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Question

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
35.5×1.2736.5A From the hydrogen atom
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B
35.5×1.2736.5A From the chlorine atom
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C
1.2736.5A From the hydrogen atom
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D
1.2736.5A From the chlorine atom
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Solution

The correct option is D 1.2736.5A 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 1015 m) is very small compared to the separation between the hydrogen and chlorine atom (which is 1.27×1010 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 = 1.27A and m2=35.5m1. Hence
xCM=35.5m1×1.27Am1+35.5m1=35.5×1.27A36.5
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
1.27A35.5×1.2736.5=1.27A36.5
Hence the correct choices are (a) and (d).

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