Question

If the rms speed of oxygen molecules at $0^{\circ }\text{C}$ is $160\text{m/s}$, find the rms speed of hydrogen molecules at $0^{\circ }\text{C}$.

• A. $80\text{m/s}$
• B. $640\text{m/s}$
• C. $40\text{m/s}$
• D. $332\text{m/s}$

Answer 1

The correct option is B $640\text{m/s}$

The rms speed is given by :
$v_{rms}=\sqrt{\frac{3KT}{M}}$
$\Rightarrow \frac{(v_{rms}{)}_{O_2}}{(v_{rms}{)}_{H_2}}=\sqrt{\frac{M_{H_2}}{M_{O_2}}}=\sqrt{\frac{2}{32}}$
$\Rightarrow (v_{rms}{)}_{H_2}=4(v_{rms}{)}_{O_2}=4\times 160$
$(v_{rms}{)}_{H_2}=640\text{m/s}$