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.


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