10.2 The radial distribution function W(r) of end-to-end distances r for an isolated flexible poly- mer chain is given by W(r) = 4л =4(b)² 1/2 π r² exp(-b²r²) where ẞ=[3/(2nl²)] 1/2 in which n is the number of links of length / forming the chain. Show by integration that this distribution function normalizes to unity, and derive equa- tions for (a) the most probable value of r, (b) the root-mean-square value of r and (c) the mean value of r. 00 Note that for 1(b) = x' exp(-ax²)dx 2 I(0)=| πα I(1)= 1/2 1(2)= 1/2 πα 2 4 a¯³/²; 1(3)=| 3 a²; 1(4)= πα 1/2 -5/2 - 2 8
10.2 The radial distribution function W(r) of end-to-end distances r for an isolated flexible poly- mer chain is given by W(r) = 4л =4(b)² 1/2 π r² exp(-b²r²) where ẞ=[3/(2nl²)] 1/2 in which n is the number of links of length / forming the chain. Show by integration that this distribution function normalizes to unity, and derive equa- tions for (a) the most probable value of r, (b) the root-mean-square value of r and (c) the mean value of r. 00 Note that for 1(b) = x' exp(-ax²)dx 2 I(0)=| πα I(1)= 1/2 1(2)= 1/2 πα 2 4 a¯³/²; 1(3)=| 3 a²; 1(4)= πα 1/2 -5/2 - 2 8
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
![10.2 The radial distribution function W(r) of end-to-end distances r for an isolated flexible poly-
mer chain is given by
W(r) = 4л
=4(b)²
1/2
π
r² exp(-b²r²)
where ẞ=[3/(2nl²)] 1/2 in which n is the number of links of length / forming the chain.
Show by integration that this distribution function normalizes to unity, and derive equa-
tions for (a) the most probable value of r, (b) the root-mean-square value of r and (c) the mean
value of r.
00
Note that for 1(b) = x' exp(-ax²)dx
2
I(0)=| πα I(1)=
1/2
1(2)=
1/2
πα
2
4
a¯³/²; 1(3)=|
3
a²; 1(4)= πα
1/2 -5/2
-
2
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf65902f-0e77-4fe2-a284-a72c9240a239%2F3585c608-3775-4f5b-9ecf-c6ec237889a2%2F7owmheo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10.2 The radial distribution function W(r) of end-to-end distances r for an isolated flexible poly-
mer chain is given by
W(r) = 4л
=4(b)²
1/2
π
r² exp(-b²r²)
where ẞ=[3/(2nl²)] 1/2 in which n is the number of links of length / forming the chain.
Show by integration that this distribution function normalizes to unity, and derive equa-
tions for (a) the most probable value of r, (b) the root-mean-square value of r and (c) the mean
value of r.
00
Note that for 1(b) = x' exp(-ax²)dx
2
I(0)=| πα I(1)=
1/2
1(2)=
1/2
πα
2
4
a¯³/²; 1(3)=|
3
a²; 1(4)= πα
1/2 -5/2
-
2
8
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