In 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
In 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
The correct options are
A 35.5×1.2736.5∘A from the hydrogen atom.
D 1.2736.5∘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 atoms (which is 1.27×10−10 m), the atoms can be treated as point masses.
The centre of mass of HCI molecule will be on the line joining the two atoms. Let us say that 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 CI atoms, then from the definition of centre of mass, we have
xCM=m1×0+m2xm1+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 is
1.27∘A−35.5×1.2736.5∘A=1.27∘A36.5
Hence, the correct choices are (a) and (d).
A
35.5×1.2736.5∘A from the hydrogen atom.
D
1.2736.5∘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 atoms (which is 1.27×10−10 m), the atoms can be treated as point masses.
The centre of mass of HCI molecule will be on the line joining the two atoms. Let us say that 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 CI atoms, then from the definition of centre of mass, we have
xCM=m1×0+m2xm1+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 is
1.27∘A−35.5×1.2736.5∘A=1.27∘A36.5
Hence, the correct choices are (a) and (d).
