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The oxygen molecule as a mass of 5.3×10^ - 26 kg  and a moment of inertia of 1.94 into 10 to the power of minsis 46 kg metre square bout an Axis through its Centre perpendicular to the lines joining the two atoms. suppose the mean speed of such molecule in a gas 500 m per second and its kinetic energy of rotation is 2/3 of its kinetic energy of translation. find the average angular velocity of the molecule?

Asked by hemanttkumarr 4th October 2017, 6:27 AM
Answered by Expert
Answer:
begin mathsize 12px style First space calculate space the space KE space of space translation space of space the space oxygen space molecule space using space the space formula
KE subscript tr space equals space 1 half straight M subscript straight o straight v squared
Substituting space the space values space and space calculating comma space we space get
KE subscript tr space equals space 6.625 space cross times space 10 to the power of negative 21 end exponent space straight J
In space the space problem space it space has space been space given space that space the space rotational space kinetic space energy space of space the space molecule space
is space two minus thirds space of space its space translational space kinetic space energy. space That space is
KE subscript rot space equals 2 over 3 space KE subscript tr
Substituting space the space values space and space calculating comma space we space get
KE subscript rot space equals space 4.416 space cross times space 10 to the power of negative 21 end exponent space space straight J
Rotational space velocity space straight omega comma space of space the space molecule space can space be space calculated space from space the space relation space
straight omega space equals space fraction numerator square root of 2 space KE subscript rot end root over denominator straight I end fraction
Substituting space the space values space and space calculating comma space we space get
straight omega space equals space 6.7 space cross times space 10 to the power of 12 space rad space straight s to the power of negative 1 end exponent end style
Answered by Expert 8th December 2017, 5:16 PM
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