If rate of diffusion of A is 11 times that of B, what will be the density ratio of A and B?

Options

A. 11:1
B. 1:11
C. 121:1
D. 1:121

Answer

To solve the problem, we need to find the density ratio of substances A and B given that the rate of diffusion of A is 11 times that of B.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The rate of diffusion (r) is inversely proportional to the square root of the density (d) of the substance. This relationship can be expressed as:
\[ r \propto \frac{1}{\sqrt{d}} \]
Therefore, we can write:
\[ \frac{r_A}{r_B} = \sqrt{\frac{d_B}{d_A}} \]

2. **Setting Up the Equation**:
We know from the problem that:
\[ r_A = 11 \times r_B \]
Substituting this into our earlier equation gives:
\[ \frac{11 \times r_B}{r_B} = \sqrt{\frac{d_B}{d_A}} \]

3. **Simplifying the Equation**:
The \( r_B \) terms cancel out:
\[ 11 = \sqrt{\frac{d_B}{d_A}} \]

4. **Squaring Both Sides**:
To eliminate the square root, we square both sides:
\[ 11^2 = \frac{d_B}{d_A} \]
This simplifies to:
\[ 121 = \frac{d_B}{d_A} \]

5. **Finding the Density Ratio**:
Rearranging the equation gives us the density ratio:
\[ \frac{d_A}{d_B} = \frac{1}{121} \]
Thus, the density ratio of A to B is:
\[ d_A : d_B = 1 : 121 \]

### Final Answer:
The density ratio of A to B is \( 1 : 121 \).

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