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

`1.03723* 10^(-20)\ J`

Step-by-step explanation:

r = Radius of atom =
`1* 10^(-10)\ m`

m = Mass of chlorine atom =
`5.88* 10^(-26)\ kg`

`\omega` = Angular speed =
`4.2* 10^(12)\ rad/s`

The moment of inertia of the system is given by

`I=2mr^2\\\Rightarrow I=2* 5.88* 10^(-26)* (10^(-10))^2\\\Rightarrow I=1.176* 10^(-45)\ kgm^2`

Kinetic energy is given by

`K=(1)/(2)I\omega^2\\\Rightarrow K=(1)/(2)* 1.176* 10^(-45)* (4.2* 10^(12))^2\\\Rightarrow K=1.03723* 10^(-20)\ J`

The rotational kinetic energy of one molecule of the atom is
`1.03723* 10^(-20)\ J`