The number of particles given by `n=-D(n_(2)-n_(1))/(x_(2)-x_(1))`
are crossing `a` unit area perpendicular to `x`-axis in unit time, where `n_(1)` and `n_(2)` are the number of particles per unit volume for the values `x_(1)` and `x_(2)` of `x` respectively. Then the dimensional formula of diffusion constant `D` is :

Options

A. `[M^(0)LT^(2)]`
B. `[M^(0)L^(2)T^(-4)]`
C. `[M^(0)LT^(-3)]`
D. `[M^(0)L^(2)T^(-1)]`

Answer

B

Explanation

Here `D=(n(x_(2)-x_(1)))/(n_(2)-n_(1))`
Putting the dimensions
`D=(1)/("area" xx "time")xx(L)/(1/(volume))`
`=(L^(-2)xxT^(-1)xxL)/(L^(-3))=L^(2)T^(-1)`
`D=[M^(0)L^(2)T^(-1)]`
`:.(b)` is correct.