In a diatomic molecule, the rotational energy at a given temperature

(a) Obeys Maxwell’s distribution

(b) Have the same value for all molecules

(c) Equals the translational kinetic energy for each molecule

(d) Is (2/3)rd the translational kinetic energy for each molecule

This is a multiple choice answer as classified in NCERT Exemplar

(a), (d) The total energy associated with the molecule is

E= $\frac{1}{2}m{v}_x^2+\frac{1}{2}m{v}_y^2+\frac{1}{2}m{v}_z^2+\frac{1}{2}{I}_x{w}_x^2+\frac{1}{2}{I}_y{w}_y^2$

The number of independent terms in the above expressions is 5. So we can predict velocities of molecule by maxwell’s distribution, hence the above expression obeys maxwell ‘s distribution .

So 2 rotational and 3 translational energies are associated with each molecule

So rotational energy at a given temperature is 2/3 of the translational KE of each molecule.

<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (a), (d) The total energy associated with the molecule is</p><p>E=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi>m</mi> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> <mo>+</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi>m</mi> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>y</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> <mo>+</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi>m</mi> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>z</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> <mo>+</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> </msub> <msubsup> <mrow> <mrow> <mi>w</mi> </mrow> </mrow> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> <mo>+</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mi>y</mi> </mrow> </mrow> </msub> <msubsup> <mrow> <mrow> <mi>w</mi> </mrow> </mrow> <mrow> <mrow> <mi>y</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> </math> </span></p><p>The number of independent terms in the above expressions is 5. So we can predict velocities of molecule by maxwell’s distribution, hence the above expression obeys maxwell ‘s distribution .</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745555478phpGMzgKl_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745555478phpGMzgKl.jpeg" alt="" width="130" height="113"></picture></div></div><p>So 2 rotational and 3 translational energies are associated with each molecule</p><p>So rotational energy at a given temperature is 2/3 of the translational KE of each molecule.</p>

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