrete (separate) frequencies rather than a continuous spectrum. The pattern of frequencies formed by a given element is called the element’s atomic spectrum.  It is the element’s finger print.

39. 39 Atomic Spectra and Spectroscope Atomic Spectra

40. 40 Bohr Model of the Atom Niels Bohr proposed a theory in 1913 of the hydrogen atom that accounted for its stability and for the frequencies of the spectral lines. Bohr applied the new quantum ideas to atomic structure to come up with the model, even though later it was replaced by a more complex picture.

41. 41 Bohr Model of the Atom Bohr proposed that an electron in an atom can circle the nucleus without losing energy only in certain specific orbits. Atomic electrons can have only certain particular energies because the energy of the electron depends on which orbit it is in.  Innermost orbit has the least energy  Orbits are identified by a quantum number, n, where n=1 is the innermost orbit.  Each orbit represents an energy level of the atom.

42. 42 Explaining Spectral Lines Atoms emit or absorb only light of certain frequencies, which we see as spectral lines. An electron in a particular orbit can absorb only those photons of light whose energy will allow it to jump to another orbit farther out, where the electron has more energy. When an electron jumps from an orbit to a closer orbit to the nucleus, where it has less energy, it emits a photon of light. Difference in energy between the two orbits is hf, where f is the frequency of the absorbed or emitted light.

43. 43 Electron Orbits in Hydrogen Atom (Bohr Model) Each electron jump gives a photon of a characteristic frequency and appears in the spectrum as a single bright line. Ground State Excited States The radius of each orbit is proportional to the square of the orbit’s quantum number.

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45. 45 Electron Waves and Orbits: Standing Waves in the Atom Why does an electron only follow certain orbits?? The de Broglie wavelength of the electron is exactly equal to the circumference of its ground-state (n=1 orbit). The n=1 orbit of the electron in a hydrogen atom corresponds to one complete electron wave joined on itself. Electron waves in an atom are analogous to standing waves in a wire loop and leads to the concept:  An electron can circle a nucleus only in orbits that contain a whole number of de Broglie wavelengths. (fig 8-27)

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48. 48 The quantum number, n, of an orbit means it is the number of electron waves that fit into the orbit.

49. 49 Quantum Mechanics The preceding theory of the hydrogen atom developed by Bohr in 1913 accounts for much experimental data. However, there are some limitations:  It does not account for the spectra of atoms that have 2 or more electrons each.  Most important of all, it does not give an understanding of how individual atoms interact with one another to form molecules, solids, and liquids. A more general approach of the atom was required and in 1925-26 Erwin Schrödinger, Werner Heisenberg, and other developed quantum mechanics.

50. 50 Quantum Mechanics Probabilities, not Certainties The real difference between Newtonian mechanics and quantum mechanics lies in what they describe.  Newtonian Mechanics (Chap 2) deals with the motion of an object under the influence of applied forces.  The values it predicts for observable quantities agree with the measured values of those quantities.

51. 51 Quantum Mechanics Probabilities, not Certainties The real difference between Newtonian mechanics and quantum mechanics lies in what they describe.  With quantum mechanics the uncertainty principle radically alters the meaning of “observable quantity” in the atomic realm, and the position and momentum of a particle cannot be simultaneously known.  Quantum mechanics explore probabilities.  Although quantum mechanics does not give us a look into the inner world of the atom, it does tell us everything we need to know about the measurable properties of atoms.

52. 52 Quantum Numbers An Atomic Electron Has 4 in All In the Bohr model of the hydrogen atom, the electron moves around the nucleus in a circular orbit.  The only quantity that changes is it position on the circle.  The single quantum number, n, is enough to specify the physical state of an electron.

53. 53 Quantum Numbers An Atomic Electron Has 4 in All In the quantum theory of the atom, an electron has NO FIXED ORBIT but is free to move about in three dimensions. Think of the electron as circulating in a probability cloud that forms a certain pattern in space.  Where the cloud is most dense (  2 is high), the electron is most likely to be found.

54. 54 Probability cloud for the ground state of hydrogen. The denser the cloud, the more likely the electron is to be found there.

55. 55 Quantum Numbers An Atomic Electron Has 4 in All Three quantum numbers determine the size and shape of the probability cloud of an atomic electron:  Principal Quantum Number – (n) is the chief factor that governs the electron’s energy.  Orbital Quantum Number – (l) determines the magnitude of the electron’s angular momentum.  Magnetic Quantum Number – (m l ) determines the direction of the electron’s angular momentum.

56. 56 The right hand rule for direction of angular momentum vector.

57. 57 Quantum Numbers An Atomic Electron Has 4 in All Spin Magnetic Quantum Number – (m s ) is the fourth quantum number and describes the direction of electron spin.  Electron aligns itself so that its spin is along a magnetic field, in which case m s has a value of +1/2.  Electron aligns itself so that its spin is opposite a magnetic field, in which case m s has a value of -1/2.

58. 58 Spin Magnetic Quantum Number

59. 59 Exclusion Principle A different set of quantum numbers for each electron in an atom In 1925, Wolfgang Pauli solved the problem of the electron arrangement in an atom that has more than one electron with his exclusion principle.  Only one electron in an atom can exist in a given quantum state. Each electron in an atom must have a different set of quantum numbers n, l, m l, and m s.

60. 60 The End This link includes all kinds of physics info but also has good info on the atom. http://www.colorado.edu/physics/2000/index. pl?Type=TOC