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.

Explanation

Let the centre of mass at a distance of hydrogen atom is `xÅ`
`m_(1)` = mass of H-atom = m unit
`m_(2)` = mass of Cl-atom = 35.5 unit the position vector of H with respect to centre of mass which is at origin is `vec(r_(1))` and position vector of Cl atom is `vec(r_(2))`
`:.` position vector of centre of mass `vecr_(cm)=0`
Position vector of centre of mass
`vec(r_(cm))=(m_(1)vec(r_(1))+m_(2)vec(r_(2)))/(m_(1)+m_(2))`
but `vec(r_(1))=-xhatiandvec(r_(2))=(1.27-x)hati`
`:.0=(m(-xhati)+35.5m(1.27-xhati))/(m+35.5m)`
`0=(-mxhati+35.5xx1.27m-35.5mxhati)/(36.5m)`
`0=(-xhati+45.085-35.5xhati)/(36.5)`
`0=-36.5xhati+45.085`
`:.36.5xhati=45.085`
`:.x=(45.085)/(36.5)` magnitude
`:.x=1.2352`
`:.x~~1.235Å~~1.24Å`
It lies on the line of joining to both atom and at a distance of `1.24Å` from H-atom.