In the HCI molecule, the separation between the nuclei of the two atoms is about 1.27 Å. Find the approximate location of the centre of mass 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.

Solution

It is given that,
Radius, r = 1.27 $straight A with 0 on top$
m_C_l = 35. 5 m_H

Therefore,
$straight r subscript 1 space equals space fraction numerator straight m subscript Cl over denominator straight m subscript Cl space plus space straight m subscript straight m end fraction space straight r space space space space equals space fraction numerator left parenthesis 35.5 right parenthesis space straight m subscript straight m over denominator 35.5 space straight m subscript straight m space plus space straight m subscript straight m end fraction space 1.27 space stack straight A space with straight o on top space space space equals space 1.2352 space stack straight A space with 0 on top space space space space equals space 1.24 space straight A with 0 on top$
Therefore,
Centre of mass is at a distance 1.24 $straight A with 0 on top$ from H end.