Question

Find the separation between carbon and oxygen atom in molecule of Co gas.Provided centre of mass is at distance of 1.09 À from carbon atom and their masses are in the ration 12:16.​

Answer 1

Let the separation between the atoms be $\sf{x}.$

Mass of the atoms are in the ratio 12 : 16 = 3 : 4.

Let,

• mass of carbon atom $\sf{=3m.}$

• mass of oxygen atom $\sf{=4m.}$

Center of mass is at a distance of $\sf{1.09\ \AA}$ from carbon atom.

$\sf{\longrightarrow \dfrac{3m(0)+4mx}{3m+4m}=1.09\ \AA}$

$\sf{\longrightarrow \dfrac{4mx}{7m}=1.09\ \AA}$

$\sf{\longrightarrow \dfrac{4}{7}\,x=1.09\ \AA}$

$\sf{\longrightarrow x=1.09\times\dfrac{7}{4}\ \AA}$

$\sf{\longrightarrow\underline{\underline{x=1.9075\ \AA}}}$

Hence carbon and oxygen atoms are separated by a distance of $\bf{1.9075\ \AA}$ from each other.