Question

Number of particles, given by $n=-D\frac{n_{2} - n_{1}}{x_{2} - x_{1}}$ , is 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.

• A. $\left[M^{0} \, L T^{2}\right]$
• B. $\left[M^{0} \, L^{2} \, T^{- 4}\right]$
• C. $\left[M^{0} \, L T^{- 3}\right]$
• D. $\left[M^{0} \, L^{2} \, T^{- 1}\right]$

Answer 1

Answer: (D)

Given, number of particle passing from unit area in unit time $=n$
$=\frac{N u m b e r \, o f \, p a r t i c l e}{A \times t}=\frac{\left[M^{0} \, L^{0} \, T^{0}\right]}{\left[L^{2}\right] \, \left[T\right]}=\left[L^{- 2} \, T^{- 1}\right]$
$\left[n_{1}\right]=\left[n_{2}\right]=Number \, of \, particle \, in \, unit \, volume=\left[L^{- 3}\right]$
Now, from the given formula $\left[D\right]=\frac{\left[n\right] \, \left[x_{2} - x_{1}\right]}{\left[n_{2} - n_{1}\right]}$
$=\frac{\left[L^{- 2} \, T^{- 1}\right] \, \left[L\right]}{\left[L^{- 3}\right]}$
$=\left[L^{2} \, T^{- 1}\right]$