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| Moment of Inertia of a Diatomic Molecule |
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| In stable equilibrium position, the two atoms in a diatomic molecule are separated by a certain distance r0. This distance is called intermolecular distance or bond length. |
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| Let us imagine the diatomic molecule as a system of two tiny spheres at either end of a thin weightless rod. |
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| Let C be the centre of mass of the molecule. Let r1 and r2 be the distances of the two atoms from the centre of mass C of the molecule. |
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| Now, r1 + r2 = r0 ---------- (1) |
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| and m1r1 = m2r2 ---------- (2) |
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| where m1 and m2 are the masses of the two atoms. |
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| From equation (1) |
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| r2 = r0 - r1 |
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| From equation (2) |
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| m1r1 = m2 (r0- r1) or m1r1 = m2r0 - m2r1 |
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| Let I be the moment of inertia of the diatomic molecule about an axis passing through the centre of mass of the molecule and perpendicular to bond length. |
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| Therefore, moment of inertia of a diatomic molecule about an axis passing through the centre of the diatomic molecule and perpendicular to bond length, is the product of reduced mass of the molecule and the square of bond length. |
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