Q130 / 160 · TS EAMCET 2015 · Physics

RMS velocity of oxygen molecules at NTP is $0.5 \mathrm{~km} / \mathrm{s}$. The RMS velocity for the hydrogen molecule at NTP is

  • A
    $4 \mathrm{~km} / \mathrm{s}$
  • Correct answer
    B
    $2 \mathrm{~km} / \mathrm{s}$
  • C
    $3 \mathrm{~km} / \mathrm{s}$
  • D
    $1 \mathrm{~km} / \mathrm{s}$

Solution

RMS velocity of molecules at NTP $$ v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}} $$ RMS velocity of oxygen molecules at NTP $$ \left(v_1\right)=\sqrt{\frac{3 R T}{M_1}}=0.5 \mathrm{~km} / \mathrm{s} $$ RMS velocity of hydrogen molecules at NTP $$ \begin{aligned} & \left(v_2\right)=\sqrt{\frac{3 R T}{M_2}} \\ & \therefore \quad \frac{v_1}{v_2}=\sqrt{\frac{M_2}{M_1}} \\ & \Rightarrow \quad \frac{0.5}{v_2}=\sqrt{\frac{2}{32}} \\ & \Rightarrow \quad \frac{0.5}{v_2}=\frac{1}{4} \\ & \Rightarrow \quad v_2=2 \mathrm{~km} / \mathrm{s} \\ & \end{aligned} $$

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

Relevant Questions