Quantum- Model of Atom

1. Quantum- Model of Atom Kim Shih Ph.D. Kim Shih

2. The Behavior of the Electrons • Electrons are incredibly small • a single speck of dust has more electrons than the number of people who have ever lived on earth • Electron behavior determines much of the behavior of atoms • Directly observing electrons in the atom is impossible, the electron is so small that observing it changes its behavior • even shining a light on the electron would affect it Kim Shih

3. A Theory that Explains Electron Behavior • The quantum-mechanical model explains the manner in which electrons exist and behave in atoms • Understand and predict the properties of atoms that are directly related to the behavior of the electrons • why some elements are metals and others are nonmetals • why some elements gain one electron when forming an anion, whereas others gain two • why some elements are very reactive while others are practically inert • and other periodic patterns we see in the properties of the elements Kim Shih

4. The Nature of Light:Its Wave Nature • Light is a form of electromagnetic radiation • composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field • an electric field is a region where an electrically charged particle experiences a force • a magnetic field is a region where a magnetized particle experiences a force • All electromagnetic waves move through space at the same, constant speed • 3.00 x 108 m/s in a vacuum = the speed of light, c Kim Shih

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6. Characterizing Waves • The amplitude is the height of the wave • the distance from node to crest • The wavelength (l)is a measure of the distance covered by the wave • the distance from one crest to the next • The frequency (n)is the number of waves that pass a point in a given period of time • the number of waves = number of cycles • units are hertz (Hz) or cycles/s = s−1 • The total energy is proportional to the amplitude of the waves and the frequency • the larger the amplitude, the more force it has Kim Shih

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8. The Relationship Between Wavelength and Frequency • For waves traveling at the same speed in the same distance, the shorter the wavelength, the more frequently they pass • This means that the wavelength and frequency of electromagnetic waves are inversely proportional • because the speed of light is constant, if we know wavelength we can find the frequency, and vice versa Kim Shih

9. Calculate the wavelength of red light with a frequency of 4.62 x 1014 s−1 Calculate the wavelength of a radio signal with a frequency of 100.7 MHz. 1MHz= 106 s-1 Kim Shih

10. What causes different color? What causes different brightness? Kim Shih

11. Color • The color of light is determined by its wavelength • or frequency • White light is a mixture of all the colors of visible light • a spectrum • RedOrangeYellowGreenBlueViolet • When an object absorbs some of the wavelengths of white light and reflects others, it appears colored • the observed color is predominantly the colors reflected Kim Shih

12. Amplitude & Wavelength Kim Shih

13. Electromagnetic Spectrum Kim Shih

14. Interference • The interaction between waves is called interference • When waves interact so that they add to make a larger wave it is called constructive interference • waves are in-phase • When waves interact so they cancel each other it is called destructive interference • waves are out-of-phase Kim Shih

15. Interference Kim Shih

16. Diffraction • When traveling waves encounter an obstacle or opening in a barrier that is about the same size as the wavelength, they bend around it – this is called diffraction • traveling particles do not diffract • The diffraction of light through two slits separated by a distance comparable to the wavelength results in an interference pattern of the diffracted waves • An interference pattern is a characteristic of all light waves Kim Shih

17. Diffraction Kim Shih

18. 2-Slit Interference Kim Shih

19. The Photoelectric Effect Many metals emit electrons when a light shines on their surface Kim Shih

20. Photoelectric Effect Photoelectric Effect: Irradiation of clean metal surface with light causes electrons to be ejected from the metal. Furthermore, the frequency of the light used for the irradiation must be above some threshold value, which is different for every metal. Kim Shih

21. Photoelectric Effect:The Problem • In experiments it was observed that there was a minimum frequency needed before electrons would be emitted • called the threshold frequency • regardless of the intensity(amplitude) • It was also observed that high-frequency light from a dim source caused electron emission without any lag time Kim Shih

22. Einstein’s Explanation • Einstein proposed that the light energy was delivered to the atoms in packets, called quanta or photons • The energy of a photon of light is directly proportional to its frequency • the proportionality constant is called Planck’s Constant, (h)and has the value 6.626 x 10−34 J∙s Kim Shih

23. Exercise Kim Shih

24. Calculate the number of photons in a laser pulse with wavelength 337 nm and total energy 3.83 mJ Hint: Step 1: Convert all the units Step 2: Find out individual photon energy Step 3: Total energy /individual energy = total photon Kim Shih

25. What is the frequency of radiation required to supply 1.0 x 102 J of energy from 8.5 x 1027 photons? Kim Shih

26. Spectra • When atoms or molecules absorb energy, that energy is often released as light energy • fireworks, neon lights, etc. • When that emitted light is passed through a prism, a pattern of particular wavelengths of light is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrum • non-continuous • can be used to identify the material • flame tests Kim Shih

27. Emission Spectra Kim Shih

28. Na K Li Ba Identifying Elements with Flame Tests Kim Shih

29. Examples of Spectra Kim Shih

30. = R∞ = R∞ 1 1 1 1 1 1 λ λ - - m2 22 n2 n2 Electromagnetic Energy and Atomic Line Spectra Johann Balmer in 1885 discovered a mathematical relationship for the four visible lines in the atomic line spectra for hydrogen. Johannes Rydberg later modified the equation to fit every line in the entire spectrum of hydrogen. R (Rydberg Constant) = 1.097 x 10-2 nm-1 Kim Shih

31. Rutherford’s Nuclear Model • The atom contains a tiny dense center called the nucleus • the volume is about 1/10 trillionth the volume of the atom • The nucleus is essentially the entire mass of the atom • The nucleus is positively charged • the amount of positive charge balances the negative charge of the electrons • The electrons move around in the empty space of the atom surrounding the nucleus Kim Shih

32. Problems with Rutherford’s Nuclear Model of the Atom • Electrons are moving charged particles • According to classical physics, moving charged particles give off energy • Therefore electrons should constantly be giving off energy • should cause the atom to glow! • The electrons should lose energy, crash into the nucleus, and the atom should collapse!! • but it doesn’t! Kim Shih

33. The Bohr Model of the Atom Neils Bohr (1885–1962) • Bohr’s major idea was that the energy of the atom was quantized, and that the amount of energy in the atom was related to the electron’s position in the atom • quantized means that the atom could only have very specific amounts of energy • The electrons travel in orbits that are at a fixed distance from the nucleus • stationary states • therefore the energy of the electron was proportional to the distance the orbit was from the nucleus • Electrons emit radiation when they “jump” from an orbit with higher energy down to an orbit with lower energy • the emitted radiation was a photon of light • the distance between the orbits determined the energy of the photon of light produced Kim Shih

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35. Bohr Model of H Atoms Kim Shih

36. Wave Behavior of Electrons Louis de Broglie (1892–1987) • de Broglie proposed that particles could have wave-like character • de Broglie predicted that the wavelength of a particle was inversely proportional to its momentum • Because it is so small, the wave character of electrons is significant Kim Shih

37. Exercise Kim Shih

38. Calculate the wavelength of an electron traveling at 2.65 x 106 m/s Hint: v = 2.65 x 106 m/s, m = 9.11 x 10−31 kg h= 6.626 x 10−34 J∙s, J = kg m2 /s2 l=h/mv Determine the wavelength of a neutron traveling at 1.00 x 102 m/s (Massneutron = 1.675 x 10−24 g) Kim Shih

39. Complementary Properties • When you try to observe the wave nature of the electron, you cannot observe its particle nature – and vice-versa • wave nature = interference pattern • particle nature = position, which slit it is passing through • The wave and particle nature of the electron are complementary properties • as you know more about one you know less about the other Kim Shih

40. Quantum Mechanics and the Heisenberg Uncertainty Principle In 1926 Erwin Schrödinger proposed the quantum mechanical model of the atom which focuses on the wavelike properties of the electron. In 1927 Werner Heisenberg stated that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle. Kim Shih

41. Uncertainty Principle • Heisenberg stated that the product of the uncertainties in both the position and speed of a particle was inversely proportional to its mass • x = position, Dx = uncertainty in position • v = velocity, Dv = uncertainty in velocity • m = mass • This means that the more accurately you know the position of a small particle, such as an electron, the less you know about its speed • and vice-versa Kim Shih

42. Heisenberg Uncertainty Principle Based on de Broglie equation, electron velocity related to λ. Electron has both wave and particle properties called Duality It means we can not measure its position and velocity at the same time. Kim Shih

43. You are wrong, because your brain was hit by an apple I know gravity Kim Shih

44. Determinacy vs. Indeterminacy • According to classical physics(Newton’s Law), particles move in a path determined by the particle’s velocity, position, and forces acting on it • determinacy = definite, predictable future • Because we cannot know both the position and velocity of an electron, we cannot predict the path it will follow • indeterminacy = indefinite future, can only predict probability • The best we can do is to describe the probability an electron will be found in a particular region using statistical functions Kim Shih

45. Trajectory vs. Probability Kim Shih

46. Schrödinger’s Equation • Schödinger’s Equation allows us to calculate the probability of finding an electron with a particular amount of energy at a particular location in the atom • Solutions to Schödinger’s Equation produce many wave functions, Y • A plot of distance vs. Y2 represents an orbital, a probability distribution map of a region where the electron is likely to be found Kim Shih

47. Solutions to the Wave Function, Y • Calculations show that the size, shape, and orientation in space of an orbital are determined to be three integer terms in the wave function • added to quantize the energy of the electron • These integers are called quantum numbers • principal quantum number, n • angular momentum quantum number, l • magnetic quantum number, ml Kim Shih

48. Probability of finding electron in a region of space (Y2) solve Wave equation Wave function or orbital (Y) Wave Functions and Quantum Numbers A wave function is characterized by three parameters called quantum numbers, n, l, ml. Kim Shih

49. Principal Quantum Number (n) • Describes the size andenergylevel of the orbital • Commonly called shell • Positive integer (n = 1, 2, 3, 4, …) • As the value of n increases: • The energy of the electron increases • The average distance of the electron from the nucleus increases • an electron would have E = 0 when it just escapes the atom Kim Shih

50. Principal Energy Levels in Hydrogen Kim Shih