Question

The temperature of a gas consisting of rigid diatomic molecules is T = 300 K. Calculate the root mean square velocity of a rotating molecule if its moment of inertia is equal to $I=2.1\times {10}^{-39}gc{m}^2.$

• A. rad/sec.
• B. rad/sec.
• C. rad/sec.
• D. rad/sec.

Answer 1

The correct option is A rad/sec.

Let ${\omega }_{\rho ms}$ be the angular root mean square velocity
$\frac{1}{2}I{\omega }_{\rho ms}^2=\frac{2}{2}kT{\omega }_{rms}=\sqrt{\left(\frac{2kT}{I}\right)}=\sqrt{\left[\frac{2\times (1.38\times {10}^{-23})\times 300}{(2.1\times {10}^{-46})}\right]}[\Theta I=2.1\times {10}^{-39}gc{m}^2=2.1\times {10}^{-46}kg{m}^2]=6.3\times {10}^{12}rad/sec.$