Question

In a crude model of a rotating diatomic molecule of chlorine (Cl2), the two Cl atoms are 2.00 ✕ 10-10 m apart and rotate about their center of mass with angular speed ω = 4.20 ✕ 1012 rad/s. What is the rotational kinetic energy of one molecule of Cl2, which has a molar mass of 70.0 g/mol?

Answer 1

Answer:

$1.03723\times 10^{-20}\ J$

Explanation:

r = Radius of atom = $1\times 10^{-10}\ m$

m = Mass of chlorine atom = $5.88\times 10^{-26}\ kg$

$\omega$ = Angular speed = $4.2\times 10^{12}\ rad/s$

The moment of inertia of the system is given by

$I=2mr^2\\\Rightarrow I=2\times 5.88\times 10^{-26}\times (10^{-10})^2\\\Rightarrow I=1.176\times 10^{-45}\ kgm^2$

Kinetic energy is given by

$K=\dfrac{1}{2}I\omega^2\\\Rightarrow K=\dfrac{1}{2}\times 1.176\times 10^{-45}\times (4.2\times 10^{12})^2\\\Rightarrow K=1.03723\times 10^{-20}\ J$

The rotational kinetic energy of one molecule of the atom is $1.03723\times 10^{-20}\ J$