ENG045_SL4

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

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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 p 26 P σ 1 r ± 14 - 7 P σ 1 r ± 8 ² = 0 (1) r m = σ 1 6 r 26 7 (2) F m = 24 E 1 σ 1 p 2 P 7 26 ± 13 / 6 - P 7 26 ± 7 / 6 ² (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 p 13 P σ 2 r ± 14 - 7 P σ 2 r ± 8 ² = 0 (4) r m = σ 2 6 r 13 7 (5) F m = 12 E 2 σ 2 p P 7 13 ± 13 / 6 - P 7 13 ± 7 /
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This note was uploaded on 12/18/2011 for the course ENG 045 taught by Professor Jensen during the Fall '11 term at UC Davis.

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

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