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In carbon monoxide molecules, the carbon and the oxygen atoms are separated by distance 1.2 angstroms.the distance of the centre of mass, from the carbon atom is 1)0.48 angstroms 2)0.51 angstroms 3)0.56 angstroms 4)0.69 angstroms Answer is option" 4 "can you explain why?
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In carbon monoxide molecules, the carbon and the oxygen atoms are sepa...
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In carbon monoxide molecules, the carbon and the oxygen atoms are sepa...
Given information:
Distance between carbon and oxygen atoms = 1.2 Å

To find:
Distance of centre of mass from the carbon atom

Solution:
The centre of mass of a diatomic molecule lies at the midpoint of the line joining the two atoms.

Let the distance of centre of mass from the carbon atom be x.

Then, the distance of centre of mass from the oxygen atom will be (1.2 - x).

The mass of carbon atom = mC
The mass of oxygen atom = mO

The total mass of the molecule = mC + mO

The position of the centre of mass is given by the formula:

xcm = (mC * 0 + mO * (1.2 - x))/(mC + mO)

Simplifying the above equation, we get:

xcm = (1.2 mO)/(mC + mO) - (mO/mC) * x

xcm + (mO/mC) * x = (1.2 mO)/(mC + mO)

xcm + (16/12) x = (1.2 mO)/(mC + mO) [Taking mO/mC = 16/12]

xcm = (1.2 mO)/(mC + mO) - (16/12) x

Substituting the values of mC and mO, we get:

xcm = (1.2 * 16)/(12 + 16) - (16/12) x

xcm = 0.69 - 1.33 x

Therefore, the distance of centre of mass from the carbon atom is 0.69 Å - Option 4.

Explanation:
The centre of mass of a diatomic molecule lies at the midpoint of the line joining the two atoms. Hence, we can use the formula for the position of the centre of mass to find the distance of centre of mass from a particular atom. We have substituted the given values of distance between carbon and oxygen atoms, and the masses of carbon and oxygen atoms in the formula to get the required answer.
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In carbon monoxide molecules, the carbon and the oxygen atoms are separated by distance 1.2 angstroms.the distance of the centre of mass, from the carbon atom is 1)0.48 angstroms 2)0.51 angstroms 3)0.56 angstroms 4)0.69 angstroms Answer is option" 4 "can you explain why?
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