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