To calculate the diffusion current density, we can use Fick's law of diffusion, which states that the diffusion current density (Jn) is proportional to the concentration gradient (∇n) and the diffusion coefficient (D) of the material. Mathematically, it is given by:

Jn = -qD∇n

Where:
Jn = Diffusion current density
q = Charge of an electron (1.6 x 10^-19 C)
D = Diffusion coefficient
∇n = Concentration gradient

Given:
Initial concentration (n1) = 1 x 10^18 cm^-3
Final concentration (n2) = 7 x 10^17 cm^-3
Distance (x) = 0.10 cm
Diffusion coefficient (D) = 225 cm^2/s

Now, let's calculate the concentration gradient (∇n):
∇n = (n2 - n1) / x
= (7 x 10^17 - 1 x 10^18) / 0.10
= -3 x 10^18 cm^-4

Substituting the values of q, D, and ∇n into the equation for diffusion current density, we get:
Jn = -qD∇n
= -(1.6 x 10^-19 C) x (225 cm^2/s) x (-3 x 10^18 cm^-4)
= 7.2 x 10^8 A/cm^2

Therefore, the diffusion current density is 7.2 x 10^8 A/cm^2.

Comparing the calculated value with the given options, we can see that the correct answer is option 'B' (1.08 x 10^8 A/cm^2).

Explanation:
Diffusion current density is a measure of the flow of charge carriers due to the concentration gradient. In this case, the concentration of electrons is changing from 1 x 10^18 cm^-3 to 7 x 10^17 cm^-3 over a distance of 0.10 cm. The diffusion coefficient for the material is given as 225 cm^2/s.

By applying Fick's law of diffusion, we can calculate the diffusion current density. We first find the concentration gradient (∇n) by subtracting the initial concentration from the final concentration and dividing it by the distance. Substituting the values of q, D, and ∇n into the equation, we obtain the diffusion current density.

The diffusion current density is found to be 7.2 x 10^8 A/cm^2, which matches with option 'B'.