Question

In crude model of a rotation diatomic molecule of chorine $(CI_2)$ , 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 $CI_2$ , 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 = $2(mr^2) = 2Mr^2$
$m = \frac{70 \times 10^{-3}}{2 \times 6.20 \times 10^{23}} = 5.81 \times 10^{-26} kg$
and $r = \frac{2.0 \times 10^{-10}}{2} = 10^{-10} m$
$I = 2(5.81 \times 10^{-26})(10^{-10} )^2$
$\therefore $ $K_g = \frac{1}{2} I \omega^2 = 2.32 \times 10^{-21} J$