Question

The distance between a carbon atom ( m = 12 u ) and an oxygen atom ( m = 16 u ) in the CO molecule is 1.13 × 10-10 m .
How far from the carbon atom is the center of mass of the molecule?
Express your answer to two significant figures and include the appropriate units.

Answer 1

6.45 ×$10^{-} ^{11}$ m is far from the carbon atom and is the center of mass of the molecule.

The sum of the products of the masses of the two particles and their respective position vectors equals the product of the total mass of the system and the position vector of the center of mass.

The center of mass of CO molecule will be on the line joining C and O atoms. Let the CO molecule be along the X- axis, the C atm being at the origin (x=0). The center of mass relative to the C atom is given by

$x_{cm} = \frac{m_{c}x_{c} + m_{o} x_{o} }{m_{c}+ m_{o} }$

Where, $m_{c}$ and $m_{o}$ are the respective masses of C and O atoms,  $x_{c}$ and  $x_{o}$ their distances relative to C atom.

Here, $m_{c}$ = 12 u , $m_{o}$ = 16 u and $x_{o} =1.13$×$10^-^{10}$ m

$x_{cm} = \frac{m_{c}x_{c} + m_{o} x_{o} }{m_{c}+ m_{o} }$

$x_{cm} =$ (12 × 0 + 16 × 1.13 × $10^{-} ^{10}$ ) / (12 + 16 )

$x_{cm}$ = 0.64571 × $10^{-} ^{10}$

$x_{cm}$ = 6.45 ×$10^{-} ^{11}$ m

Therefore, 6.45 ×$10^{-} ^{11}$ m is far from the carbon atom is the center of mass of the molecule.

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