Question:
The rms speed of gas molecules is given by:
The rms speed of gas molecules is given by:
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Remember "3-R-T over M" under the root for RMS speed.
Updated On: May 5, 2026
- $\sqrt{3RT/M}$
- $\sqrt{2RT/M}$
- $\sqrt{RT/M}$
- $3RT/M$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The root-mean-square (rms) speed is the measure of the speed of particles in a gas, which is the square root of the average of the squares of the velocities.
Step 2: Meaning
It represents the speed of a molecule possessing average kinetic energy.
Step 3: Analysis
From the kinetic theory of gases, the average kinetic energy of a mole of gas is $\frac{3}{2}RT$. Since kinetic energy is also $\frac{1}{2}Mv^{2}$, equating the two gives $v_{rms} = \sqrt{\frac{3RT}{M}}$.
Step 4: Conclusion
Therefore, the correct mathematical expression for rms speed involves the square root of three times the product of the gas constant and temperature, divided by molar mass. Final Answer: (A)
The root-mean-square (rms) speed is the measure of the speed of particles in a gas, which is the square root of the average of the squares of the velocities.
Step 2: Meaning
It represents the speed of a molecule possessing average kinetic energy.
Step 3: Analysis
From the kinetic theory of gases, the average kinetic energy of a mole of gas is $\frac{3}{2}RT$. Since kinetic energy is also $\frac{1}{2}Mv^{2}$, equating the two gives $v_{rms} = \sqrt{\frac{3RT}{M}}$.
Step 4: Conclusion
Therefore, the correct mathematical expression for rms speed involves the square root of three times the product of the gas constant and temperature, divided by molar mass. Final Answer: (A)
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