The rms speed of a gas molecule is

Options

A. `sqrt((M)/(3RT))`
B. `(M)/(3RT)`
C. `sqrt((3RT)/(M))`
D. `((3RT)/(M))^(2)`

Answer

To find the root mean square (rms) speed of a gas molecule, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding RMS Speed**:
The rms speed of gas molecules is defined as the square root of the average of the squares of the speeds of the molecules.

2. **Formula for RMS Speed**:
The formula for the rms speed \( v_{rms} \) is given by:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin,
- \( M \) is the molar mass of the gas in kg/mol.

3. **Units of RMS Speed**:
The SI unit of rms speed is meters per second (m/s), as it is a measure of velocity.

4. **Identifying Variables**:
- Ensure you know the values of \( R \), \( T \), and \( M \) for the specific gas you are considering.

5. **Substituting Values**:
If specific values for \( R \), \( T \), and \( M \) are provided, substitute them into the formula to calculate \( v_{rms} \).

6. **Calculating RMS Speed**:
After substituting the values, perform the calculations to find the rms speed.

7. **Conclusion**:
The final result will give you the rms speed of the gas molecules.