Compare Total Number of Atoms in Given Quantities of Substances

To determine the correct order of the total number of atoms in the given samples, we calculate the total number of atoms in terms of Avogadro's number ($N_A$) for each case:

1. Sample (A): $2\text{ moles}$ of cyclohexane

   • The molecular formula of cyclohexane is $\text{C}_6\text{H}_{12}$.
   • Atomicity (number of atoms per molecule) $= 6 + 12 = 18\text{ atoms}$.
   • Total number of atoms $= (\text{Moles}) \times (\text{Atomicity}) \times N_A$ $\text{Total atoms in (A)} = 2 \times 18 \times N_A = 36 N_A$

2. Sample (B): $684\text{ g}$ of sucrose

   • The molecular formula of sucrose is $\text{C}_{12}\text{H}_{22}\text{O}_{11}$.
   • Molar mass of sucrose $= (12 \times 12) + (22 \times 1) + (11 \times 16) = 144 + 22 + 176 = 342\text{ g mol}^{-1}$.
   • Moles of sucrose $= \frac{684\text{ g}}{342\text{ g mol}^{-1}} = 2\text{ moles}$.
   • Atomicity $= 12 + 22 + 11 = 45\text{ atoms}$.
   • Total number of atoms $= (\text{Moles}) \times (\text{Atomicity}) \times N_A$ $\text{Total atoms in (B)} = 2 \times 45 \times N_A = 90 N_A$

3. Sample (C): $90.8\text{ L}$ of dihydrogen at STP

   • At STP (where molar volume of gas is $22.7\text{ L mol}^{-1}$): $\text{Moles of } \text{H}_2 = \frac{90.8\text{ L}}{22.7\text{ L mol}^{-1}} = 4\text{ moles}$
   • Dihydrogen ($\text{H}_2$) is a diatomic molecule, so its atomicity is $2$.
   • Total number of atoms $= (\text{Moles}) \times (\text{Atomicity}) \times N_A$ $\text{Total atoms in (C)} = 4 \times 2 \times N_A = 8 N_A$

Comparing the total number of atoms in each sample: $90 N_A > 36 N_A > 8 N_A \implies \text{B} > \text{A} > \text{C}$

Thus, the correct option is D.