In the HCl molecule, the separation between the nuclei of the two atoms is about $1.27\mathring{\text{A}}\big(1\mathring{\text{A}}= 10^{-10} \text{m}\big).$ Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.
Exercise
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Distance between H and Cl atoms $=1.27\mathring{\text{A}}$Mass of H atom = m
Mass of Cl atom = 35.5m
Let the centre of mass of the system lie at a distance x from the Cl atom.
Distance of the centre of mass from the H atom = (1.27 - x)
Let us assume that the centre of mass of the given molecule lies at the origin. Therefore, we can have,
[m(1.27 - x) + 35.5mx] / (m + 35.5m) = 0
m(1.27 - x) + 35.5mx = 0
1.27 - x = -35.5x
$\therefore\text{ x}=-1.27/(35.5-1)=-0.37\mathring{\text{A}}$
Here, the negative sign indicates that the centre of mass lies at the left of the molecule. Hence, the centre of mass of the HCl molecule lies $0.37\mathring{\text{A}}$ from the Cl atom.
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