Question

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

The given situation can be shown as :

Distance between H and Cl atoms = 1.27 $\AA$
Mass of H atom = $m$
Mass of Cl atom = $35.5\, m$
Let the centre of mass of the system lie at a distance x from the CI 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:
$\frac{m(1.27-x)+35.5mx}{m+35.5m}$ = $0$

$m(1.27-x)+35.5\,mx$ = $0$

$1.27-x$ = $35.5x$

$\therefore$ $x$ = $\frac{-1.27}{(35.5-1)}$ = $-0.037 \AA$

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 $0.037 \AA$ from the Cl atom.