Which one fo the following statements is false

Options

A. Avagadro number `= 6.02 xx 10^(21)`
B. The relationship 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 `(3 RT // M)^(1//2)`

Explanation

To determine which statement is false, we will analyze each statement provided in the question step by step.

**Step 1: Analyze the Value of Avogadro's Number**
- The value of Avogadro's number (Na) is approximately \(6.02 \times 10^{23}\) particles per mole.
- If any statement claims that this value is less than or different from this, it would be false.

**Step 2: Examine the Relation Between Average Velocity and Root Mean Square Velocity**
- The average velocity (U) of gas molecules can be calculated using the formula:
\[ U = \sqrt{\frac{8RT}{\pi m}} \]
- The root mean square velocity (\(v_{rms}\)) is given by:
\[ v_{rms} = \sqrt{\frac{3RT}{m}} \]
- The relationship between average velocity and root mean square velocity is:
\[ v_{rms} = 0.9213 U \]
- This statement is correct.

**Step 3: Consider the Mean Kinetic Energy of an Ideal Gas**
- The mean kinetic energy (KE) of an ideal gas is given by:
\[ KE = \frac{3}{2} kT \]
where \(k\) is the Boltzmann constant and \(T\) is the temperature.
- The kinetic energy is dependent only on temperature and is independent of pressure. Thus, this statement is also correct.

**Step 4: Identify the False Statement**
- Since we have analyzed the statements regarding Avogadro's number, the relationship between average and root mean square velocities, and the mean kinetic energy of an ideal gas, we can conclude that the first statement regarding Avogadro's number is incorrect if it states that its value is less than \(6.02 \times 10^{23}\).

**Final Conclusion:**
The false statement among the options provided is the one regarding the value of Avogadro's number.