Question

Calculate the radius of He atoms if its the Van der Waals constant 'b' is $271{\text{mL.mol}}^{-1}$.
(Take $N_A=6\times {10}^{23}$)

• A. $3\stackrel{o}{\text{A}}$
• B. $2\stackrel{o}{\text{A}}$
• C. $4\stackrel{o}{\text{A}}$
• D. $5\stackrel{o}{\text{A}}$

Answer 1

The correct option is A $3\stackrel{o}{\text{A}}$

We know that, $b=4V$
where, V is the total volume of all the gas molecules.
V= $4\times \frac{4}{3}\pi r^3\times N_A=271{\text{cm}}^3$
where, r is the radius of the gas molecule.
$4\times \frac{4}{3}\pi r^3\times N_A=271{\text{cm}}^3$

$r^3=\frac{271\times 3}{4\times 4\times 3.14\times 6\times {10}^{23}}$

$\Rightarrow r^3=27\times {10}^{-24}$ (approx)
$\Rightarrow r=3\times {10}^{-8}\text{cm}$
$\Rightarrow r=3\stackrel{o}{\text{A}}$