# The number of fundamental electric charges on the oil

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The number of fundamental electric charges on the oil drop is 18 19 2.40 10 C 15 1.60 10 C q e × = = ×

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38.49. Model: Assume the classical electric force is the centripetal force. 2 2 2 e 2 e Ke v Ke F m v r r m r = = = Visualize: We are given 600 nm. λ = We also know that for electromagnetic waves . c f λ = Solve: (a) The speed is the circumference of the orbit divided by the period. 2 2 r v rf T π π = = 2 e 2 2 2 Ke m r v v r f c c λ λ π π π = = = Square both sides. 2 e 2 2 2 2 4 Ke m r r c λ π = Multiply both sides by . r 2 2 3 2 2 e 4 Ke r c m λ π = Take cube roots. 10 2 2 3 2 2 9 2 2 19 2 9 2 3 2 8 2 31 4 (8 99 10 N m C )(1 60 10 C) (600 10 m) 4 (3 00 10 m s) (9 11 10 kg) 2 95 10 m 0 295 nm e Ke r c m λ π π = . × / . × × = . × / . × = . × = . (b) The total mechanical energy of the classical atom was found in Problem 38.47. 19 2 2 19 12 2 2 10 0 (1 60 10 C) 3 90 10 J 2 44eV 8 8 (8 85 10 C N m )(2 95 10 m) e E r πε π . × = − = − = − . × = − . . × / . × Assess: While we don’t expect the classical analysis to be perfect, the result is in a reasonable range.
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