1. Interpret the 2D square unit cell

   In a two-dimensional square packing, particles (circles) are located at the four corners of a square.

   If the radius of each circle is $r$, then for square packing the circles touch along the side of the square.

   Hence, side of the square unit cell is $a = 2r$

2. Find the effective number of circles in one unit cell

   Each corner circle contributes only one-fourth to the unit cell.

   Since there are 4 corner circles, $4 \times \frac{1}{4} = 1$

   So, the unit cell contains effectively 1 circle.

3. Area occupied by circles inside the unit cell

   Area of one circle is $\pi r^2$

   Since effectively there is 1 circle in the unit cell, total occupied area is $A_{\text{occupied}} = \pi r^2$

4. Total area of the square unit cell

   $A_{\text{cell}} = a^2 = (2r)^2 = 4r^2$

5. Packing efficiency

   $\text{Packing efficiency} = \frac{A_{\text{occupied}}}{A_{\text{cell}}} \times 100$

   $= \frac{\pi r^2}{4r^2} \times 100$

   $= \frac{\pi}{4} \times 100$

   Using $\pi \approx 3.1416$, $\text{Packing efficiency} = \frac{3.1416}{4} \times 100 \approx 78.54\%$

6. Match with options

   $78.54\%$ corresponds to Option D.

Comparison with stored correct answer:

Stored correct answer = D

Derived answer = D

So, they agree.