Chapter 38 The Atom and the Quantum

1. Chapter 38 The Atom and the Quantum Conceptual Physics Chapter 38

2. Atomic Models • No one actually knows what an atom’s internal structure looks like, for there is no way to see it with our eyes. • To visualize the processes that occur in the subatomic realm, we construct models. Conceptual Physics Chapter 38

3. Atomic Models • One of the earliest notions of the atom was introduced by the Greek philosopher Democritus in 400 BC. • He reasoned that matter could not be divided into smaller and smaller pieces forever, but that eventually the smallest possible piece would be obtained. • He named the smallest piece of matter “atomos,” meaning “not to be cut.” Conceptual Physics Chapter 38

4. Atomic Models • Democritus’ atomos was ignored and forgotten for more than 2000 years. • The notion of a smallest piece of matter was revived in the early 1800s when the English chemist John Dalton performed a number of experiments that eventually led to the acceptance of the atom. • Dalton described the atom quite simply as tiny, indivisible and indestructible building-blocks of which all matter is made. Conceptual Physics Chapter 38

5. Atomic Models • In 1897, the English scientist J.J. Thomson provided the first hint that an atom is made up of even smaller particles. • Thomson is generally credited with discovering the electron and introduced what is often called the “Plum Pudding” model of the atom. • Atoms were made from a positively charged substance with negatively charged electrons scattered about, like raisins in a pudding. Conceptual Physics Chapter 38

6. Atomic Models • In 1908, the English physicist Ernest Rutherford discovered the nucleus of the atom while firing a stream of tiny, positively charged alpha particles (helium nuclei) at a thin sheet of gold foil. Conceptual Physics Chapter 38

7. Atomic Models • It was expected, based on Thomson’s model, that all of the alpha particles would pass through the gold foil unaffected by the evenly distributed positively charge matter. • Rutherford found that most of the alpha particles did indeed pass through the foil with no change to their direction. • A small percentage of the alpha particles, however, were deflected off their course – some by as much as 180°! Run Simulation Conceptual Physics Chapter 38

8. Atomic Models • Rutherford concluded that an atom had a small, dense, positively charged center that repelled the positively charged alpha particles. • He called the center of the atom the nucleus. • The nucleus is tiny compared to the atom as a whole – the atom is comprised primarily of empty space. Conceptual Physics Chapter 38

9. Atomic Models • The positive charges associated with an atom are located solely within the nucleus. • There are an equal number of negative charges that keep the net charge of the atom neutral. • The negative charges orbit the nucleus in a way similar to the planets orbiting the sun. • Rutherford’s model is often called the “planetary model”. Conceptual Physics Chapter 38

10. Atomic Models • In 1913, Danish physicist Niels Bohr improved upon the planetary model. • The electrons occupy specific energy levels that are located at predictable distances from the nucleus. • This model is still useful for understanding the absorption and emission of light. Run Simulation Conceptual Physics Chapter 38

11. Atomic Models • Although the Bohr model is the most well known model of the atom, it is not the most current model. • The quantum model or modern model of the atom is best understood as a mathematical model described by probability and statistics rather than a physical model. • It is most likely that an electron would be found within a certain region of space (the electron cloud) at any given time. Conceptual Physics Chapter 38

12. Atomic Models • Most of what we know about atoms we learn from light and other radiations they emit. • Most light comes from the motion of electrons within the atom. • Any useful model of the atom must be consistent with a model for light. • There have been two primary models of light: the particle model and the wave model. Conceptual Physics Chapter 38

13. The Duality of Light • Isaac Newton believed light was composed of tiny particles. • Christian Huygens believed that light was a wave phenomenon. • The wave model was reinforced when Thomas Young demonstrated constructive and destructive interference of light. • Most scientists now agree that light can not be fully explained without recognizing that it demonstrates properties of both waves and particles. Conceptual Physics Chapter 38

14. The Duality of Light • In 1905, Albert Einstein resurrected the particle theory of light. • Einstein visualized particles of light as concentrated bundles of electromagnetic energy. • Max Planck believed that light existed as continuous waves, but that emission and absorption occurred in tiny, finite chunks. • Each chunk was considered a quantum, or a fundamental unit. Run Simulation Conceptual Physics Chapter 38

15. Continuous versus Quantized • Quantities that are quantized can only be increased or decreased in specific, finite amounts. • Matter is quantized, equal to some whole-number multiple of the mass of a single atom. • Money is quantized – we can only earn or spend integer multiples of a penny. • Electric charge is quantized as a multiple of the charge of a single electron. Conceptual Physics Chapter 38

16. Continuous versus Quantized • The opposite of quantized is continuous. Continuous quantities can be increased or decreased by any amount. • Real numbers are continuous – any real number can be increased or decreased by infinitely small amounts. • Time and distance are also examples of continuous quantities. Conceptual Physics Chapter 38

17. The Photon • Einstein went a step beyond Planck and proposed that light itself is composed of quanta. • One quantum of light energy is now called a photon. Conceptual Physics Chapter 38

18. The Photon • The energy in a light beam is due to an integer number of photons – the fundamental unit of light energy. • Photons move at the speed of light. • The total energy of a photon is the same as its kinetic energy. Conceptual Physics Chapter 38

19. The Photon • The energy of a photon of light is proportional to its vibrational frequency. • When the energy E of a photon (in Joules) is divided by its frequency f (in Hertz), the quantity that results is known as Planck’s constant, h. • The energy of every photon is therefore E = hf Conceptual Physics Chapter 38

20. The Photoelectric Effect • Einstein found support for his quantum theory of light in the photoelectric effect. • The photoelectric effect is the ejection of electrons from certain metals when light falls upon them. • These metals are said to be photosensitive. • Every photosensitive material has its own work function – the minimum energy required to free an electron from the surface of the material. Conceptual Physics Chapter 38

21. The Photoelectric Effect • If an electron is to be ejected, the photon that ejects it must have an energy that equals or exceeds the work function of the material. Conceptual Physics Chapter 38

22. The Photoelectric Effect • High-frequency light, even from a dim source, is capable of ejecting electrons from a photosensitive metal surface. • Low-frequency light, even from a very bright source, cannot dislodge electrons. Conceptual Physics Chapter 38

23. The Photoelectric Effect • Since bright light carries more energy than dim light, it was puzzling that dim blue light could dislodge electrons when bright red light could not. Conceptual Physics Chapter 38

24. The Photoelectric Effect • No electrons are ejected if the frequency of the incident light falls below the threshold frequency. • The intensity of light does not matter. From E = hf, the critical factor is the frequency, or color, of the light. Conceptual Physics Chapter 38

25. The Photoelectric Effect • The energy of a wave is spread out along a broad front. • For the energy of a light wave to be concentrated enough to eject a single electron from a metal surface is unlikely. • The photoelectric effect suggests that light interacts with matter as a stream of particle-like photons. Conceptual Physics Chapter 38

26. The Photoelectric Effect • Einstein explained the photoelectric effect in terms of photons. • Only one photon is absorbed by each electron ejected from the metal. • If the energy in the photon is large enough, the electron will be ejected from the metal. • The absorption of a photon by an atom in the metal surface is an all-or-nothing process. • The number of photons that hit the metal has nothing to do with whether a given electron will be ejected. Conceptual Physics Chapter 38

27. The Photoelectric Effect • The number of photons in a light beam controls the brightness of the whole beam. • The frequency of the light controls the energy of each individual photon. • In 1916, every aspect of Einstein’s interpretation of the photoelectric effect was confirmed by American physicist Robert Millikan, including the direct proportionality of photon energy to frequency. Run Simulation Conceptual Physics Chapter 38

28. The Particle Nature of Light • Light behaves like waves when it travels in empty space, and like particles when it interacts with solid matter. • The photograph below, taken in exceedingly feeble light, is another demonstration of the particle nature of light. 3.0 x 103 photons 1.2 x 104 photons 9.3 x 104 photons 3.6 x 106 photons 2.8 x 107 photons 7.6 x 105 photons Conceptual Physics Chapter 38

29. The Wave Nature of Particles • If waves can have particle properties, can particles have wave properties? • This question was posed by the French physicist Louis de Broglie and his answer later won the Nobel Prize in physics. • De Broglie suggested that all matter could be viewed as having wave properties. Conceptual Physics Chapter 38

30. The de Broglie Wavelength • All particles—electrons, protons, atoms, marbles, and even humans—have a wavelength: where h is Planck’s constant. Conceptual Physics Chapter 38

31. h h 6.63 x 10-34 J·s 6.63 x 10-34 J·s λ = = = = mv p (9.1 x 10-31 kg)·(1 x 106 m/s) (1 kg)·(10 m/s) The de Broglie Wavelength • A particle of large mass and ordinary speed has too small a wavelength to be detected by conventional means. • A tiny particle—such as an electron—moving at typical speed has a detectable wavelength. = 6.63 x 10-35 m = 7.29 x 10-10 m Conceptual Physics Chapter 38

32. Electron Waves • The wavelength of electrons is smaller than the wavelength of visible light but large enough for noticeable diffraction. • A beam of electrons can be diffracted and undergoes wave interference under the same conditions that light does. Conceptual Physics Chapter 38

33. Electron Waves • The diffraction pattern of an electron beam shown on the left is very similar to the diffraction pattern of light shown on the right. Conceptual Physics Chapter 38

34. Electron Waves • An electron microscope uses the wave nature of electrons. • The wavelength of electron beams is typically thousands of times shorter than the wavelength of visible light which allows an electron microscope to distinguish details thousands of times smaller than is possible with normal light microscopes. Conceptual Physics Chapter 38

35. Electron Waves • Bohr knew that electrons could only occupy orbits at discrete distances from the atomic nucleus – but WHY? • This was explained by thinking of the electron not as a particle whirling around the nucleus but as a wave. • According to de Broglie’s theory of matter waves, electron orbits exist only where an electron wave closes in on itself in phase. Conceptual Physics Chapter 38

36. Electron Waves • Electron orbits exist only when the circumference of the orbit is a whole-number multiple of the wavelength. • When the wave does not close in on itself in phase, it undergoes destructive interference. Conceptual Physics Chapter 38

37. Electron Waves • Orbit circumferences are whole-number multiples of the electron wavelengths, which differ for the various elements. • This results in discrete energy levels, which characterize each element. • Since the circumferences of electron orbits are discrete, the radii of these orbits, and hence the energy levels, are also discrete. Conceptual Physics Chapter 38

38. Electron Waves • In this simplified version of de Broglie’s theory of the atom, the waves are shown only in circular paths around the nucleus. Run Simulation Conceptual Physics Chapter 38

39. Electron Waves • In the modern wave model of the atom, electron waves also move in and out, toward and away from the nucleus. • The electron wave is in three dimensions, an electron “cloud.” Conceptual Physics Chapter 38

40. Relative Sizes of Atoms • A common misconception is that more massive atoms are larger in size than less massive atoms. • Helium, which is approximately twice as massive as hydrogen, is actually smaller in size than hydrogen. Conceptual Physics Chapter 38

41. Relative Sizes of Atoms • The single proton in a hydrogen atom holds one negatively charged electron in an orbit at a particular radius. Conceptual Physics Chapter 38

42. Relative Sizes of Atoms • In helium, there are twice as many protons in the nucleus, which requires twice as many electrons surrounding the nucleus (to remain neutral). • Twice as much electrical charge means there is twice as much electrical force acting between the protons and electrons. • This draws the electrons in closer to the nucleus making helium smaller than hydrogen. Conceptual Physics Chapter 38

43. Relative Sizes of Atoms • In a lithium atom, an additional proton pulls the electrons into an even closer orbit, but holds a third electron in a second orbit. • Lithium is slightly larger than helium due to the additional orbit that is required. Conceptual Physics Chapter 38

44. Relative Sizes of Atoms • As the number of protons in the nucleus increases from 3 to 4 (for Beryllium), the inner orbits shrink due to the stronger electrical attraction to the nucleus. • This trend continues as you move across the periodic table from left to right. Conceptual Physics Chapter 38

45. Relative Sizes of Atoms • As the number of protons in the nucleus increases from 10 to 11 (for Sodium), the atom size increases slightly again with the addition of the third energy level. • In general, the heavier elements are not much larger in diameter than the lighter elements. • The diameter of the uranium atom, for example, is only about three times the diameter of hydrogen, even though it is 238 times more massive. Conceptual Physics Chapter 38

46. Quantum Physics • The branch of physics that is the general study of the microworld of photons, atoms, and nuclei is called quantum physics. • The study of the motion of these particles is called quantum mechanics. • Physicists believe that the Newtonian laws that work so well for macroscopic objects simply do not apply to the microworld of the atom. Conceptual Physics Chapter 38

47. Quantum Physics • The subatomic interactions described by quantum mechanics are governed by laws of probability, not laws of certainty. • There are fundamental uncertainties in the measurements of the atomic domain. • Subatomic measurements, such as the momentum and position of an electron or the mass of an extremely short-lived particle, may have uncertainties that are comparable to the magnitude of the quantities themselves! Conceptual Physics Chapter 38