Which of the following statement is false ?

Options

A. Avogadro number `= 6.01 xx 10^(21)`
B. The relastionship between average velocity `(bar(v))` and root mean square velocity `(u)` is `bar(v) = 0.9213 u`
C. The mean kinetic energy of an ideal gas is independent of the pressure of the gas
D. The root mean square velocity of the gas can be calculated by the formula `(3RT//M)^(1//2)`

Explanation

To determine which statement is false, we need to analyze each statement provided in the question.

### Step-by-Step Solution:

1. **Identify the Statements**:
- Statement 1: Avogadro's number is equal to \(6.01 \times 10^{21}\).
- Statement 2: The relationship between average velocity and root mean square velocity is equal to \(0.9213 v\).
- Statement 3: The kinetic energy of an ideal gas is independent of the pressure of the gas.
- Statement 4: The root mean square velocity of gas can be calculated by the formula \(\sqrt{\frac{3RT}{M}}\).

2. **Evaluate Statement 1**:
- Avogadro's number is actually \(6.022 \times 10^{23}\). Therefore, Statement 1 is **false**.

3. **Evaluate Statement 2**:
- The relationship between average velocity (\(v_{avg}\)) and root mean square velocity (\(v_{rms}\)) can be derived. The ratio \(v_{avg}/v_{rms}\) is calculated and found to be approximately \(0.9213\). Thus, Statement 2 is **true**.

4. **Evaluate Statement 3**:
- The kinetic energy of an ideal gas is given by the formula \(\frac{3}{2}RT\), which depends only on temperature and not on pressure. Therefore, Statement 3 is **true**.

5. **Evaluate Statement 4**:
- The formula for root mean square velocity is indeed \(\sqrt{\frac{3RT}{M}}\). Thus, Statement 4 is **true**.

6. **Conclusion**:
- The only false statement among the given options is Statement 1 regarding Avogadro's number.

### Final Answer:
The false statement is: **Avogadro's number is equal to \(6.01 \times 10^{21}\)**.

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