Alright class we are going back to quantum numbers.

1. Alright class we are going back to quantum numbers. I decided this would be a better lead into dipole then just throwing you into the mess.

2. Do you remember Wave and Frequency? • Do you remember plank. Well he is back it is time to work on his constant and what it means. • Also the electromagnetic spectrum.

3. Properties of Waves Wavelength (l) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. Frequency (n) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (u) of the wave = l x n 3

4. Maxwell (1873), proposed that visible light consists of electromagnetic waves. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 108 m/s All electromagnetic radiation l x n = c 4

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6. A photon has a frequency of 6.0 x 104 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? 6

7. The wavelength of the green light from a traffic signal is centered at 522 nm. What is the frequency of this radiation? 7

8. Problem 1 What is the wavelength (in meters) of an electromagnetic wave whose frequency is 3.64 x 107 Hz? 8

9. Mystery #1, “Heated Solids Problem”Solved by Planck in 1900 When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths. Radiant energy emitted by an object at a certain temperature depends on its wavelength. Energy (light) is emitted or absorbed in discrete units (quantum). E = h x n Planck’s constant (h) h = 6.63 x 10-34 J•s 9

10. Calculate the energy (in joules) of a photons with a wavelength of 5.00 x 104 nm (infrared region). 10

11. Calculate the energy (in joules) of a photons with a wavelength of 5.00 x 10-2 nm (x-ray region). 11

12. Problem 2 The energy of a photon is 5.87 x 10-20 J. What is its wavelength in nanometers? 12

13. Mystery #2, “Photoelectric Effect”Solved by Einstein in 1905 hn • Light has both: • wave nature • particle nature KE e- Photon is a “particle” of light hn = KE + W KE = hn - W where W is the work function and depends how strongly electrons are held in the metal 13

14. When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is 0.154 nm. 14

15. The work function of cesium metal is 3.42 x 10-19 J. Calculate the minimum frequency of light necessary to eject electrons from the metal. 15

16. The work function of cesium metal is 3.42 x 10-19 J. Calculate the kinetic energy of the ejected electron if light of frequency 1.00 x 1015 s-1 is used for irradiating the metal. 16

17. Problem 3 The work function of titanium metal is 6.93 x 10-19 J. Calculate the energy of the ejected electrons if light of frequency 2.50 x 1015 s-1 is used to irradiate the metal. KE = _____x 10-19 J 17

18. Line Emission Spectrum of Hydrogen Atoms Mystery #3, “Emission Spectra” 18

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20. ( ) En = -RH 1 n2 Bohr’s Model of the Atom (1913) • e- can only have specific (quantized) energy values • light is emitted as e- moves from one energy level to a lower energy level n (principal quantum number) = 1,2,3,… RH (Rydberg constant) = 2.18 x 10-18J 20

21. E = hn E = hn 21

22. ni = 3 ni = 3 f i ni = 2 nf = 2 DE = RH i f ( ) ( ) ( ) Ef = -RH Ei = -RH nf = 1 nf = 1 1 1 1 1 n2 n2 n2 n2 Ephoton = DE = Ef - Ei 22

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24. Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. 24

25. Problem 4 What is the wavelength (in nm) of a photon emitted during a transition from ni=6 to nf=4 in the H atom? ν = _____x 103 nm 25

26. h 2pr = nll = mu Why is e- energy quantized? De Broglie (1924) reasoned that e- is both particle and wave. u = velocity of e- m = mass of e- 26

27. What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s? 27

28. Calculate the wavelength of the ‘particle’ in each of the following two cases: (a) The fastest serve ever recorded in tennis was about 150 miles per hour, or 68 m/s. Calculate the wavelength associated with a 6.0 x 10-2 kg tennis ball travelling at this speed. 28

29. Calculate the wavelength of the ‘particle’ in each of the following two cases: (b) Calculate the wavelength associated with an electron (9.1094 x 10-31kg) travelling at this speed. 29

30. Problem 5 Calculate the wavelength (in nm) of a H atom (mass = 1.674 x 10-27 kg) moving at 7.00 x 102 cm/s. 30

31. Chemistry in Action: Laser – The Splendid Light Light Amplification by Stimulated Emission of Radiation Laser light is (1) intense, (2) monoenergetic, and (3) coherent 31

32. Chemistry in Action: Electron Microscopy le = 0.004 nm STM image of iron atoms on copper surface Electron micrograph of a normal red blood cell and a sickled red blood cell from the same person 32

33. Shortcomings of Bohr’s model • Did not account for the emission spectra of atoms containing more than on electron. • Did not explain extra lines in the emission spectra for hydrogen when magnetic field is applied. • Conflict with discovery of ‘wavelike’ properties – how can you define the location of a wave? Heisenberg Uncertainty Principle It is impossible to know simultaneously both the momentum p (defined as mass times velocity) and the position of a particle with certainty. 33

34. Schrodinger Wave Equation In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e- 34

35. Schrodinger Wave Equation • Wave function (y) describes: • . energy of e- with a given y • . probability of finding e- in a volume of space • Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems. 35

36. Schrodinger Wave Equation n=1 n=2 n=3 y is a function of four numbers called quantum numbers (n, l, ml, ms) principal quantum number n n = 1, 2, 3, 4, …. distance of e- from the nucleus 36

37. Where 90% of the e- density is found for the 1s orbital 37

38. Schrodinger Wave Equation quantum numbers:(n, l, ml, ms) angular momentum quantum number l for a given value of n, l= 0, 1, 2, 3, … n-1 l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e- occupies 38

39. l = 1 (p orbitals) l = 0 (s orbitals) 39

40. l = 2 (d orbitals) 40

41. Schrodinger Wave Equation quantum numbers: (n, l, ml, ms) magnetic quantum number ml for a given value of l ml = -l, …., 0, …. +l if l = 1 (p orbital), ml = -1, 0, or1 if l = 2 (d orbital), ml = -2, -1, 0, 1, or2 orientation of the orbital in space 41

42. 3 orientations is space ml = -1, 0, or1 42

43. ml = -2, -1, 0, 1, or2 5 orientations is space 43

44. Schrodinger Wave Equation (n, l, ml, ms) spin quantum number ms ms = +½or -½ ms = +½ ms = -½ 44

45. Schrodinger Wave Equation quantum numbers:(n, l, ml, ms) Existence (and energy) of electron in atom is described by its unique wave function y. Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time 45

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47. Schrodinger Wave Equation quantum numbers:(n, l, ml, ms) Shell – electrons with the same value of n Subshell – electrons with the same values of nandl Orbital – electrons with the same values of n, l, andml How many electrons can an orbital hold? 47

48. How many 2p orbitals are there in an atom? How many electrons can be placed in the 3d subshell? 48

49. List the values of n, ℓ, and mℓ for orbitals in the 4d subshell. What is the total number of orbitals associated with the principle quantum number n=3? 49

50. Problem 6 Give the values of the quantum numbers associated with the orbitals in the 3p subshell. n = ____ ℓ = ____ mℓ=____ 50