Question

AT NTP the rms velocity of hydrogen molecules is 1.8 km/s. Under the same conditions the rms velocity of oxygen molecules in km/s will be:

• A. $16\times 1.8\text{ }km/s$
• B. $8\times 1.8\text{ }km/s$
• C. $4\times 1.8\text{ }km/s$
• D. $1/4\times 1.8\text{ }km/s$

Answer 1

Answer: (D)

$1/4\times 1.8\text{ }km/s$

Answer 2

From the relation of rms velocity, we know ${{c}_{rms}}\propto \sqrt{\frac{1}{M}}$ Hence, $\frac{{{c}_{rms(H)}}}{{{c}_{rms(H)}}}=\sqrt{\frac{1/{{M}_{H}}}{1/{{M}_{O}}}}=\sqrt{\frac{{{M}_{O}}}{{{M}_{H}}}}$ $=\sqrt{\frac{32}{2}}=\sqrt{16}=4$ ${{c}_{rms}}=\frac{{{c}_{rms(H)}}}{4}=\frac{1}{4}\times 1.8\,km/s$