Physics And Measurement Question 193
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
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:
[d] [n]= Number of particles crossing a unit area in unit time = $ [{{L}^{-2}}{{T}^{-1}}] $
$ [n _{2}]=[n _{1}] $ =number of particles per unit valume= $ [{{L}^{-3}}] $
$ [x _{2}]=[x _{1}] $ = positions
$ \therefore D=\frac{[n][x _{2}-x _{1}]}{[n _{2}-n _{1}]}=\frac{[{{L}^{-2}}{{T}^{-1}}]\times [L]}{[{{L}^{-3}}]}=[L^{2}{{T}^{-1}}] $
