Published by:
CGP EDU Academic Team
Published on: September 12, 2026
For a monoatomic gas at temp T, match the following.
Column-I | Column-I |
(i) Mean square speed | [A] |
(ii) RMS speed of gas molecule | [B] |
(iii) Average speed of gas molecule | [C] |
(iv) Most probable speed of gas molecule | [D] |
Correct Matrix Matching
Text Solution
Verified by ExpertsThe correct answer is:
B
For a monoatomic gas, the properties of molecular speeds are defined as follows:
- Mean square speed: Given by the formula
\bar{v^2} = \frac{3kT}{m}wherekis the Boltzmann constant,Tis the absolute temperature, andmis the mass of one molecule. This relates to option [A]. - RMS speed: The root mean square speed is defined as
v_{rms} = \sqrt{\bar{v^2}} = \sqrt{\frac{3kT}{m}}. This corresponds to option [B]. - Average speed: The average speed for a gas molecule can be derived and is represented by
v_{avg} = \frac{2}{3} v_{rms}, relating to option [C]. - Most probable speed: The speed that corresponds to the maximum of the Maxwell-Boltzmann distribution, given by
v_{mp} = \sqrt{\frac{2kT}{m}}, which matches with option [D].
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