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Ch12 Even Solns - CHAPTER TWELVE QUANTUM MECHANICS AND...

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CHAPTER TWELVE QUANTUM MECHANICS AND ATOMIC THEORY Light and Matter 22. v = 3.84 × 10 14 s -1 ; E = 2.54 × 10 -19 J 24. Wave a: λ = 4.0 × 10 -4 m Wave b: λ = 2.0 × 10 -4 m Wave a has the longer wavelength. Since frequency and photon energy are both inversely proportional to wavelength, then wave b will have the higher frequency and larger photon energy since it has the shorter wavelength. v = 1.5 × 10 12 s -1 E = 9.9 × 10 -22 J Since both waves are examples of electromagnetic radiation, then both waves travel at the same speed, c, the speed of light. From Figure 12.3 of the text, both of these waves represent infrared electromagnetic radiation. 26. E = 8.0 × 10 -18 J/photon; 4.8 × 10 6 J/mol 28. The photon energy and frequency order will be the exact opposite of the wavelength ordering because E and v are both inversely related to λ . From the calculated wavelengths above, the order of photon energy and frequency is: FM radiowaves < visible (green) light < X-rays longest λ shortest λ lowest v highest v smallest E largest E Hydrogen Atom: The Bohr Model 30. When something is quantized, it can only have certain discrete values. In the Bohr model of the H-atom, the energy of the electron is quantized. 32. λ = 820.8 nm 34. Since wavelength and energy are inversely related, then visible light ( λ ≈ 400 - 700 nm) is not energetic enough to excite an electron in hydrogen from n = 1 to n = 5.
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Visible light with λ = 410.4 nm will excite an electron from the n = 2 to the n = 6 energy level. Wave Mechanics and Particle in a Box 36. a. λ = 8.8 × 10 -6 nm b. λ = 1.6 × 10 -2 nm c. λ = 4.4 × 10 -25 nm This number is so small that it is essentially zero. We cannot detect a wavelength this small. The meaning of this number is that we do not have to consider the wave properties of large objects. 38. For λ = 1.0 × 10 2 nm v = 7.3 × 10 3 m/s For λ = 1.0 × 10 -9 nm v = 7.3 × 10 5 m/s 40. Units of ∆E × ∆t = J × s, the same as the units of Planck's constant. Linear momentum, p, is equal to mass times velocity, p = mv. Units of ∆p∆x = kg × (m/s) × m = (kgm 2 /s) = J × s 42. λ = 0.220 nm 44. n = 5 Total Area = 1; Area of one hump = 1/3 Shaded area = 1/6 = probability of finding the electron between x = 0 and x = L/ 6 in a one dimensional box with n = 3. 48. n: gives the energy (it completely specifies the energy only for the H-atom or ions with one
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electron) and the relative size of the orbitals. : gives the type (shape) of orbital. m: gives information about the direction in which the orbital is pointing in space. 50. b. must be smaller than n. d. For = 0, m = 0 only allowed value. f. For = 3, m can range from -3 to +3; thus +4 is not allowed. g. n cannot equal zero. h. cannot be a negative number. 52. 5p: three orbitals; 3d z 2 : one orbital; 4d: five orbitals n = 5: = 0 (1 orbital), = 1 (3 orbitals), = 2 (5 orbitals), = 3 (7 orbitals), = 4 (9 orbitals) Total for n = 5 is 25 orbitals. n = 4: = 0 (1), = 1 (3), = 2 (5), = 3 (7); Total for n = 4 is 16 orbitals.
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