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Review Problem Set 9

Review Problem Set 9. Chapter 7 The Quantum Mechanical Model of the Atom. Quantum mechanics — microscopic particles. Classical mechanics — macroscopic objects. Some properties of light. Light travels and carries energy. Speed of light c = 3.00 x 10 8 m/s. Light has many colors.

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Review Problem Set 9

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  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

  9. Light is an electromagnetic radiation Light is a wave

  10. Some parameters of a wave

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

  12. 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

  13. 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

  14. ν

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

  16. ρ(λ) (kJ/nm)

  17. 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

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

  19. Photoelectric Effect Occurs only if ν > ν0

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

  21. 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

  22. ν

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

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

  25. Pink Floyd: Dark Side of the Moon

  26. λ Continuous spectrum

  27. Ne gas in tube

  28. Hg He H

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

  30. 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.

  31. H atom

  32. 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

  33. 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.

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

  35. 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

  36. 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.

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