Question

In the HCl molecule, the separation between the nuclei of the two atoms is about $1.27\mathring{A}(1\mathring{A}={10}^{-10}m)$. 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.

Answer 1

Let Mass of H atom $=m$
Mass of Cl atom $=35.5m$
Let the centre of mass of the system lie at a distance $x\mathring{A}$ from the Cl atom.
Distance of the centre of mass from the H atom =$(1.27-x)\mathring{A}$
Let us assume that the centre of mass of the given molecule lies at the origin. Let Hydrogen lie to the left of the origin and chlorine to the right.

Position of Hydrogen atom $=-(1.27-x)\mathring{A}$

Position of chlorine atom $=x\mathring{A}$

Therefore, we can have:

$\frac{-m(1.27-x)+35.5mx}{m+35.5m}=0$

$⟹-m(1.27-x)+35.5mx=0$

$⟹x=\frac{1.27}{35.5+1}=0.035\mathring{A}$

Hence, the centre of mass of the HCl molecule lies $0.035\mathring{A}$ from the Cl atom.