1222_Physics ProblemsTechnical Physics

1222_Physics ProblemsTechnical Physics - 563 Chapter 43...

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Chapter 43 563 P43.53 The total potential energy is given by Equation 43.17: U ke r B r e m total =− + α 2 . The total potential energy has its minimum value U 0 at the equilibrium spacing, rr = 0 . At this point, dU dr = = 0 0, or dU dr d dr r B r r mB r e m e m = = + + F H G I K J = 0 0 22 0 2 0 1 0 αα . Thus, B m r e m = 2 0 1 . Substituting this value of B into U total , U r m r r rm ee m m e 0 2 0 2 0 1 0 2 0 1 1 1 + F H G I K J F H G I K J . P43.54 Suppose it is a harmonic-oscillator potential well. Then, 1 2 448 3 2 396 hf hf += + .. eV eV is the depth of the well below the dissociation point. We see hf = 0520 . eV, so the depth of the well is 1 2 1 2 474 hf . . eV eV eV eV a f . P43.55 (a) For equilibrium, dU dx = 0: d dx Ax Bx Ax Bx −− −= −+ = 31 42 30 ej x →∞ describes one equilibrium position, but the stable equilibrium position is at 3 0 2 Ax B = . x A B 0 3 30150 368 0350 == = . . . eV nm eV nm nm 3 (b) The depth of the well is given by UU A x B x AB A BB A xx 0 0 3 0 32 32 32 12 12 12 0 33 = = B A 0 32 12 0 2 3 2368 1 5 0 702 = = . . . eV nm eV nm eV
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