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 chorine atom ia about `35.5` times as massive as a hydrogen atom and nearly all the mass of an atom is cocentrated in its uncleus ?

Explanation

Let the mass of the `H` atom `= m` unit, mass of the `Cl` atom `= 35.5 m` units
Let c.m be at a distance `x Å` from `H` atom `:.` Distance of c.m from `Cl` atom `= (1.26 - x)Å`
If c.m is taken at the origin, then `m x + (1.27 - x) 35.5 m = 0`
`mx = - (1.27 - x) 35.5 m`
Negative sign indicates that if chlorine atom is on the right side of `c.m(+)`, the hydrogen atom is on the left side of `c.m`, Fig. So leaving negative sign, we get
`x + 35.5 x = 1.27 xx 35.5`
i.e. `36.5 x = 45.085 = (45.085)/(36.5) = 1.235`
`x = 1.235 Å`
Hence `c.m` is located on the line joining centres of `H` and `Cl` atoms at a distance `1.235 Å` from `H` atom.