Question

In crude model of a rotation diatomic molecule of chorine $(C{I}_2)$ , the two CI atoms are $2.0\times 10^{-10}m$ apart and rotate about their centre of mass with angular speed $w=2.0\times 10^{12}rad/s$. What is the rotational kinetic energy of one molecule of $C{I}_2$ , which has a molar mass of 70.0g/mol ?

• A. $2.32\times 10^{-21}J$
• B. $2.32\times 10^{21}J$
• C. $2.32\times 10^{-21}erg$
• D. $2.32\times 10^{21}erg$

Answer 1

Answer: (B)

moment of Inertia I = $2(m{r}^2)=2M{r}^2$
$m=\frac{70\times 10^{-3}}{2\times 6.20\times 10^{23}}=5.81\times 10^{-26}kg$
and $r=\frac{2.0\times 10^{-10}}{2}=10^{-10}m$
$I=2(5.81\times 10^{-26})(10^{-10}{)}^2$
$\therefore$ $K_g=\frac{1}{2}I{\omega }^2=2.32\times 10^{-21}J$