Question

The temperature at which the r.m.s. speed of $O_2$ is equal to that of neon at 300 K is:
(atomic mass of $O_2$ = 32 u and Ne = 20 u)

• A. $280K$
• B. $480K$
• C. $680K$
• D. $180K$

Answer 1

The correct option is B $480K$

rms velocity $\propto \sqrt{\frac{T}{M}}$
where, T is the temperature and M is the molar mass.
Given,
$\text{rms velocity of oxygen at T K}=\text{rms velocity of neon at 300 K}$
$\sqrt{\frac{T}{32\times {10}^{-3}}}=\sqrt{\frac{300}{20\times {10}^{-3}}}$

$\frac{u_1}{u_2}=\sqrt{\frac{T_1\times M_2}{T_2{M}_1}}$

Hence, $T=480K$