First slide

Dimensions of physical quantities

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 n₁ and n₂ are number of particles per unit volume for the value of x meant to x₂ and x₁. Find dimensions of D called as diffusion constant.

Moderate

A

$M^{0} L T^{2}$
B

$M^{0} L^{2} T^{- 4}$
C

$M^{0} L T^{- 3}$
D

$M^{0} L^{2} T^{- 1}$

Solution

$\begin{array}{l} [n] = Number of particles crossing a unit area in unit time \\ = [L^{- 2} T^{- 1}] \end{array}$
$\begin{array}{l} [n_{2}] = [n_{1}] = number of particles per unit volume = [L^{- 3}] \\ [x_{2}] = [x_{1}] = positions \\ ∴ D = \frac{[n] [x_{2} - x_{1}]}{[n_{2} - n_{1}]} = \frac{[L^{- 2} T^{- 1}] \times [L]}{[L^{- 3}]} = [L^{2} T^{- 1}] \end{array}$

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