Question

Temperature at which the rms speed of $O_2$ is equal to that of neon at $300\text{K}$ is:

• A. $280\text{K}$
• B. $480\text{K}$
• C. $680\text{K}$
• D. $180\text{K}$

Answer 1

The correct option is B $480\text{K}$

Let $u_1$ be the rms speed of $O_2$
$u_1=\sqrt{\frac{3R{T}_1}{M_1}}$
Let $u_2$ be the rms speed of $Ne$
$u_2=\sqrt{\frac{3R{T}_2}{M_2}}$
now,
$u_1=u_2\sqrt{\frac{T_1}{M_1}}=\sqrt{\frac{T_2}{M_2}}$

$\sqrt{\frac{T_1}{32}}=\sqrt{\frac{300}{20}}$
$T_1=480K$