Question

The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room temperature the rms speed of oxygen oelcules is v, The rms speed of the hydrogen molecules at the same temperature will be

• A. v/16
• B. v/4
• C. 4v
• D. 16v

Answer 1

Answer: (B)

Given, Mass of oxygen $=16 \times$ Mass of hydrogen RMS speed of oxygen is $V$.
To find, RMS speed of hydrogen
we know, $V_{r m s}=\sqrt{\frac{3 R T}{M}} \propto \frac{1}{\sqrt{M}}$
Now, $ \frac{\left(V_{r m s}\right)_{O_{2}}}{\left(V_{r m s}\right)_{H_{2}}}=\frac{(1 / \sqrt{M})}{(1 / \sqrt{M \times 16})}=4 $
$\Rightarrow \frac{V}{\left(V_{r m s}\right)_{H_{2}}}=4 $ as, $\left(V_{r m s}\right)_{0_{2}}=V $
$\Rightarrow \left(V_{r m s}\right)_{H_{2}}=\frac{V}{4} $