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 (say) Since chlorine atom is 35.5 times as massive as hydrogen atom,

∴ mass of the cholorine atom, m₂ = 35.5 units

Now, `x_1 = 0 " and " x_2 = 1.27 Å = 1.27 xx 10^(-10) m`

distance of centre of mass of HCL molecule from its origin is given by

`X = (m_1x_1+m_2x_2)/(m_1+m_2) = (1xx0+ 35.5 xx 1.27 xx 10^(-10))/(1+35.5) m`

`= (35.5 xx 1.27)/36.5 xx 10^(-10) m`

`= 1.235 xx 10^(-10) m`

`= 1.235 Å`