Q. The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1\ \mathring{\mathrm{A}}$. Given, mass of carbon atom is $12\ a.\ m.\ u.$ and mass of oxygen atom is $16\ a.m.u.$, calculate the position of the centre of mass of the carbon monoxide molecule
A) $6.3\ \mathring{\mathrm{A}}$ from the carbon atom
B) $1\ \mathring{\mathrm{A}}$ from the oxygen atom
C) $0.63\ \mathring{\mathrm{A}}$ from the carbon atom
D) $0.12\ \mathring{\mathrm{A}}$ from the oxygen atom
Explanation
(c) $m_{1} = 12,m_{2} = 16$
${\overrightarrow{r}}_{1} = 0\widehat{i} + 0\widehat{j},r_{2} = 1.1\widehat{i} + 0\widehat{j}$
$\overrightarrow{r} = \frac{m_{1}{\overrightarrow{r}}_{1} + m_{2}{\overrightarrow{r}}_{2}}{m_{1} + m_{2}}$
$\overrightarrow{r} = \frac{16 \times 1.1}{28}\widehat{i} = 0.63\widehat{i}\ i.e.0.36\mathring{\mathrm{A}}$ from carbon atom
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.