The dimension of a physical quantity represents the fundamental units in which it is measured. In the case of the diffusion coefficient, it is a measure of how quickly particles or molecules spread out in a medium. It is commonly denoted by the symbol D and has units of length squared per time.

The correct answer for the dimension of the diffusion coefficient is option 'B': L2T-1. Let's break down this answer and explain it in detail.

Heading 1: Dimension of Diffusion Coefficient

Heading 2: Explanation

The diffusion coefficient represents the rate at which particles or molecules diffuse or spread out in a medium. It is defined as the proportionality constant between the flux of particles and the concentration gradient. Mathematically, it is expressed as:

J = -D * (∇C)

Where J is the flux of particles, D is the diffusion coefficient, and (∇C) is the concentration gradient.

To determine the dimension of the diffusion coefficient, we need to analyze the units of the various terms in the equation.

Heading 2: Units of Flux

The flux of particles, J, represents the amount of particles passing through a unit area per unit time. It has units of mass per area per time, which can be expressed as M L-2 T-1.

Heading 2: Units of Concentration Gradient

The concentration gradient, (∇C), represents the change in concentration per unit distance. It has units of concentration per length, which can be expressed as M L-3.

Heading 2: Units of Diffusion Coefficient

Now, let's substitute the units of flux and concentration gradient into the equation:

M L-2 T-1 = -D * (M L-3)

To solve for the units of D, we can rearrange the equation as follows:

D = - (M L-2 T-1) / (M L-3)

Simplifying further, we get:

D = L2 T-1

Heading 1: Conclusion

Therefore, the correct answer for the dimension of the diffusion coefficient is option 'B': L2T-1. This represents the units of length squared per time.