Which of the following is true about the mass of molecules `m` and `u_("rms")`?

Options

A. `u_("rms") prop m`
B. `u_("rms") prop (1)/(m)`
C. `u_("rms") prop 1//sqrtm`
D. `u_("rms") prop 1//m^(2)`

Explanation

To solve the question regarding the relationship between the mass of molecules \( m \) and the root mean square velocity \( u_{\text{rms}} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: The root mean square velocity \( u_{\text{rms}} \) of gas molecules is given by the formula:
\[ u_{\text{rms}} = \sqrt{\frac{3RT}{m}} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin,
- \( m \) is the mass of one molecule (or molecular mass).

2. **Identify the Relationship**: From the formula, we can see that \( u_{\text{rms}} \) is related to the mass \( m \) of the molecule. Specifically, it is evident that:
\[ u_{\text{rms}} \propto \frac{1}{\sqrt{m}} \]
This means that as the mass of the molecule increases, the root mean square velocity decreases.

3. **Conclusion**: Therefore, we can conclude that the root mean square velocity \( u_{\text{rms}} \) is inversely proportional to the square root of the mass of the molecule \( m \). This leads us to the correct option in the question.

### Final Answer:
The correct statement is that \( u_{\text{rms}} \) is inversely proportional to the square root of the mass of the molecule \( m \).