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1214_Physics ProblemsTechnical Physics

1214_Physics ProblemsTechnical Physics - Chapter 43 P43.20...

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Chapter 43 555 P43.20 The emission energies are the same as the absorption energies, but the final state must be below v J = = 1 0 , b g . The transition must satisfy J = ± 1 , so it must end with J = 1 . To be lower in energy, it must be v J = = 0 1 , b g . The emitted photon energy is therefore hf E E E E E E E E hf hf hf v J v J v v J J photon vib rot vib rot vib vib rot rot photon vib rot = + + = = = = = = = = = = 1 0 0 1 1 0 1 0 e j e j e j e j Thus, f f f photon vib rot Hz Hz Hz = = × × = × 6 42 10 1 15 10 6 41 10 13 11 13 . . . . P43.21 The moment of inertia about the molecular axis is I mr mr m x = + = × 2 5 2 5 4 5 2 00 10 2 2 15 2 . m e j . The moment of inertia about a perpendicular axis is I m R m R m y = F H G I K J + F H G I K J = × 2 2 2 2 00 10 2 2 10 2 . m e j . The allowed rotational energies are E I J J rot = F H G I K J + = 2 2 1 a f , so the energy of the first excited state is E I 1 2 = = . The ratio is therefore E E I I I I m m x y x y y x 1 1 2 2 10 2 15 2 5 2 9 1 2 2 00 10 4 5 2 00 10 5 8 10 6 25 10 , , . . . = = = × × = = × = = e j e j b g e j b g e j e j m m . Section 43.3 Bonding in Solids P43.22 Consider a cubical salt crystal of edge length 0.1 mm. The number of atoms is 10 10 4 9 3 17
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