A sample of oxygen is compressed to half of its original volume at constant temperature. If the rms velocity of gas molecules was originally C, their new rms velocity is

Options

A. `4 C`
B. `2C`
C. `C`
D. `C//2`

Explanation

To solve the problem, we need to analyze how the root mean square (RMS) velocity of gas molecules changes when the volume of the gas is halved at constant temperature.

### Step-by-Step Solution:

1. **Understand the RMS Velocity Formula**:
The RMS velocity (C) of gas molecules is given by the formula:
\[ C = \sqrt{\frac{3RT}{M}} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature,
- \( M \) is the molar mass of the gas.

2. **Identify Constants**:
In this scenario, we are told that the temperature (T) and the molar mass (M) of the gas do not change when the volume is halved.

3. **Analyze the Effect of Volume Change**:
According to the ideal gas law, when the volume of a gas is compressed at constant temperature, the pressure of the gas increases. However, the RMS velocity is not directly dependent on the volume of the gas.

4. **Conclusion on RMS Velocity**:
Since neither the temperature nor the molar mass of the gas changes, the RMS velocity remains the same. Therefore, the new RMS velocity after the volume is halved is still:
\[ C \]

### Final Answer:
The new RMS velocity of the gas molecules after compressing the volume to half at constant temperature is \( C \).