SATHEE: States of Matter - Result Question 28

States of Matter - Result Question 28

####28. Root mean square velocity of a gas molecule is proportional to

(a) $m^{1 / 2}$

(b) $m^{0}$

(c) $m^{- 1 / 2}$

(d) $m$

[1990]

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Solution:

(c) According to kinetic gas equation $P V = \frac{1}{3} m N u^{2}, u =$ root mean square velocity $\Rightarrow u^{2} = \frac{3 P V}{m N}$ or $u \propto \frac{1}{\sqrt{m}}$ i.e $u \propto m^{- \frac{1}{2}}$

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