Electronic Configurations and the Periodic Table

1. Chapter 7 Electronic Configurations and the Periodic Table Niels H. Bohr 1885-1962.* Related Periodic Table to atomic atomic structure and spectral behavior. Robert W. Bunsen 1811-1899. Established the science of spectroscopy.

2. The Wave Nature of Light • Modern atomic theory arose out of studies of the interaction of radiation with matter. • Electromagnetic radiation moves through a vacuum with a speed of 2.99792458  108 m/s. • (We will usually round off to 3 x 108 m/s) • Electromagnetic waves have characteristic wavelengths (l) and frequencies (n) . • Example: visible radiation has wavelengths between • l = 400 nm (violet) and 750 nm (red).

3. The Wave Nature of Light Some examples of EM radiation: visible light ultraviolet radiation (UV) infrared radiation (IR) radio waves microwaves x-rays ?sound waves?

4. The Wave Nature of Light The wavelength, λ, is the distance between crests in a wave The frequency, n, of a wave is the number of cycles which pass a point in one second. The speed of a wave, c, is given by its frequency multiplied by its wavelength: c = nl where c = 3 x 108 m.s-1 (the “speed of light”)

5. ν ν as λ as λ Short wavelength High frequency Long wavelengthSmall frequency

6. The Wave Nature of Light

8. Quantized Energy and Photons Some problems affecting science in 1900: Blackbody radiation Photoelectric effect Line spectra Spiraling of electrons into nucleus

9. Quantized Energy and Photons Planck: energy can only be absorbed or released from atoms in certain amounts called quanta. This energy is proportional to the frequency ,, of the radiation. The proportionality constant, h, is called Planck’s constant and is equal to: 6.626  10-34 J.s E = h Matter can absorb or emit energy only in quantum units which are multiples of h : ΔE = nh where n=integer

10. Quantized Energy and Photons • The Photoelectric Effect • The photoelectric effect provides evidence for the particle nature of light -- “quantization”. • If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal. • The electrons will only be ejected once the thresholdfrequency, υ, is reached. • Below the threshold frequency, no electrons are ejected. • This is consistent with the Planck statement that light energy depends only on frequency.

11. Quantized Energy and Photons The Photoelectric Effect

12. The Photoelectric Effect threshold frequency Energy of ejected electrons no frequency,n • Einstein assumed that light traveled in energy packets called photons. • The energy of one photon, E = hn.

13. Calculate the wavelength and energy of a photon with frequency of 2.3 x 1014 Hz • 2. Calculate the frequency and energy of a photon with a wavelength of 420 nm

14. Lothar Meyer 1830-1895. Codiscoverer of Periodic Table. Meyer noticed a periodic trend in atomic sizes and suggested there was an inner structure to the atom, although it was too early to guess what the nature of this structure was.

15. Bohr’s Model of the Hydrogen Atom • Bohr’s Model • Rutherford assumed the electrons orbited the nucleus analogous to planets around the sun. • However, a charged particle moving in a circular path should lose energy. • This means that the atom should be unstable according to Rutherford’s theory. • Bohr noted the line spectra of certain elements and assumed the electrons were confined to specific energy states. These were called orbits.

16. Bohr’s Model of the Hydrogen Atom Line Spectra Colors from excited gases arise because electrons move between energy states in the atom. These are called line spectra. Na H

17. Line Spectra prism gas discharge tube

18. Bohr’s Model of the Hydrogen Atom Absorption Emission E4 E3 E2 E1

19. E3 E2 Absorption E1 N Emission

20. Bohr’s Model of the Hydrogen Atom The first orbit in the Bohr model has energy E1 and is assigned a quantum number, n=1. The next orbit has energy E2 and quantum number, n=2. Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (hn). The amount of energy absorbed or emitted on movement between states is given by BUT....... The Bohr model doesn’t work!

21. The Wave Behavior of Matter Knowing that light has a particle nature, it seems reasonable to ask if matter has a wave nature. Using Einstein’s and Planck’s equations, de Broglie supposed: The momentum, mv, is a particle property, where as  is a wave property. In one equation de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small.

22. Quantum Mechanics and Atomic Orbitals • Schrödinger proposed an equation that contains both wave and particle terms. (impress your friends) • Solving the equation leads to the wave function ΨThese are later referred to as orbitals. • Wave functions (orbitals, Ψ ) are mathematical quantities. • The square of the wave function, Ψ2 gives the probability of finding the electron in some region of space. • Orbitals have shapes and spatial orientations. • The old Newtonian, classical theory is deterministic. • The new quantum wave theory is probabilistic.

23. Quantum Mechanics and Atomic Orbitals Ψ2 = probability of finding electron in box

24. Quantum Mechanics and Atomic Orbitals • Orbitals and Quantum Numbers • If we solve the Schrödinger equation, we get wave functions (orbitals), energies and quantum numbers. • Schrödinger’s equation requires 3 quantum numbers: • Principal Quantum Number, n. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus.

25. Quantum Mechanics and Atomic Orbitals • Orbitals and Quantum Numbers • Azimuthal Quantum Number, l. This quantum number depends on the value of n. l=0,1,2,....n-1 • We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3). l has to do with orbital shape. l = 0 1 2 3 4 s p d f g Magnetic Quantum Number, ml. This quantum number depends on l. The magnetic quantum number has integral values between -l and +l. Magnetic quantum numbers give the 3D orientation of each orbital.

26. Sub Shell n lml 1 0 (s) 0 1s 2 0 (s) 0 2s 1 (p) 1,0,-1 2p 3 0 (s) 0 3s 1 (p) 1,0,-1 3p 2 (d) 2,1,0,-1,-2 3d 4 0 (s) 0 4s 1 (p) 1,0,-1 4p 2 (d) 2,1,0,-1,-2 4d 3 (f) 3,2,1,0,-1,-2,-3 4f Shell K L M N

27. All s-orbitals are spherical in shape. Representation of Orbitals The s Orbitals As n increases, the s-orbitals get larger.

28. Representation of Orbitals The p Orbitals There are three p-orbitals px, py, and pz in each l=1 subshell. These correspond to allowed values of ml of -1, 0, and +1.) The orbitals are dumbbell shaped. As n increases, the p-orbitals get larger. All p-orbitals have a node at the nucleus.

29. Representation of Orbitals The p Orbitals

30. Representation of Orbitals The d and f Orbitals There are 5 d-orbitals in l=2 subshells. There are 7 f-orbitals in l=3 subshells Four of the d-orbitals have four lobes each. One d-orbital has two lobes and a collar. (We will not be concerned with the f-orbitals)

31. Representation of Orbitals The d Orbitals

32. Quantum Mechanics and Atomic Orbitals Orbitals and Quantum Numbers Orbitals can be ranked in terms of increasing energy to yield an Aufbau diagram. Note that the Aufbau diagram on next slide is for a single electron system. As n increases, note that the spacing between energy levels becomes smaller.

33. Each square is an orbital. Quantum Mechanics and Atomic Orbitals Orbitals and Quantum Numbers There are n2 orbitals in each shell. Note that orbitals with same value of n have the same energy

34. < < Orbitals in Many Electron Atoms (everything above hydrogen) Energies of Orbitals Note: 2pabove 2s 3pabove 3s 3dabove 3p BUT: 4sbelow 3d All due to screening (next chapter). Rule:for given value of n energy of orbital increases with increasing value of l Example: for n=3 l = 0 1 2 s p d Increasing energy

35. Orbitals in Many Electron Atoms Mnemonic Device to remember Orbital Sequence 1s 2s 2p3s 3p4s 3d4p5s 4d5p6s 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 5g 6s 6p When filled with electrons, it’s 1s22s22p63s23p64s23d104p65s2... (superscripts are numbers of electrons in orbital series)

36. Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle Studies in the 1920s demonstrated that the electron has a property called spin. This introduced a new (and fourth) quantum number, the electron spin (or just spin) quantum number, ms There are two values for ms: +1/2 and -1/2

37. ms=+1/2 ms =-1/2 Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle

38. Can use arrows ( and ) to represent +1/2 and -1/2 spins, respectively. For example, in the 1s orbital, n=1, l=0 and ml=0. One electron can be placed (+1/2) and the other at (-1/2). But, that’s it! No more electrons in the 1s orbital. Why? Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle Pauli’s Exclusion Principle:no two electrons can have the same set of 4 quantum numbers. Therefore, two electrons in the same orbital must have opposite (+1/2 and -1/2) spins.

39. Electron Configurations Periods 1, 2, and 3 Electron configurations tell us in which orbitals the electrons for an element are located. Three rules: • electrons fill orbitals starting with lowest n and moving upwards; • no two electrons can fill one orbital with the same spin (Pauli); • for degenerate orbitals (orbitals with same energy), electrons fill each orbital singly before any orbital gets a second electron (Hund’s rule).

40. 3d (Hund’s Rule) 4s 3p Hund’s Rule 3s 2p Hund’s Rule 2s 1s 1s2 3p6 4s2 2s2 2p6 3s2 3d10

41. Electron Configurations

42. Electron Configurations and the Periodic Table

43. Electron Configurations and the Periodic Table There is a shorthand way of writing electron configurations Write the core electrons corresponding to the preceding filled Noble gas in square brackets. Write the valence electrons explicitly. Example, P: 1s22s22p63s23p3 but Ne is : 1s22s22p6 Therefore, P: [Ne]3s23p3.

44. Development of the Periodic Table • How do we organize elements in a meaningful way that will allow us to make predictions about undiscovered elements? • Arrange elements to reflect the trends in chemical and physical properties. • First attempt (Mendeleev and Meyer) arranged the elements in order of increasing atomic weight. • Modern periodic table: arrange elements in order of increasing atomic number. • Elements in same column (group) have same or similar properties. • Properties are periodic.

45. this electron This electron experiences an effective nuclear charge, Zeff Effective Nuclear Charge and Screening Screening occurs when you have more than one electron to consider. e- is partially shielded from this nucleus e by all the other surrounding electrons in atom + e e

46. Effective nuclear charge, Zeff, and screening Outer (valence) electrons experience an effective (not full) nuclear charge because of screening (or shielding). Effective nuclear charge Zeff = Z – no. of core electrons (Z = actual nuclear charge) e.g., for Na (1s22s22p63s1) Zeff = 11-10 = +1 Mg (1s22s22p63s2) Zeff = 12-10 = +2 Al (1s22s22p63s23p1) Zeff = 13-10 = +3 Note that Zeffincreases across a row

47. The Periodic Table The Periodic Table is used to organize the 114 elements in a meaningful way As a consequence of this organization, there are periodic properties associated with the periodic table.

48. Development of the Periodic Table

49. Don’t forget to review historical questions regarding the Periodic Table that are found in the Problem Bank: Dalton, Mendeleev, Rutherford, Lavoisier, Bunsen, Berzelius, Seaborg, Curie, Davy, Bohr, Moseley, Soddy, the Ancients, all discussed in Chapters 2 and 7. Review groups (families) of elements in Chapter 2: alkali metals, alkaline earths, rare earths (lanthanides), actinides, transuraniums, halogens, noble (inert) gases.

50. Sizes of Atoms Covalent (atomic) radii Array of Au atoms: (1 Å = 10-10 m) In Au, internuclear distance = 2.88 Å Therefore, atomic radius = 2.88 = 1.44 Å 2