Question

At what temperature will oxygen molecules have same root mean square speed as hydrogen molecules at 200K?

• A. 527${}^o$C
• B. 1027${}^o$C
• C. 1527${}^o$C
• D. 2927${}^o$C

Answer 1

The correct option is D 2927${}^o$C

rms speed $u_{rms}=\sqrt{\frac{3RT}{M}}$

Equating rms speed expression for oxygen and hydrogen molecules:

$\sqrt{\frac{3R\times 200}{2}}=\sqrt{\frac{3RT}{32}}$

Solving for $T$,

$T$=3200K=(3200-273)${}^{\circ }C$=2927${}^{\circ }C$