Question

The $RMS$ velocity of a gas whose each molecule weighs ${10}^{-12}g$ and at temperature ${27}^{o}C$ is:

• A. 0.70 $cm/s$
• B. 0.35 $cm/s$
• C. 0.35 $m/s$
• D. 0.70 $m/s$

Answer 1

The correct option is B 0.35 $cm/s$

As we know,
$U_{rms}=\sqrt{\frac{3RT}{M}}$

Each molecule weighs $={10}^{-12}g$
$N_A$ molecule has weight $=Mg$

So, $\frac{M}{N_A}={10}^{-12}g={10}^{-15}kg$

$N_A=6.023\times {10}^{23}$
Using all the parameters in SI unit

$U_{rms}=\sqrt{\frac{3\times 8.314\times 300}{{10}^{-15}\times 6.023\times {10}^{23}}}=35.24\times {10}^{-4}m/sec$
$\Rightarrow U=0.352cm/sec$.