Chapter 7, Problem 47P

To determine

The distance of centre of mass of system of carbon atom and oxygen atom from carbon atom

Answer to Problem 47P

  $6.46\times {10}^{-11}\text{m}$

Explanation of Solution

Given:

Mass of the carbon atom $=m_c=12u$

Mass of the oxygen atom $=m_o=16u$

Distance of centre of mass of carbon atom $=r_c=0$

Distance of centre of mass of oxygen atom $=r_o=1.13\times {10}^{-10}\text{m}$

Distance of centre of mass molecule from carbon atom $=r_{cm}$

Formula Used:

Centre of mass of system of masses is given as

  $\begin{array}{l}{r}_{cm}=\frac{m_1{r}_1+m_2{r}_2+m_3{r}_3+\mathrm{..}}{m_1+m_2+m_3+\mathrm{..}}\\ \text{Where }{m}_1,m_2\text{,}{m}_3\text{ are the masses and }{r}_1,r_2\text{,}{r}_3\text{ are their respective centre of masses}\text{.}\end{array}$

Calculation:

Centre of mass of the molecule is given as

  $r_{cm}=\frac{m_c{r}_c+m_o{r}_o}{m_c+m_o}$

Substituting the values

  $\begin{array}{l}{r}_{cm}=\frac{(12)(0)+(16)(1.13\times {10}^{-10})}{12+16}\\ r_{cm}=6.46\times {10}^{-11}\text{m}\end{array}$

Conclusion:

Therefore, the distance of the centre of mass comes out to be $6.46\times {10}^{-11}\text{m}$