Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • The oxygen molecule has a mass of 5.30 × 10^-26 kg and a moment of inertia of 1.94×10^-46 kg m2 about an axis through its centre perpendicular to the lines joining the two atoms.

Q7.20     The oxygen molecule has a mass of 5.30\times 10^{-26}kg  and a moment of inertia of
              1.94\times 10^{-46}kg\: m^{2}about an axis through its centre perpendicular to the lines joining
             the two atoms. Suppose the mean speed of such a molecule in a gas is 500m/s and
             that its kinetic energy of rotation is two thirds of its kinetic energy of translation.
            Find the average angular velocity of the molecule.

Answers (1)

best_answer

We are given the moment of inertia and the velocity of the molecule.

Let the mass of oxygen molecule be m.

So the mass of each oxygen atom is given by :      \frac{m}{2}

Moment of inertia is :

                                       I\ =\ \frac{m}{2}r^2\ +\ \frac{m}{2}r^2\ =\ mr^2

or                                   r\ =\ \sqrt{\frac{I}{m}}

or                                  r\ =\ \sqrt{\frac{1.94\times 10^{-46}}{5.36\times 10^{-26}}}\ =\ 0.60\times 10^{-10}\ m

We are given that :

                                     E_{rot}\ =\ \frac{2}{3}E_{tra}

or                                  \frac{1}{2}I\omega ^2\ =\ \frac{2}{3}\times \frac{1}{2}mv^2

or                                 \omega \ =\ \sqrt{\frac{2}{3}}\times \frac{v}{r}

or                                        =\ 6.80\times 10^{12}\ rad/s

Posted by

Devendra Khairwa

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Date Sheet 2025 (Out) Live: Class 10, 12 board exam time table at cbse.gov.in; syllabus, sample papers
anam-khan

CBSE Class 12 board exam date sheet 2025 out; exams from February 15 to April 4
anam-khan

When will CBSE Board exam 2025 date sheet be released for Class 10, 12?

Latest Question