Q. In the $HCl$ molecule, the separation between the nuclei of the two atoms is about $1.27\ \mathring{\mathrm{A}}\ (1\ \mathring{\mathrm{A}} = 10^{- 10}m)$. The approximate location of the centre of mass of the molecule, assuming the chlorine atom to be about 35.5 times massive as hydrogen is
A) $1\ \mathring{\mathrm{A}}$
B) $2.5\ \mathring{\mathrm{A}}$
C) $1.24\ \mathring{\mathrm{A}}$
D) $1.5\ \mathring{\mathrm{A}}$
Explanation
(c) $m_{1} = 1,m_{2} = 35.5,\ {\overrightarrow{r}}_{1} = 0,{\overrightarrow{r}}_{2} = 1.27\widehat{i}$
$\overrightarrow{r} = \frac{m_{1}{\overrightarrow{r}}_{1} + m_{2}{\overrightarrow{r}}_{2}}{m_{1} + m_{2}}$
$\overrightarrow{r} = \frac{35.5 \times 1.27}{1 + 35.5}\widehat{i}$
$\overrightarrow{r} = \frac{35.5}{36.5} \times 1.27\widehat{i} = 1.24\widehat{i}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.