Question

In the $HCl$ molecule, the separation between the nuclei of the two atoms is about $1.27\mathop A\limits^o $. Find the approximate location of the COM 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

Hint: In this question, we need to evaluate the approximate location of the COM of the molecule such that 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. For this, we will assume the mass of hydrogen to be one unit, then find out the mass of the chlorine atom. Use the formula for COM to calculate the position of COM relative to any of the two atoms. Neglect the mass of the electron as said in the question above.

Complete step by step answer:
Let the mass of hydrogen atom be $1amu$
Then mass of chlorine atom will be $35.5amu$
Here one $amu$ means the mass of ${\left( {\dfrac{1}{{12}}} \right)^{th}}$ of Carbon$ - 12$ atom
For ease of calculation, we assume that both the atoms are situated in x axis.
For simplicity let us assume the chlorine atom to be at origin. Therefore the coordinates of chlorine atom will be $(0,0)$
Given the atomic separation to be
Thus the coordinate of hydrogen will be $(1.27,0)$
Now we apply the formula for COM of two masses
Thus COM will be
$
  COM = \dfrac{{1.27}}{{1 + 35.5}} \\
   = \dfrac{{1.27}}{{36.5}} \\
   = 0.036\mathop A\limits^o \\
 $
Thus, the COM of the two molecules will be located at a distance from the chlorine atom.

Note:
In the above solution there is no rule to assume the atoms at x-axis or the chlorine atom to be at origin, it totally depends on the personal perspective point of view.
Students can assume any other frame as well. A hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.