Question

Root mean square velocity of a gas molecule is proportional to

• A. $m^{1/2}$
• B. $m^0$
• C. $m^{-1/2}$
• D. m

Answer 1

The Correct Option is C

Root mean square speed is given by the expression
$\, \, \, \, \, \, \, \, \, U_{rms}=\sqrt{\frac{3RT}{M}}\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, [becuse M=mN]$
$\, \, \, \, \, \, \, \, \, U_{rms}\sqrt{\frac{1}{m}}\, \, \, \, \Rightarrow U_{rms} \propto (m)^{-1/2}$

Answer 2

Here, MO = molar mass and M = mass of gas molecule,

U_rms = \(\frac{\sqrt{3}RT}{M}\)

U_rms ∝ \(\sqrt{\frac{1}{m}}\) ⇒ U_rms ∝ \(\frac{1}{m^{\frac{1}{2}}}\)

⇒ U_rms ∝ \(m^{-\frac{1}{2}}\)

Hence, the correct option is ‘C '.i.e. \(m^{-\frac{1}{2}}\)

Answer 3

Root mean square velocity(U_rms) is the square root of the average square of velocity.

U_rms = \(\frac{\sqrt{3}RT}{M}\), where R= gas constant, T= temperature, M= molar mass 

U_rms ∝ \(\sqrt{\frac{1}{m}}\) ⇒ U_rms ∝ \(\sqrt{\frac{1}{m}}\)

⇒ U_rms ∝ \(\frac{1}{m^{\frac{1}{2}}}\)

⇒ U_rms ∝ \(m^{-\frac{1}{2}}\)

Hence, the correct option is ‘C '.i.e. \(m^{-\frac{1}{2}}\)