Question

If the rate of diffusion of $A$ is $5times$ that of $B$, what will be the density ratio of $A$ and $B$?

• A. $\frac{1}{5}$
• B. $5$
• C. $25$
• D. $\frac{1}{25}$

Answer 1

The correct option is D

$\frac{1}{25}$

Explanation for the correct option.

Compute the required density ratio.

Given: The rate of diffusion of $A$ is $5times$ that of $B$.

We know that rate of diffusion is inversely proportional to the square root of its density.

So, $\frac{r_A}{r_B}=\sqrt{\frac{d_B}{d_A}}$ where, $d_A,d_B$ are the densities of respective mediums.

$$\begin{gathered} \Rightarrow \frac{5r_B}{r_B}=\sqrt{\frac{d_B}{d_A}} \\ \Rightarrow \frac{25}{1}=\sqrt{\frac{d_B}{d_A}} \\ \Rightarrow \sqrt{\frac{d_B}{d_A}}=\frac{1}{25} \end{gathered}$$

Hence the density ratio of $A$ and $B$ is $\frac{1}{25}$.

Therefore, Option $D$ is the correct answer.