Solveeit Logo
Login

Question

Question: Number of particles is given by \(n = - D\frac{n_{2} - n_{1}}{x_{2} - x_{1}}\) crossing a unit area ...

Number of particles is given by n=−Dn2−n1x2−x1n = - D\frac{n_{2} - n_{1}}{x_{2} - x_{1}} crossing a unit area perpendicular to X- axis in unit time, where n1n_{1} and n2n_{2} are number of particles per unit volume for the value of x meant to x2x_{2} and x1.x_{1}. Find dimensions of D called as diffusion constant

A

M0LT2M^{0}LT^{2}

B

M0L2T−4M^{0}L^{2}T^{- 4}

C

M0LT−3M^{0}LT^{- 3}

D

M0L2T−1M^{0}L^{2}T^{- 1}

Answer

M0L2T−1M^{0}L^{2}T^{- 1}

Explanation

Solution

(n) = Number of particle passing from unit area in unit time

= No. of particleA×t=[M0L0T0][L2][T]\frac{\text{No. of particle}}{A \times t} = \frac{\lbrack M^{0}L^{0}T^{0}\rbrack}{\lbrack L^{2}\rbrack\lbrack T\rbrack}= [L−2T−1]\lbrack L^{- 2}T^{- 1}\rbrack

[n1]=[n2]=\lbrack n_{1}\rbrack = \lbrack n_{2}\rbrack = No. of particle in unit volume = [L−3]\lbrack L^{- 3}\rbrack

Now from the given formula [D]=[n][x2−x1][n2−n1]\lbrack D\rbrack = \frac{\lbrack n\rbrack\lbrack x_{2} - x_{1}\rbrack}{\lbrack n_{2} - n_{1}\rbrack}

=[L−2T−1][L][L−3]=[L2T−1]= \frac{\lbrack L^{- 2}T^{- 1}\rbrack\lbrack L\rbrack}{\lbrack L^{- 3}\rbrack} = \lbrack L^{2}T^{- 1}\rbrack.