According to Graham's law, at a given temperature, the ratio of the rates of diffusion `r_(A)//r_(B)` of gases `A` and `B` is given by

Options

A. `((P_(A))/(P_(B)))((M_(A))/(M_(B)))^(1//2)`
B. `((M_(A))/(M_(B)))((P_(A))/(P_(B)))^(1//2)`
C. `((P_(A))/(P_(B)))((M_(B))/(M_(A)))^(1//2)`
D. `((M_(A))/(M_(B)))((P_(B))/(P_(A)))^(1//2)`

Explanation

To solve the question regarding Graham's law and the ratio of the rates of diffusion of gases A and B, we can follow these steps:

### Step 1: Understand Graham's Law
Graham's law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass (molecular weight). Mathematically, it can be expressed as:
\[ r \propto \frac{1}{\sqrt{M}} \]
where \( r \) is the rate of diffusion and \( M \) is the molar mass of the gas.

### Step 2: Write the Expressions for Gases A and B
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