Q125 / 170 · Manipal (MET) 2016 · Physics

A mixture of two gases is contained in a vessel. The gas 1 is monoatomic and gas 2 is diatomic and the ratio of their molecular masses $M_1 / M_2=1 / 4$. What is the ratio of root mean square speeds of the molecules of two gases?

  • Correct answer
    A
    $2$
  • B
    $4$
  • C
    $8$
  • D
    $16$

Solution

From kinetic theory of gases $p=\frac{1}{3} \frac{M}{V} \cdot e^2$ Since, $p$ and $V$ are constant (same) $\therefore \quad M_1 e_1^2=M_2 e_2^2$ $\Rightarrow \quad \frac{e_1^2}{e_2^2}=\frac{M_2}{M_1}$ $\Rightarrow \quad \frac{e_1}{e_2}=\sqrt{\frac{M_2}{M_1}}=\sqrt{4 / 1}=2 \quad\left[\right.$ given, $\left.\frac{M_1}{M_2}=\frac{1}{4}\right]$

Hence, the correct answer is option: 'A'.

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