ENG045_SL4 - DATE DUE ENG45 Solution to homework set#4 1...

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DATE: October 23, 2011 DUE: October 28, 2011 ENG45, Solution to homework set #4. 1. For each of the three functional forms of the van der Waals interaction given in HW3 (1- 3), determine the characteristic distance r m for which the force between two weakly interacting atoms is most attractive. Also determine the maximum attractive force F m . Express the distance r m and force F m as a function of a. σ 1 and E 1 . We have (also from HW3-1b, Eq.(4)) that the curvature of the potential (nega- tive derivative of the force) is C ( r ) = - ∂F ∂r = 24 E 1 σ 2 1 parenleftBigg 26 parenleftbigg σ 1 r parenrightbigg 14 - 7 parenleftbigg σ 1 r parenrightbigg 8 parenrightBigg = 0 (1) r m = σ 1 6 radicalBigg 26 7 (2) F m = 24 E 1 σ 1 parenleftBigg 2 parenleftbigg 7 26 parenrightbigg 13 / 6 - parenleftbigg 7 26 parenrightbigg 7 / 6 parenrightBigg (3) b. σ 2 and E 2 . We have (also from HW3-1c, Eq.(5)) that the curvature of the potential (nega- tive derivative of the force) is C ( r ) = - ∂F ∂r = 12 E 2 σ 2 2 parenleftBigg 13 parenleftbigg σ 2 r parenrightbigg 14 - 7
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