Chapter 7: Electronic Structure

1. Chapter 7: Electronic Structure • Electrons in an atom determine virtually all of the behavior of the atom. • Quantum theory – the study of how energy and matter interact on an atomic level. • To understand the electron, we must first understand light. • Reason =

2. Light • Also known as electromagnetic radiation. • Ex) Visible light, Infrared, X-ray, Radio. • All electromagnetic radiation have several common characteristics. • Light as a wave • Light as a particle • “Duality of Light”

3. Electromagnetic Radiation

4. Light as a Wave • Wavelength (l – lambda) = • Frequency (n – nu) =

5. Light as a Wave • Wavelength and Frequency are inversely related.

6. Electromagnetic Spectrum • Shows the full range of electromagnetic radiation that exists.

7. Light as a Wave • The product of the wavelength and the frequency, though, is a constant. • c = l  n, where c is the speed of light. • Thus, if we know the frequency, we can find the wavelength and vice versa. • LEP #1(a).

8. Proof of Waves • Waves exhibit certain properties when they interact with each other. • Young’s Double Slit experiment.

9. Proof of Waves

10. Proof of Waves

11. Light as a Particle • The wave nature of light does not explain all of the properties of light. • Blackbody radiation – when solids are heated, they will glow. • Color depends on the temperature.

12. Light as a Particle • Max Planck – proposed a theory that energy from blackbody radiation could only come in discrete “chunks” or quanta. • E = h n • h = 6.626 x 10-34 Js • LEP #1(b).

13. Light as a Particle • The photoelectric effect (Einstein) also is proof that light must have a tiny mass and thus act as a particle (photon). • LEP #2, #3.

14. Line Spectra • When a gas like H2, Hg, or He is subjected to a high voltage, it produces a line spectrum consisting of specific wavelengths.

15. Line Spectra

16. High Voltage Excitation

17. Identifying Metals Na = yellow K = violet Li = red Ba = pale green

18. Line Spectra • The four lines for hydrogen were found to follow the formula: • Where the values of n are integers with the final state being the smaller integer.

19. Bohr Theory • How could such a simple equation work? • Niels Bohr some thirty years later came up with a theory. • Classic physics would predict that an electron in a circular path should continuously lose energy until it spiraled into the nucleus.

20. Bohr Theory • An electron can only have precise energies according to the formula: E = -RH / n2 ; n = 1, 2, 3, etc. and RH is the Rydberg constant. • An electron can travel between energy states by absorbing or releasing a precise quantity of energy.

21. Bohr Theory

22. Bohr Theory • Can not explain the line spectra for other elements due to electron-electron interactions. • Thus, the formula for Hydrogen can only be applied for that atom. • LEP #4.

23. Matter as a Wave • Louis de Broglie proposed that if light could act as both a wave and a particle, then so could matter. • Where h is Planck’s constant, m is the objects mass, and v is its velocity. • Size, though, matters. LEP #5.

24. Matter as a Wave • De Broglie was later proven correct when electrons were shown to have wave properties when they pass through a crystalline substance. • Electron microscope picture of carbon nanotubes.

25. Uncertainty Principle • German scientist Werner Heisenberg proposed his Uncertainty Principle in 1927. • History

26. Uncertainty Principle • For a projectile like a bullet, classic physics has formulas to describe the motion – velocity and position – as it travels down range.

27. Uncertainty Principle • Any attempt to observe a single electron will fail.

28. Uncertainty Principle • If you want to measure length, there is always some uncertainty in the measurement. • To improve the certainty, you would make a better measuring device. • Heisenberg, though, stated that the precision has limitations. Dx  mDv  h / 4p

29. Uncertainty Principle • Once again, size makes a big difference. • LEP #6

30. Uncertainty Principle • Determinacy vs. Indeterminacy • According to classical physics, 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

31. Uncertainty Principle

32. Quantum Mechanics • The quantum world is very different from the ordinary world. • Millions of possible outcomes and all are possible! • Quantum Café • “I am convinced that He (God) does not play dice.” Albert Einstein

33. Hy = Ey • Erwin Shrödinger proposed an equation that describes both the wave and particle behavior of an electron. • The mathematical function, y, describes the wave form of the electron. Ex) a sine wave. • Squaring this function produces a probability function for our electron.

34. Atomic Orbitals • A graph of y2 versus the radial distance from the nucleus yields an electron “orbital”. • An “orbital” is a 3D shape of where an electron is most of the time. • An “orbital” can hold a maximum of two electrons.

35. Atomic Orbitals • The Probability density function represents the probability of finding the electron.

36. Atomic Orbitals • A radial distribution plot represents the totalprobability of finding an electron within a thin spherical shell at a distancer from the nucleus • The probability at a point decreases with increasing distance from the nucleus, but the volume of the spherical shell increases

37. Atomic Orbitals • The net result for the Hydrogen electron is a most probable distance of 52.9pm.

38. Atomic Orbitals • For n=2 and beyond, the orbital will have n-1 nodes. • A node is where a zero probability exists for finding the electron.

39. Atomic Orbitals  2s orbital = 1 node 3s orbital = 2 nodes 

40. Quantum Numbers • An electron can be described by a set of four unique numbers called quantum numbers. • Principle quantum number, n = describes the energy level of the electron. As n increases so does the energy and size of the orbital. n can have values of integers from 1 to infinity.

41. Quantum Numbers • Azimuthal quantum number, l, defines the shape of the orbital. The possible values of l depends on n and can be all of the integers from 0 to n-1. However, the values of 0, 1, 2, and 3 have letter designations of s, p, d, and f, respectively.

42. Quantum Numbers • Magnetic quantum number, mldescribes the orientation in space of the orbital. The possible values of this quantum number are –l 0  +l. When l is not zero, the magnetic q.n. has more than one value. These multiple values produce degenerative orbitals – orbitals of equal energy.

43. Quantum Numbers • Spin quantum number, ms describes the electron spin of the electron. This value is either +1/2 or –1/2.

44. Quantum Numbers

45. Quantum Numbers • Pauli Exclusion Principle – no electron in an atom can have the same set of four quantum numbers. • Ne = 10 electrons • LEP #7.

46. Subshell Designations

47. Orbitals • s type orbitals are spherical in shape.

48. Orbitals • p type orbitals have two lobes.

49. Orbitals • d type orbitals generally have four lobes.