The document discusses several key concepts regarding waves and electromagnetic radiation including: 1) Wavelength, amplitude, frequency, and speed are fundamental properties of waves. 2) Electromagnetic radiation consists of electromagnetic waves that travel at the speed of light. 3) Maxwell proposed that visible light is a form of electromagnetic radiation with wavelengths in the visible spectrum.

3. Properties of Waves Wavelength (  ) 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. 7.1

4. Properties of Waves Frequency (  ) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed ( u ) of the wave =  x  7.1

5. 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 10 8 m/s All electromagnetic radiation  x  c 7.1

6. z y x Electric field component Magnetic field component

7. x

8. z x Electric field component

9. z x Electric field component

10. x

11. y x Magnetic field component

12. y x Magnetic field component

13. z y x Electric field component Magnetic field component

14. 7.1

15.  x  = c  = c/   = 3.00 x 10 8 m/s / 6.0 x 10 4 Hz  = 5.0 x 10 3 m  = 5.0 x 10 12 nm 7.1 Radio wave A photon has a frequency of 6.0 x 10 4 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region?  

16. Mystery #1, “Black Body Problem” Solved by Planck in 1900 Energy (light) is emitted or absorbed in discrete units (quantum). E = h x  Planck’s constant (h) h = 6.63 x 10 -34 J • s 7.1

18. E = h x  E = 6.63 x 10 -34 (J•s) x 3.00 x 10 8 (m/s) / 0.154 x 10 -9 (m) E = 1.29 x 10 -15 J E = h x c /  7.2 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.

19. 7.3 Line Emission Spectrum of Hydrogen Atoms

20. Fig. 7.p267middle

21. 7.3

23. 7.3 E = h  E = h 

24. De Broglie (1924) reasoned that e - is both particle and wave . 2  r = n   = h/mu u = velocity of e - m = mass of e - 7.4 Why is e - energy quantized?

25.  = h/mu  = 6.63 x 10 -34 / (2.5 x 10 -3 x 15.6)  = 1.7 x 10 -32 m = 1.7 x 10 -23 nm m in kg h in J • s u in (m/s) 7.4 What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s?

26. Chemistry in Action: Element from the Sun In 1868, Pierre Janssen detected a new dark line in the solar emission spectrum that did not match known emission lines In 1895, William Ramsey discovered helium in a mineral of uranium (from alpha decay). Mystery element was named Helium

28. Schrodinger Wave Equation  fn( n , l , m l , m s ) principal quantum number n n = 1, 2, 3, 4, …. 7.6 distance of e - from the nucleus n=1 n=2 n=3

29. 7.6 e - density (1s orbital) falls off rapidly as distance from nucleus increases Where 90% of the e - density is found for the 1s orbital

30.  = fn(n, l , m l , m s ) angular momentum quantum number l for a given value of n , l = 0, 1, 2, 3, … n-1 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 l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrodinger Wave Equation 7.6

31. 7.6 l = 0 (s orbitals) l = 1 (p orbitals)

32. 7.6 l = 2 (d orbitals)

33.  = fn(n, l , m l , m s ) magnetic quantum number m l for a given value of l m l = - l , …., 0, …. + l orientation of the orbital in space if l = 1 (p orbital), m l = -1, 0, or 1 if l = 2 (d orbital), m l = -2, -1, 0, 1, or 2 Schrodinger Wave Equation 7.6

34. m l = -1 m l = 0 m l = 1 m l = -2 m l = -1 m l = 0 m l = 1 m l = 2 7.6

35.  = fn(n, l , m l , m s ) spin quantum number m s m s = +½ or -½ Schrodinger Wave Equation m s = -½ m s = +½ 7.6

36. Detecting screen Slit screen Magnet Oven

37. Detecting screen Slit screen Magnet Oven

38. Detecting screen Slit screen Magnet Atom beam Oven

39. Detecting screen Slit screen Magnet Atom beam 1 2 m s = + – Oven

40. Detecting screen Slit screen Magnet m s = – – 1 2 Atom beam Oven

41. Detecting screen Slit screen Magnet m s = – – 1 2 1 2 m s = + – Atom beam Oven

42. Existence (and energy) of electron in atom is described by its unique wave function  . Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Schrodinger Wave Equation  = fn(n, l , m l , m s ) Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time 7.6

43. 7.6

44. Schrodinger Wave Equation  = fn(n, l , m l , m s ) Shell – electrons with the same value of n Subshell – electrons with the same values of n and l Orbital – electrons with the same values of n, l , and m l If n, l, and m l are fixed, then m s = ½ or - ½  = (n, l , m l , ½ ) or  = (n, l , m l , - ½ ) An orbital can hold 2 electrons 7.6 How many electrons can an orbital hold?

45. 2p If l = 1, then m l = -1, 0, or +1 3 orbitals 3d If l = 2, then m l = -2, -1, 0, +1, or +2 5 orbitals which can hold a total of 10 e - 7.6 How many 2p orbitals are there in an atom? n=2 l = 1 How many electrons can be placed in the 3d subshell? n=3 l = 2