CHAPTER 5

1. CHAPTER 5 • Periodicity an Atomic Structure

2. The Periodic Table Developed in 1869 by Dmitri Mendeleev.

3. Electromagnetic Radiation • wavelengthl(Greek lower case lambda) • distance from the top (crest) of one wave to the top of the next wave • units of distance - m, cm, Å • 1 Å = 1  10–10 m = 1  10–8 cm • frequency(Greek lower case nu) • this is sometimes represented as  (italicized v) • number of crests (wavelengths) that pass a given point per second • units of frequency = 1/time or s–1 or Hertz (Hz)

4. Electromagnetic Radiation • Relationship for electromagnetic radiation • c = l • c = velocity of light • 3.00  108 m/s or 3  1010 cm/s

5. Electromagnetic Radiation • Example 1: What is the frequency of green light of wavelength 5200Å? (c = 3.00  108 m/s) • First convertÅto m

6. Atomic Spectra and Bohr Theory • Rydberg’s equation is an empirical equation that relates the wavelengths of the lines in the hydrogen spectrum. You will encounter the universal gas constant R later. Don’t confuse it with Rydberg’s constant R.

7. Electromagnetic Radiation • Why worry about wavelength and frequency? • These can be used to calculate energy. • Again, why? • Energy does lots of things both good and bad. • How much light at what frequency is needed to cause cancer? • How many cells are required to work a calculator in dim light? • How sensitive is a motion detector or electric eye timer? • How much light is required to darken light sensitive glasses? • Etc.

8. Electromagnetic Radiation • Max Planck calculated the energy that is quantized in a photon. • The energy of light can be expressed as

9. Electromagnetic Radiation • Example 2: What is energy of a photon of green light with wavelength 5200 Å? (c = 3.00  108 m/s; h = 6.626 10–34 J·s) 5200 Å = 5.200  10–7 m

10. Electromagnetic Radiation • Example 3: What is energy of 1 mole of photons of green light with wavelength 5200 Å? • From the previous example

11. The Wave Nature of the Electron • Louis de Broglie postulated that electrons have wave-like properties • The wavelengths of electrons are described by the de Broglie relationship.

12. Photoelectric Effect • Albert Einstein explained that light had both particle and energy characteristics. • The particle/energy unit of light was called a photon. • FYI. Einstein won the 1921 Nobel Prize in Physics for this discovery.

13. Atomic Spectra and Bohr Theory • It had been known that an electric current passing through a gas in a vacuum tube (at very low pressure) caused the gas to emit light. • This light could be broken into its components and was found to be a series of bright lines. This is a bright line or emission spectrum

14. Atomic Spectra and Bohr Theory • It was also known that if you passed a beam of white light through a sample of gas, the spectrum would show a series of dark lines where the specific wavelengths of light had been absorbed. This is dark line or absorption spectra.

15. Atomic Spectra and Bohr Theory • These spectra are as characteristic as fingerprints and can be used to identify elements. • This is commonly used to identify the elements in individual stars and the atmospheres of their planets.

16. Atomic Spectra and Bohr Theory • The spectra of atoms provides quite a bit of information about their internal structure. • Bohr, Schrodinger, and Heisenberg were some of the first to translate the language of atoms.

17. The Origin of Spectral Lines • Light of a characteristic wavelength (and frequency) is absorbed when an electron jumps from lower E (orbit) to higher E (orbit). • This jump in energy is the original quantum leap. • This is the origin of absorption spectrum. • The energy is specifically characteristic of the energy quantum levels available to the electrons in an elements electron shell.

18. The Wave Nature of the Electron • Electrons, all particles for that matter, have both a particle and a wave like character. • Wave-particle duality is a fundamental property of submicroscopic particles. • Newtonian physics (gravity, friction, etc.) deals with regular objects. • Subatomic particles follow their own laws of physics called quantum mechanics.

19. Quantum Mechanical Picture • Heisenberg Uncertainty Principle • It is impossible to determine simultaneously both the position and momentum of an electron. • Any device for detecting the motion of an electron disturbs its position and/or momentum. • Therefore the positions and momentum of electrons must be described in terms of probability functions (, the Greek psi).

20. Quantum Numbers • Basic Postulates of Quantum Theory Atoms and molecules can exist only in certain energy states. In each energy state, the atom or molecule has a definite energy. When an atom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition). The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers.

21. Quantum Numbers • Quantum numbers are solutions of the Schrödinger, Heisenberg & Dirac equations • Four quantum numbers are necessary to describe the energy states of electrons in atoms n –the principle quantum number  – subsidiary quantum number m – magnetic quantum number ms – spin quantum number

22. Quantum Numbers • Principal Quantum Number – n • This is the first quantum number and describes the shell or layer that the electrons are found in. • These are numbered sequentially with the innermost level beginning with the number 1. • n = 1, 2, 3, 4, ...... • There is an alternate numbering system using letters, the first level begins with letter K. • n = K, L, M, N, ...... • The electron’s energy depends principally on n.

23. Quantum Numbers • Subsidiary Quantum number – • The subsidiary quantum number, , describes theshape of the orbital the electron occupies. • These have the value of n-1 and are assigned the values of  = 0, 1, 2, 3, 4, 5, .......(n-1) Like n, these values may also be described as letters •  = s (0), p (1), d (2), f (3), g (4), h (5),.. • This is the shape (volume) that the electrons occupy 90-95% of the time.

24. Quantum Numbers • Magnetic quantum number –m • This quantum number indicates specifically which orbital the electron resides in. • Unlike , m is only described by numbers and may have a value of + , 0, –  (or ±  and 0). • For n = 1,  =0, and m= 0 • this describes the s orbital • there is only 1 s orbital per quantum level (shell) • and the first shell only has one type of orbital

25. Quantum Numbers • Magnetic quantum number –m • For n = 2,  = 0 and 1 • for n = 2  = 0, m = 0 • this is an s orbital (remember 1 s per level) • for n = 2  = 1, m = +1, 0, –1 • this is a p orbital, there are 3 p orbitals • Row 2 (the L shell) is the first shell to have p orbitals. • The 3 p orbitals are described according to the axis they lie along.

26. Quantum Numbers • Magnetic quantum number –m • For n = 3,  = 0, 1, and 2 • for n = 3  = 0, m = 0 • this is an s orbital (remember 1 s per level) • for n = 3  = 1, m = +1, 0, –1 • this is a p orbital, beginning with row 2 there are 3 p orbitals per shell • for n = 3  = 2, m = +2, +1, 0, –1, –2 • this is a d orbital, beginning with row 3, the possibility of d orbitals exists (even though d orbitals don’t show up until an element has already begun to fill shell 4)

27. Quantum Numbers • Magnetic quantum number –m • For n = 4,  = 0, 1, 2,and 3 • for n = 4  = 0, m = 0(1 orbital) • this is an s orbital (remember 1 s per level) • for n = 4  = 1, m = +1, 0, –1 • this is a p orbital, 1 group of 3 p orbitals per shell beginning with Row 2 • for n = 4  = 2, m = +2, +1, 0, –1, –2 • this is a d orbital, 1 group of 5 d orbitals (possible) per shell beginning with Row 3 • for n = 4  = 3, m = +3, +2, +1, 0, –1, –2, –3 • these are f orbitals, 1 group of 7 f orbitals (possible) per shell beginning with Row 4

28. Quantum Numbers • Spin Quantum Number - ms • This is the final quantum number and represents the spin of the electron. • The spin of an electron is arbitrarily assigned a value of ± ½. • Each orbital may hold a maximum of 2 electrons, one with a spin of +½, the other with a spin of –½ • Pauli Exclusion Principle • No two electrons in an atom can have the same set of 4 quantum numbers.

29. Atomic Orbitals • Atomic orbitals are defined as regions of space where the probability of finding an electron about an atom is highest. • The orbital levels are described either as: • n = 1, 2, 3, 4, 5… • or by K, L, M, N, ….. • FYI. There is a specific type of nuclear decay in which the nucleus captures an interior electron as part of its radioactive decay. This decay is called K-capture after the orbital the electron came from.

30. Atomic Orbitals • The innermost orbital of any level is the s orbital. • There is one s orbital per level. •  = 0 and m = 0 • The s orbital is spherically symmetrical.

31. Atomic Orbitals • Row 2 is the first to have p orbitals •  = 1 and m = 1, 0, –1 These orbitals are described as dumbbell or peanut shaped. There are 3 mutually perpendicular p orbitals directed along the axes of a Cartesian coordinate.

32. Atomic Orbitals • Row 3 is the first to have d orbitals allowed •  = 2 and m = 2, 1, 0, –1, –2 • There are 4 clover leaf shaped d orbitals rotated 45° off the Cartesian axes And 1 peanut shaped orbital with a halo or donut around it.

33. Atomic Orbitals • Row 4 is the first to have f orbitals allowed •  = 3 and m = 3, 2, 1, 0, –1, –2, –3 • These are the most complex shaped orbitals. • Four are described as double cloverleaf or double dumbbell shaped orbitals. The remaining three f orbitals are dumbbell shaped each with a pair of halos or donuts

34. Atomic Orbitals • Each atom from H through the most recently discovered is built up sequentially one electron at a time.

35. Atomic Orbitals • The last quantum number deals with the spin of the electrons. • Electrons spin and since they carry a charge, this spinning results in a magnetic field. • Experimentally it has been determined that unpaired electrons have their spin aligned (their magnetic fields add together). • Each orbital may contain a maximum of 2 electrons. • For electrons to pair, they must have opposite spins.

36. Atomic Orbitals • Compounds which contain unpaired electrons are paramagnetic. • paramagnetic – attracted to a magnet • Compounds in which all electrons are paired are diamagnetic. • diamagnetic – repelled by a magnet • There is one more type of magnetism associated with compounds, ferromagnetism. • ferromagnetic – compounds of Fe, Co, or Ni, which may be permanently magnetized

37. Atomic Orbitals • The maximum number of orbitals per n level is may be calculated by n2 • The maximum number of electrons that may exist per n level is 2n2 • Energy Level # of Orbitals Max. # of e– • n n2 2n2 • 1 1 2 • 2 4 8 • 3 9 18 • 4 16 32

38. Quantum Mechanics and Atomic Line Spectra Lyman series – ultraviolet Balmer series – visible Paschen series - infrared

39. Electronic Configurations • Aufbau Principle • The electron that distinguishes an element from the previous element enters the lowest energy atomic orbital available. • Hund’s Rule • Electrons will occupy all orbitals singly before pairing can begin. • The spins of these electrons will be aligned.

40. Electronic Configurations • According to the Aufbau Principle, electrons enter the lowest energy atomic orbital available. • The first hitch in this orderly progression occurs at the end of row 3 of the periodic table. • 4s is lower in energy than 3d which is followed by 4p • This is repeated again at the end of row 4 • 5s is lower in energy than 4d which is followed by 5p • This is repeated again and develops a new twist at the lanthanides.

41. Electronic Configurations • The reason for this anomaly is Hund’s Rule. • Electron Orbital Stability • Completely filled orbitals are very stable. • Completely empty orbitals are very stable. • Half-filled orbitals, while not as stable as filled or empty orbitals, are much more stable than partially filled orbitals. • Reactions occur to obtain orbital stability.

42. Electronic Configurations • Consider the two possibilities available to an electron entering after 3p. partially filled orbital unstable half filled orbital stable Now add the second electron to these two possibilities. partially filled orbitals unstable filled orbital verystable

43. Electronic Configurations • The easiest way to see this is to use the periodic table.

44. 1 2 3 4 3d 5 4d 6 5d 7 6d 4f 5f Electronic Configurations • An alternate method to view the periodic table is: d-transition elements f-transition elements

45. Electronic Configurations • Just as each element differs from its predecessor by the addition of one proton, each element differs from the preceding element by the addition of 1 electron to its orbital configuration. • Atomic orbitals are built up by this step-wise addition of electrons.

46. Electronic Configurations • 1st Row Elements Remember, the atomic number is equal to the number of electrons found in the neutral atom. Each positive charge means 1 less electron than this number. Each negative charge means 1 more electron than the number of protons present.

47. Electronic Configurations • 2nd Row Elements

48. Electronic Configurations • 3rd Row Elements

49. Electronic Configurations • 4th Row Elements Two half filled orbitals are more stable than a filled and partially filled orbital. This is seen throughout the elements.

50. Electronic Configurations • 4th Row Elements