Direction for: In each of the following questions a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements mark the correct answer as
Assertion: The root mean square and most probable speeds of the molecules in a gas are the same. Reason: The Maxwell distribution for the speed of molecules in a gas is symmetrical.A) If both assertion and reason are true and the reason is the correct explanation of assertion.
B) If both assertion and reason are true but the reason is not the correct explanation of the assertion.
C) If assertion is true statement but reason is false.
D) If both assertion and reason are false.
Correct Answer: D
Solution :
Root mean square speed of molecules in a gas is defined as the square root of mean of squares of the speed of different molecules, i.e., \[{{\upsilon }_{rms}}=\sqrt{\frac{(\upsilon _{1}^{2}+\upsilon _{2}^{2}+....)}{N}}\] or \[{{\upsilon }_{rms}}=\sqrt{\frac{3RT}{M}}\] (according to kinetic theory of gases) while most probable speed is the speed which maximum number of molecules in a gas have at constant temperature and is given by \[{{\upsilon }_{mp}}=\sqrt{\frac{2RT}{M}}\] It is obvious that \[{{\upsilon }_{rms}}>{{\upsilon }_{mp}}.\] Also Maxwell distribution for the speed of molecules in a gas is asymmetrical. Hence, option (d) is true
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