The rms speed of helium at `24^(@)C` and 1 atm pressure is `450ms^(-1)`. Then the rms speed of the helium molecules at `24^(@)C` and 2 atm pressure is

Options

A. `450ms^(-1)`
B. `1800ms^(-1)`
C. `900ms^(-1)`
D. `750ms^(-1)`

Explanation

To find the root mean square (rms) speed of helium molecules at 24°C and 2 atm pressure, we can use the relationship between rms speed, temperature, and pressure.

### Step-by-Step Solution:

1. **Understanding the RMS Speed Formula**:
The rms speed (Vrms) of a gas is given by the formula:
\[ V_{\text{rms}} = \sqrt{\frac{3RT}{M}} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin,
- \( M \) is the molar mass of the gas.

2. **Temperature Conversion**:
Convert the given temperature from Celsius to Kelvin:
\[ T = 24°C + 273.15 = 297.15 \, K \]

3. **Understanding the Effect of Pressure**:
According to the kinetic theory of gases, if the temperature is constant, the rms speed of the gas is independent of pressure. This means that even if the pressure changes, as long as the temperature remains constant, the rms speed will not change.

4. **Given Information**:
The rms speed of helium at 24°C and 1 atm pressure is given as:
\[ V_{\text{rms}} = 450 \, m/s \]

5. **Conclusion**:
Since the temperature remains constant and the only change is in pressure (from 1 atm to 2 atm), the rms speed of helium at 24°C and 2 atm pressure will still be:
\[ V_{\text{rms}} = 450 \, m/s \]

### Final Answer:
The rms speed of helium molecules at 24°C and 2 atm pressure is **450 m/s**.

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