In the `HCI` molecule, the separation between the nuclei of the two atoms is about `1.27Å (1Å = 10^(-10)m)`. Find the approximate location of the c.m 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 ?

Explanation

Let us choose the nucleus of the hydrogen atom as the origin for measuring distance. Mass of hydrogen atom, `m_(1)=1` unit (say) Since cholorine atom is 35.5 times as massive as hydrogen atom,
`therefore` mass of cholorine atom, `m_(2)=35.5 ` units

Now, `x_(1)=0 " and " x_(2)=1.27 " Å" =1.27xx10^(-10)m`
Distance of centre of mass of HCl molecule from the origin is given by
`X=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))=(1xx0+35.5xx1.27xx10^(-10))/(1+35.5)m`
`=(35.5xx1.27)/(36.5)xx10^(-10)m=1.235xx10^(-10)m=1.235` Å