In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 Å (1 Å = 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.
Let, Mass of the Hydrogen = m
Mass of the Chlorine = 35.5m
and given that, Separation between atoms = 1.27 Å
= 1.27×10-10 m
Let centre of mass for the molecule is a ‘x’ Å distance from the Cl atom then distance from Hydrogen atom be (1.27 – x) Å.
(As shown in the above diagram)
For one dimension, centre of mass CM can calculate by,
m
Where, m1 = mass of the first body,
m2 = mass of the second body,
x1 = Distance from centre of mass to the first body,
x2 = Distance from centre of mass to the second body,
Suppose Centre of mass of the molecule lies at origin (Zero) then,
(∵ It is in 1 dimension)
⇒
⇒ 1.27m – mx + 35.5mx = 0
⇒ 1.27 – x = -35.5x
∴ 
Å = -0.037 Å = -0.037×10-10 m
But, negative sign just indicates that CM lies left to chlorine (as assumed in figure) and it lies at a distance of 0.037×10-10 m.