Some Basic Concepts of Chemistry - Result Question 4 — JEE PYQ Chapterwise

Answer:

Correct Answer: 4. (a)

Solution:

Given, volume $=10 mL$

Molarity $=1 mM=10^{-3} M$

$\therefore$ Number of millimoles $=10 mL \times 10^{-3} M=10^{-2}$

Number of moles $=10^{-5}$

Now, number of molecules

$ \begin{aligned} & =\text { Number of moles } \times \text { Avogadro’s number } \\ & =10^{-5} \times 6 \times 10^{23}=6 \times 10^{18} \end{aligned} $

Surface area occupied by $6 \times 10^{18}$ molecules $=0.24 cm^{2}$

$\therefore$ Surface area occupied by 1 molecule

$ =\frac{0.24}{6 \times 10^{18}}=0.04 \times 10^{-18} cm^{2} $

As it is given that polar head is approximated as cube. Thus, surface area of cube $=a^{2}$, where

$ \begin{aligned} a & =\text { edge length } \\ \therefore \quad a^{2} & =4 \times 10^{-20} cm^{2} \\ a & =2 \times 10^{-10} cm=2 pm \end{aligned} $