Number of particles is given by `n=-D(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^(0)]`
B. `[M^(0)L^(2)T^(-4)]`
C. `[M^(0)LT^(-3)]`
D. `[M^(0)L^(2)T^(-1)]`

Answer

D

Explanation

From the given relation, D = `(n(x_(2) - x_(1)))/(n_(2)-n_(1))`
Here `[n],=[(1)/("area"xx"time")]=(1)/([L^(2)T])-[L^(-2)T^(-1)]`
`x_(2)-x_(1)=[L]andn_(2)-n_(1)=[(1)/("volume")]=[(1)/(L^(3))]`
`= [L^(-3)]`
So, `[D]=([L^(-2)T^(-1)L])/([L^(-3)])=[L^(2)T^(-1)]`