Review Problem Set 9

1. Review Problem Set 9

2. Chapter 7 The Quantum Mechanical Model of the Atom

3. Quantum mechanics — microscopic particles Classical mechanics — macroscopic objects

4. Some properties of light

5. Light travels and carries energy

6. Speed of light c = 3.00 x 108 m/s

7. Light has many colors

8. Light can be invisible to human

10. Light is an electromagnetic radiation Light is a wave

11. Some parameters of a wave

12. Wavelength λ: distance between two consecutive peaks. Unit: m Amplitude A: height of the peak. Unit: depends on the type of wave

14. ν = 1/T c= λ/T = λ ν Wavelength λ: distance between two consecutive peaks. Unit: m Frequency ν: number of complete wavelengths, or cycles, that pass a given point each second. Unit: 1/s = s−1 = Hz Period T: time required for a complete wavelength or cycle to pass a given point. Unit: s

15. Demo on Sr salt λ = 6.50 x 102 nm, what is the frequency of the red light? What is the period of the light? c= λ/T = λ ν ν = 1/T

16. ν

18. Phenomena that could not be explained by classic mechanics 1. Blackbody radiation

19. ρ(λ) (kJ/nm)

20. Energy can only be gained or lost in whole-number multiples of the quantity hv, a quantum. Planck’s constant: h = 6.63 x 10−34 J·s

23. Phenomena that could not be explained by classic mechanics 1. Blackbody radiation 2. Photoelectric effect

24. Photoelectric Effect Occurs only if ν > ν0

25. Light can be viewed as a stream of particles called photons. Energy of one photon is E = hν

27. What is the energy of one photon from the red light? 4.61 x 1014 Hz 3.06 x 10−19 J What is the energy of one photon from a blue light whose wavelength is 452 nm? 6.64 x 1014 Hz 4.40 x 10−19 J

28. ν

29. Electromagnetic Radiation Exhibits Wave Properties and Particulate Properties Is light a stream of particles or waves?

31. Phenomena that could not be explained by classic mechanics 1. Blackbody radiation 2. Photoelectric effect 3. Atomic spectra

32. Pink Floyd: Dark Side of the Moon

33. λ Continuous spectrum

34. Ne gas in tube

36. Hg He H

38. Neils Bohr Electrons in an atom can only occupy certain energy levels

42. According to quantum mechanics, the state of a system is completely specified by a function Ψ, called the wave function or state function, that depends on the coordinates of the particles.

43. H atom

44. Schrödinger’s Equation Ĥ — an operator related to energy E — energy Ψ — wave function Ψ contains all the information of a system Ψ = Ψ(x,y,z) In an atom, x,y,z: coordinates of electrons

45. Ψ — wave function Ψ contains all the information of a system What is the physical significance of Ψ? Max Born In an atom,│Ψ(x,y,z)│2 is the probability density distribution of electrons.

48. A specific wave function Ψ is called an orbital. An atomic orbital is characterized by three quantum numbers.

49. Three Quantum Numbers Principle quantum number n. Only positive integers. n = 1, 2, 3, 4, · · · shell Angular momentum quantum number l. l = 0, 1, 2, 3, 4, · · ·, (n − 1) subshell s p d f g

50. Magnetic quantum number ml ml = −l, −l +1, −l + 2, · · · , 0, · · ·, l − 1, l Must remember the possible values for quantum numbers One set of n, l, and ml specify One atomic orbital.