(II) Given the Maxwell speed distribution function, the aver- age value of v" is U² = Un f(v) du N v" where N is the total number of particles. (a) Show that the average speed is 8kT Vav = Vam Note that fo x³ exp(-ax²)dx = 1/2a².

(II) Given the Maxwell speed distribution function, the aver- age value of v" is U² = Un f(v) du N v" where N is the total number of particles. (a) Show that the average speed is 8kT Vav = Vam Note that fo x³ exp(-ax²)dx = 1/2a².

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Nuclear Reactions

Nuclear reactions are processes in which the fundamental characteristics of a nucleus changes. They change into a completely different nucleus. These processes occur naturally in an unstable nucleus. Bombarding an energetic particle can induce nuclear reactions. In this article, both the naturally occurring nuclear reactions are termed as radioactive decay and the induced nuclear reactions are further categorized as nuclear fission and nuclear fusion.

Question

(II) Given the Maxwell speed distribution function, the aver-
age value of un is
Un
v² = 5" v² f(v) du
N
where N is the total number of particles.
(a) Show that the average speed is
8kT
Vav = V πM
Note that fo x³ exp(-ax²)dx = 1/2a².

(b) Show that the rms speed is
Urms =
3kT
m
Note that fo x*exp(-ax²)dx = √9π/64a³.

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