question_answer

In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance \[1.12\times {{10}^{-10}}m\]. The distance of the centre of mass, from the carbon atom is :

A) \[o.64\times {{10}^{-10}}m\]                     

B) \[o.56\times {{10}^{-10}}m\]

C) \[o.51\times {{10}^{-10}}m\]                     

D) \[o.48\times {{10}^{-10}}m\]

Correct Answer: A

Solution :

                Key Idea: The cartesian co-ordinate of the centre of mass is \[\frac{\underset{i}{\mathop{\Sigma }}\,{{m}_{i}}{{x}_{i}}}{\Sigma {{m}_{i}}}\] Let the distance of the centre of mass from the carbon atom be r. The mass of carbon, \[{{m}_{1}}=12\text{ }amu\] The mass of oxygen, \[{{m}_{2}}=16amu\] From definition of centre of mass                 \[{{x}_{cm}}=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] \[=\frac{(12amu)\times 0+(16amu)\times r}{12amu+16amu}\] \[=\frac{16}{28}r=\frac{16}{28}\times 1.12\times {{10}^{-10}}m\] \[=0.64\times {{10}^{-10}}m\]