In the HCl molecule, the separation between the nuclei of hydrogen and chlorine atoms is 1.27 ∘A. If the mass of a chlorine atom is 35.5 times that of a hydrogen atom, the centre of mass of the HCl molecule is at a distance of
A
35.5×1.2736.5∘A From the hydrogen atom
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B
35.5×1.2736.5∘A From the chlorine atom
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C
1.2736.5∘A From the hydrogen atom
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D
1.2736.5∘A From the chlorine atom
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Solution
The correct option is D1.2736.5∘A From the chlorine atom Since most of the mass of an atom is concentrated in its nucleus and the size of a nucleus (which is of the order of 10−15 m) is very small compared to the separation between the hydrogen and chlorine atom (which is 1.27×10−10 m), the atoms can be treated as point masses. The centre of mass of HCl molecule will be on the line joining the two atoms. Let us say the the H atom is located at, say, x = 0 and the Cl atom at x = x. Let xCM be the position of the centre of mass between X = 0 and x = x. If m1 and m2 are the masses of H and Cl atoms, then from the definition of centre of mass,
we have xCM=m1×0+m2x0m1+m2=m2xm1+m2
Now x = separation between H and Cl atoms = 1.27∘A and m2=35.5m1. Hence xCM=35.5m1×1.27∘Am1+35.5m1=35.5×1.27∘A36.5
This gives the distance of the centre of mass from the hydrogen atom. The distance of the centre of mass from the chlorine atom is 1.27∘A−35.5×1.2736.5=1.27∘A36.5
Hence the correct choices are (a) and (d).