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, $V_{rms}=\sqrt{\frac{3RT}{M}}\propto \frac{1}{\sqrt{M}}$
Now, $\frac{{\left(V_{rms}\right)}_{O_2}}{{\left(V_{rms}\right)}_{H_2}}=\frac{(1/\sqrt{M})}{(1/\sqrt{M\times 16})}=4$
$\Rightarrow \frac{V}{{\left(V_{rms}\right)}_{H_2}}=4$ as, ${\left(V_{rms}\right)}_{0_2}=V$
$\Rightarrow {\left(V_{rms}\right)}_{H_2}=\frac{V}{4}$