Physics And Measurement Question 27
Question: Number of particles is given by $ n=-D\frac{n _{2}-n _{1}}{x _{2}-x _{1}} $ crossing a unit area perpendicular to X-axis in unit time, where $ n _{1} $ and $ n _{2} $ are number of particles per unit volume for the value of $ x $ meant to $ x _{2} $ and $ x _{1} $ . Find dimensions of $ D $ called as diffusion constant
[CPMT 1979]
Options:
A) $ M^{0}LT^{2} $
B) $ M^{0}L^{2}{{T}^{-4}} $
C) $ M^{0}L{{T}^{-3}} $
D) $ M^{0}L^{2}{{T}^{-1}} $
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Answer:
Correct Answer: D
Solution:
[n] = Number of particles crossing a unit area in unit time = $ [{{L}^{-2}}{{T}^{-1}}] $
$ [ n _{2} ]=[ n _{1} ]= $ number of particles per unit volume = [L?3]
$ [x _{2}]=[x _{1}] $ = positions
$ D=\frac{[n]\ [ x _{2}-x _{1} ]}{[ n _{2}-n _{1} ]}=\frac{[ {{L}^{-2}}{{T}^{-1}} ]\times [L]}{[{{L}^{-3}}]} $ = $ [ L^{2}{{T}^{-1}} ] $
