1. Given a one-dimensional random coil with in total 1000 monomers, the bond length between two adjacent monomer is 0.4 nm. Suggesting in a moment when 40% of the bonds of the chain pointing to the right, according to the freely-joined chain model, calculate the (1) the end-to-end distance of the chain in this configuration (2) the probability that the chain presents the above configuration. (3) The root-mean-square separation of this chain after averaging all possible configurations. (4) The radius of gyration of the chain after averaging all possible configurations. (5) The persistent length of the chain in the context of a freely-joined chain model. (6) To increase the root-mean-square separation calculated in (3) by 200 percent, please give the persistence length of the chain in that case.

1. Given a one-dimensional random coil with in total 1000 monomers, the bond length between two adjacent monomer is 0.4 nm. Suggesting in a moment when 40% of the bonds of the chain pointing to the right, according to the freely-joined chain model, calculate the (1) the end-to-end distance of the chain in this configuration (2) the probability that the chain presents the above configuration. (3) The root-mean-square separation of this chain after averaging all possible configurations. (4) The radius of gyration of the chain after averaging all possible configurations. (5) The persistent length of the chain in the context of a freely-joined chain model. (6) To increase the root-mean-square separation calculated in (3) by 200 percent, please give the persistence length of the chain in that case.

Organic Chemistry

8th Edition

ISBN:9781305580350

Author:William H. Brown, Brent L. Iverson, Eric Anslyn, Christopher S. Foote

Publisher:William H. Brown, Brent L. Iverson, Eric Anslyn, Christopher S. Foote

Chapter23: Amines

Section23.5: Basicity

Problem GQ

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