Question

The unit of diffusional flux is

• A. atoms/m\(^2\).s
• B. atoms/m\(^3\).s
• C. atoms/m.s\(^2\)
• D. atoms/m.s\(^3\)

Hint:

Diffusional flux measures the rate of diffusion per unit area, and its unit is derived using Fick’s First Law.

Answer 1

The Correct Option is A

Diffusional flux, denoted as \( J \), represents the amount of mass or number of particles diffusing through a unit area per unit time. It is given by Fick’s First Law: \[ J = -D \frac{dC}{dx} \] where: - \( J \) is the diffusional flux (amount per unit area per unit time), - \( D \) is the diffusion coefficient (m\(^2\)/s), - \( C \) is the concentration of diffusing species (atoms/m\(^3\)), - \( x \) is the distance (m). Step 1: Finding the Unit of \( J \) - The concentration gradient (\( dC/dx \)) has units of: \[ \frac{\text{atoms/m}^3}{\text{m}} = \text{atoms/m}^4 \] - The diffusion coefficient (\( D \)) has units of: \[ \text{m}^2/\text{s} \] - Thus, the unit of diffusional flux is: \[ J = D \times \frac{dC}{dx} = \left( \frac{\text{m}^2}{\text{s}} \right) \times \left( \frac{\text{atoms}}{\text{m}^4} \right) \] \[ = \frac{\text{atoms}}{\text{m}^2 \cdot \text{s}} \]


Step 2: Evaluating the Options - Option (A) - Correct: \( \text{atoms/m}^2 \cdot \text{s} \) matches the derived unit. - Option (B) - Incorrect: \( \text{atoms/m}^3 \cdot \text{s} \) represents a concentration change over time, not flux. - Option (C) - Incorrect: \( \text{atoms/m} \cdot \text{s}^2 \) is not physically meaningful for diffusion. - Option (D) - Incorrect: \( \text{atoms/m} \cdot \text{s}^3 \) is incorrect.


Step 3: Conclusion Since the diffusional flux has units of atoms/m\(^2\).s, the correct answer is option (A).