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(A) The root mean square speed $(v_{rms})$ of a gas molecule is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$ where $R$ is the universal gas

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$m^{-\frac{1}{2}} T^{\frac{1}{2}}$

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(A) The root mean square speed $(v_{rms})$ of a gas molecule is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$ where $R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass. Since $M = m 	imes N_A$ (where $m$ is the mass of one molecule and $N_A$ is Avogadro's number),we can substitute this into the equation: $v_{rms} = \sqrt{\frac{3RT}{mN_A}}$ Since $3$,$R$,and $N_A$ are constants,we have: $v_{rms} \propto \sqrt{\frac{T}{m}}$ $v_{rms} \propto m^{-\frac{1}{2}} T^{\frac{1}{2}}$

If $m'$ represents the mass of each molecule of a gas and $T'$ its absolute temperature,then the root mean square speed of the gas molecule is proportional to

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