Question

At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at ${1327}^{\circ }C$ ?

• A. $173K$
• B. $100K$
• C. $400K$
• D. $523K$

Answer 1

The correct option is B $100K$

$u_{rms}=\sqrt{\frac{3RT}{M}}$
According to the question, $\left(\sqrt{\frac{3R{T}_1}{M_{H_2}}}\right)=\left(\sqrt{\frac{3R{T}_2}{M_{O_2}}}\right)\sqrt{\frac{T_1}{2}}=\sqrt{\frac{1600}{32}}\Rightarrow \frac{T_1}{2}=\frac{1600}{32}\therefore T_1=100K.$