How to Find the Distance Between Atoms With the Moment of Inertia

Inertia is a quantitative term that identifies the resistance of any object to a change in motion. The calculation for inertia varies based on the specific object and its particular type of motion. For rotating objects, such as a diatomic molecule composed of two atoms, the inertia is directly proportional to the mass and the square of the distance, or radius, between the atoms and the point of rotation. Thus, given the inertia mass of the molecule, the distance between two atoms can easily be calculated.

Things You'll Need

  • Calculator
  • Periodic table of elements
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Instructions

    • 1

      Determine the mass of the two atoms that make up the molecule. These measurements can be found directly under the symbol for the respective elements in the periodic table. The value should be reported in atomic mass units, or amu.

    • 2

      Identify the inertia of the specific molecule in question. For this problem, the inertia must be given to determine the unknown distance between the two atoms. If not given, this radius cannot be determined.

    • 3

      Plug these values into the formula for inertia. The formula for inertia of a rotating molecule is I = ([M1*M2]/[M1+M2])*L^2, where I is the inertia, M1 and M2 are the masses of the two respective atoms and L is the bond length.

    • 4

      Solve for the bond length, L. This is accomplished using simple algebra and multiplying the inertia by the reciprocal of mass terms and taking the square root of this value, or:

      L = sqrt{ I*([M1+M2]/[M1*M2]) }

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