Question

The distance between the centres of carbon and oxygen atoms in the carbon monoxide gas molecules is $1.12\times {10}^{-10}m$. Find the distance of centre of mass of molecules from carbon atom.

Answer 1

Let $m_1$ and $m_2$ be the masses of carbon and oxygen atom respectively. Let 'd' be the distance of separation between the center of carbon and oxygen atoms.

Let $x_1$ be the position of the carbon

and $x_2$ be the position of the oxygen atom

We can write the center of mass of this system as:

$x_{CM}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}......\left(1\right)$

Here we need to find the position of the center of mass of $CO$ molecule with respect to carbon atom

So, $x_1=0m$$and$x_2=1.12\times10^{-10}\ m$

$m_1$ mass of carbon atom $=12U$

and $m_1$ mass of oxygen atom $=16U$

Now,

$x_{CM}=\frac{12\times 0+16\times 1.12\times {10}^{-10}}{12+16}$

$x_{CM}=6.4\times {10}^{-11}m$

$x_{CM}=0.64\times {10}^{-10}m$

Hence the position of center of mass of $CO$ molecule with respect to carbon atom $=0.64\times {10}^{-10}m$