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In a crude model of a rotating diatomic ...

In a crude model of a rotating diatomic molecule of chlorine `(Cl_2)`, the two `(C l)` atoms are `2.0 xx 10^-10 m` apart and rotate about their centre of mass with angular speed `omega = 2.0 xx 10^12 "rad" //s`. What is the rotational kinetic energy of one molecule of `C l_(2)` , Which has a molar mass of `70.0 g // mol` ?
.

A

`2.32xx10^(-20)J`

B

`2.32xx10^(-21)J`

C

`2.32xx10^(-19)J`

D

`2.32xx10^(-22)J`

Text Solution

Verified by Experts

The correct Answer is:
B
Let =moment of inertia
`l=2(mr^(2))`
`m=(70xx10^(-3)/(2xx6.02xx10^(23)) = 5.81xx10^(-26)kg`
`r=(2xx10^(-10)/(2)=1xx10^(-10)m`
`l=1.16xx10^(-45)k//m^(2)`
`therefore k=(1)/(2)//omega^(2)`
`=(1)/(2)(1.16xx10^(-45))(2xx10^(12))6(2)`
`=2.32xx10^(-21)J`
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