Periodic Table: Why the repetition

1. Periodic Table: Why the repetition • The periodic table is the most important organizing principle in chemistry. • Chemical and physical properties of elements in the same group are similar. • All chemical and physical properties vary in a periodic manner, hence the name periodic table. For instance, hydrogen, lithium, sodium, and potassium, were all known to make chlorides in a 1:1 mole ratio. The “wrapping around” of the periodic table was done to capture these similarities into columns.

2. Periodic Table Most tables in your book (other than the periodic table) look nothing like the periodic table. Instead they are a few columns of data. The periodic table, done this way, would look like this: Notice that the actual periodic table does not uniformly order the elements by atomic mass. (Compare argon to potassium.) etc.

3. So how did we get the atomic numbers? • The atomic masses are clearly pretty good guides (almost perfect, in fact) • In 1913, an English spectroscopist H.G.J. Moseley performed a series of x-ray experiments with the following data:

4. Periodic Table: Predictions

5. Periodic Table: Microscopic Explanation The whole rest of the chapter is generally about developing this explanation. • The proton and the electron were the two sub-atomic particles known, so the explanation had to involve them somehow. • But Moseley showed the protons uniformly increase as you go along the periodic table; they don’t behave periodically. • So the electrons must be explanation. • This makes sense: electrons are the outer part of the atom. Any time two atoms meet, the electrons meet first, So they should be most important in how two atoms interact.

6. Periodic Electron Behavior

7. Electromagnetic Radiation • Frequency (, Greek nu): • Number of peaks that pass a • given point per unit time. • Wavelength (, Greek lambda): • Distance from one wave peak • to the next. • Amplitude: Height measured from the center of the wave. The square of the amplitude gives intensity.

8. Electromagnetic Spectrum

9. Electromagnetic Spectrum: Math • Speedof a wave is the wavelength (in meters) multiplied by its frequency in reciprocal seconds. • Wavelength x Frequency = Speed •  (m) x  (s–1) = c (m/s–1)

10. Atomic Spectra: Line spectra • Line spectra:run the emitted light through a monochromator. very distinctive results. Called “atomic fingerprints.”

11. Atomic Spectra: Hydrogen spectrum “explained” Balmer showed: Works for all n integers (getting weaker are n increases). R is now called Rydberg constant. Rydberg showed it could be generalized to: For all n>m Sadly, this equation only worked for one-electron systems like H or He+ or Li2+. Many tried to generalize the equation for many-electron systems. All attempts failed.

12. The state of affairs in ~1900: • A mathematical description of the hydrogen atom spectrum was available, but it had no physical basis. (That is, there was no real “why”.) • There were two kinds of “things” in the universe: particles and waves • Particles come in discrete chunks that can be counted. That is, they are quantized. They carry energy as kinetic energy which is infinitely adjustable. • Waves do not come in discrete chunk but instead are continuous and thus are not countable like particles. They are not quantized. They have wavelengths (or frequencies) that are infinitely adjustable. They carry energy that is measurable as the intensity of the wave. How waves carry energy is unknown. • Phenomena yet to be explained: • Blackbody radiation • Photoelectric effect • How the atom works

13. Blackbody radiation When a metal chunk is resistively heated to a high enough temperature, It starts to glow. This glow depends only on the temperature and not on the material. The wavelengths of light emitted decrease as the temperature increases, starting first down in the microwave and infra-red region and sliding through the visible from red to violet, and then into the ultraviolet. Classically, blackbodies emit light at the frequency they vibrate. Because most of the atoms are highly constrained, most should vibrate very quickly and thus emit high frequency light, but in truth most emit low frequency light.

14. Waves as Particles:Quantized Energy • Blackbody radiation is the visible glow that objects with unbound electrons emit when heated. • Max Planck (1858–1947): proposed that energy is only emitted in discrete packets called quanta. • The amount of energy depends on the frequency:

15. Blackbodies explained At the time Planck’s solution was considered a mathematical oddity. That is, he had found an equation that had the same shape as the experimental blackbody curves, but the explanation behind the equation was all wrong. In fact, Planck never fully embraced quantum theory and doubted the work of Einstein and others for the rest of his life. But the key ideas were now out there: light comes in discrete chunks the energy of light is related to its frequency and not to its amplitude the energy of these chunks of light could not be just any value

16. Photoelectric Effect If you put a piece of metal in a vacuum tube, and then shine light of certain frequency on it, the metal emits electrons. This is called the photoelectric effect. Experimentally it was found that the light had to be of a high enough frequency or no electrons would be emitted. And as the light increased in frequency above this “threshhold frequency” the kinetic energy of the electrons increased. Classically, electrons oscillate at the frequency of the incoming light. And the higher the amplitude of the oscillating light, the bigger the amplitude of the electron’s oscillations. Thus any frequency of light should be able to make a metal emit electrons, and the kinetic energy should vary only as the intensity of the light increases.

17. Waves as Particles: Quantized Energy • Albert Einstein (1879–1955): • Used the idea of quanta to explain the photoelectric effect. • He proposed that light behaves as a stream of particles called photons.

18. Waves as Particles:Quantized Energy • A photon’s energy must exceed a minimum threshold for electrons to be ejected. • Energy of a photon depends only on the frequency.

19. Photoelectric Effect Explained When Einstein solved his equations to fit the experimental photoelectric effect data, he found that the photons must be carrying energy in multiples of 6.626*10-34 J s. This was exactly the constant that Planck found with entirely different experiments! At this point, this quantum theory of light was taken much more seriously. While many doubters remained for decades to come, most reasoned that the presence of the same constant (found independently) showed that there must be something real behind the theory. But still this does not explain the atom.

20. h h : For Light l = = mc p h h For a Particle : l = = mv p Particles as Waves: de Broglie wavelengths • Louis de Broglie (1892–1987): Suggested waves can behave as particles and particles can behave as waves. This is called wave–particle duality.

21. Rydberg and the Atom: Bohr Model

22. Heisenberg Uncertainty Principle • Werner Heisenberg (1901–1976): Showed that it is impossible to know (or measure) precisely both the position and velocity (or the momentum) at the same time. • The simple act of “seeing” an electron would change its energy and therefore its position.

23. Heisenberg Uncertainty Principle

24. Electron wave functions • Wave functions describe the behavior of electrons. • Each wave function contains four variables called quantum numbers. Quantum numbers must be integers. (That is, they are quantized.)The three we need now are: • • Principal Quantum Number (n) • • Angular-Momentum Quantum Number (l) • • Magnetic Quantum Number (ml)

25. Principal Quantum Number (n) • Principal Quantum Number (n):Defines the size and energy level of the orbital. n = 1, 2, 3,  • As n increases, the electrons get farther from the nucleus. • As n increases, the electrons’ energy increases. • Each value of n is called a shell.

26. Angular Momentum (l) • Angular-Momentum Quantum Number (l): Defines the three-dimensional shape of the orbital. • For an orbital of principal quantum number n, the value of l can have an integer value from 0 to n – 1. • This gives the subshell notation:l = 0= s orbital l = 1 = p orbital l = 2= d orbitall = 3= f orbital l = 4= g orbital

27. Magnetic Quantum Number (ml) • Magnetic Quantum Number (ml):Defines the spatial orientation of the orbital. • For orbital of angular-momentum quantum number, l, the value of ml has integer values from –l to +l. • This gives a spatial orientation of:l = 0 giving ml = 0 l = 1 giving ml = –1, 0, +1l = 2 giving ml = –2, –1, 0, 1, 2, and so on…...

28. Quantum Numbers

29. Orbitals and Energy

30. Electron Positions • s Orbital Shapes:

31. Electron Positions (II) • p Orbital Shapes:

32. Electron Positions (III) • d and f Orbital Shapes:

33. What are orbitals? • Orbitals (and shells & subshells) are equations (fundamentally). They are four-dimensional equations that solve the Schrodinger equation. • They are theoretical entities. • Two questions: • What do orbitals represent? • What experimental evidence do we have to support them?

34. What are orbitals? • Orbitals can be considered in two ways: • 1. Orbitals represent the “cage” in which the electron resides. The calculated probabilities represent the “pacing of the tiger in the cage.” • 2. Orbitals represent the electron itself. In the atom the electron has a wave-like existence and the orbital is the spatial area over which the wave has non-zero amplitude. The electron has no fixed shape.

35. What experimental evidence? How do atoms use shells, subshells, and orbitals? They use shells, subshells, and orbitals to organize electrons. Why do atoms organize electrons? They organize electrons in order to minimize the energy. So to find evidence of shells, subshells, and orbitals we need to measure the energies of electrons in the atom.

36. Experimental Evidence:Shells

37. Ionization Energy (IE) Experiment X-ray (hn) e- KE detector hn – KE(e-) = IE Only capable of seeing the most easily removed electron (1IE). We can rejigger the experiment to see 2IE, 3IE, etc. We also cannot see how many electrons come off.

38. What Determines theElectron’s Energy? Proximity to the nucleus The closer to the nucleus, the lower the electron’s energy (and therefore the higher the ionization energy of the electron.) The greater the number of protons in the nucleus, the greater the attraction is going to be.

39. What should IE vs. Z look like? • What should IE depend on? • As Z increases, what if the new electron is placed randomly? • As Z increases, what if new electron is placed in same shell? • As Z increases, what if each electron is placed further away from nucleus? • Any other possibilities to be considered?

40. IE Experiment Actual Data

41. Evidence for Subshells: PES experiments The PES experiment works rather like the IE experiment, but is more subtle. It allows one to see the energy at which each of the electrons comes off (not just the easiest one), and how many electrons come off at each energy. We are still making ions.

42. PES Data (Hydrogen) The most easily removed electrons from the PES data must match the IE expt. data The number of electrons coming off is shown by the height of the peak Higher ionization energies to the left, so electrons that are further from the nucleus are to the right

43. PES Data (Hydrogen and Helium)

44. PES Data (H – Li) Two different shells show as two peaks with a big gap between them

45. PES Data (H – Be)

46. PES Data (H – B) Two different shells Two subshells in the same shell

47. PES Data (B – Ne)

48. So apparently, the way the system works is that we completely fill a subshell and then move on to the next subshell, completely filling it, until there are no more subshells in a shell and then we move on to the next shell.

49. PES Data (MJ/mol)

50. PES Data (Na – Sc) 1s 2s 2p 3s 3p 3d? 4s? 4s? 3d?