Question

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.

Answer 1

Let us choose the nucleus of the hydrogen atom as the origin for measuring distance.

Mass of hydrogen atom, m₁ = 1 unit (let)

Mass of chlorine atom, m₂ = 35.5 units (let)

Now, x₁ = 0 and x₂ = 1.27 Å

= 1.27 x 10^-10 m

Distance of CM of HCl molecule from the origin is given by

x = {m₁x₁ + m₂x₂}/{m₁ + m₂}

= {1 x 0 + 35.5 x 1.27 x 10^-10}/{1 + 35.5}

= 1.235 x 10^-10 m

= 1.235 Å