The Quantum Mechanical Model of the Atom

1. The Quantum Mechanical Model of the Atom Chapter 7

5. Light and the Electromagnetic Spectrum

7. Wave - A vibrational disturbance which transmits energy.

8. Definitions • Wavelength (, Greek lambda) - The distance between identical points on successive waves. • Frequency (, Greek nu) - The number of peaks that pass a given point in a second • frequency = cycles/sec = hertz = Hz • Speed of light, c =  - 3.00 x 108 m/sec = 3.00 x 1010 cm/sec

9. Sodium vapor lamps - the yellow street lights - emit light with  = 589.2 nm. What is its frequency?

10. KPBS has a frequency of 89.5 MHz (MHz = 106 cycles/sec). What is the wavelength of this radiation in meters?

11. Planck’s Quantum Theory • Max Planck • Blackbody radiation • Intensity varies with wavelength (red-orange-white) • Classical physics doesn’t explain

12. Experiment 1 • Add an elemental gas to a cathode ray tube and get ----- colors • Hydrogen (H2) purple blue • Neon (Ne) red orange • Helium (He) yellow pink • Argon (Ar) lavender • Xenon (Xe) blue

13. Experiment 2 • Shine white light through a prism -- rainbow • A prism separates light of different wavelength, each color represents a different wavelength. Sundog – caused by ice acting as a prism.

14. Experiment 3 • Shine the colored light from our gas discharge tubes through a prism  get distinct bands of color (light). • http://jersey.uoregon.edu/vlab/elements/Elements.html

15. Quantization of energy • Energies in atoms are quantized, not continuous. • Quantized means only certain energies allowed.

16. Bohr model of the atom • Electrons orbit the nucleus like little planets (planetary model) each with its own energy. Electrons can move from one energy level to another by absorbing or releasing energy. • Energy is released as radiant energy or light.

18. Quantum of energy • the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation. • Energy (1 quantum) = h • or energy = n h  • n = number of quanta of energy (must be a whole number) • h = Planck’s constant = 6.626 x 1034 J sec •  = frequency

19. What is the minimum energy of a sodium lamp (with  = 5.892 x 107 m and  = 5.09 x 1014/sec)?

20. Calculate the energy of a quantum of blue light with wavelength = 410 nm.

22. Photoelectric Effect Observation - • Electrons can be ejected from some metals when they are exposed to light. • Is light behaving like a particle which can bounce electrons out of atoms? Light can behave as both a wave and a particle and energy is quantized the same either way.

24. If a light with a wavelength of 200 nm shines on sodium atoms with an ionization energy of 496 kJ/mol, what will be the speed of the electrons emitted?

25. deBroglie

26. deBroglie Wavelength • Calculate the wavelength in nanometers associated with a 0.072 kg golf ball moving at 30 m/sec?

27. Quantized Energy

28. Energy Levels for H • where n in an integer.

32. Derivation of Balmer-Rydberg equation E = EnfinalEninitial

35. What Next? • Light behaves like waves --- and particles. • Particles can behave like waves. • Energy is quantized. • ???????

36. Heisenberg Uncertainty Principle • The first thing we would like to learn about electrons is where they are and how they travel. • Heisenberg Uncertainty principle says this is impossible. • (x)(mv)  h/4 (1034 kg m2/sec)

37. Schrodinger’s quantum mechanical model of the atom •  E = H •  is the wave function or orbital • 2 (probability function) represents the probability of finding an electron at any given position in an atom.

38. Quantum Numbers • The behavior of an electron is described mathematically by Schrodinger’s wave equation and each orbital contains as set of three variables called quantum numbers.

39. The principal quantum number (n) -- ·an integer ·determines energy level of orbital

40. Angular momentum quantum number (l)-- equal to (n-1) to 0 • so for n = 1, l = 0 • for n = 2, l = 0, or 1 • for n = 3, l = 0, 1, or 2 • ·determines type of subshell of an electron • quantum number subshell type • 0 s • 1 p • 2 d • 3 f

41. Magnetic quantum number (ml) ·equal to -l to +l in integer increments ·identifies number of orbitals within a sublevel • describes spatial orientation orbitals within a sublevel

42. ·equal to +1/2 or 1/2 ·necessary because each orbital contains 2 electrons and each electron needs its own space. Spin quantum number (ms)

44. s orbitals ·spherical in shape ·one spatial orientation (ml = 0) ·contain nodes as move to higher quantum levels (nodes are places probability of finding an electron goes to zero) ·makes sense if we look at electrons as waves, waves have nodes.