Question

Finally divided catalyst has a greater surface area and has greater catalytic activity than the compact solid. If a total surface area of $6291456c{m}^2$ is required for adsorption of gaseous reaction in a catalyzed reaction,then how many splits should be made in a cube of exactly 1 cm in length.[Given: One split of a cube gives eight cubes of the same size]

• A. 60
• B. 80
• C. 20
• D. 22

Answer 1

The correct option is C 20

Apply the formula,

Surface area on n split of a cube $=8^n\times 6\times (\frac{1}{2}{)}^{2n}$

$6291456=8^n\times 6\times (\frac{1}{2}{)}^{2n}$
$2^n\times 6=6291456$

$nlog\left(2\right)=log\left(1048576\right)$

n=20

Option C is correct.