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.