The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is 1.1 Å. 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 center of mass of the carbon monoxide molecule

The correct option is 0.63 Å from the carbon atom.

To find the position of the center of mass of the carbon monoxide (CO) molecule, we can use the formula for the center of mass of a two-particle system:

$x_{\mathrm{CM}}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

Let us choose the position of the carbon (C) atom as the origin of our coordinates:
Position of the carbon atom, $x_C=0\text{Å}$
Mass of the carbon atom, $m_C=12\text{a.m.u.}$

The oxygen (O) atom is located at a distance of 1.1 Å from the carbon atom:
Position of the oxygen atom, $x_O=1.1\text{Å}$
Mass of the oxygen atom, $m_O=16\text{a.m.u.}$

Substitute these values into the center of mass formula to calculate the distance of the center of mass from the carbon atom:

$x_{\mathrm{CM}}=\frac{(12\times 0)+(16\times 1.1)}{12+16}$

Simplify the expression:

$x_{\mathrm{CM}}=\frac{17.6}{28}$

$x_{\mathrm{CM}}\approx 0.63\text{Å}$

Therefore, the position of the center of mass of the carbon monoxide molecule is 0.63 Å from the carbon atom.