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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^(-21)J`

B

`2.32xx10^(21)J`

C

`2.32xx10^(-21)erg`

D

`2.32zz10^(21)erg`

Text Solution

Verified by Experts

The correct Answer is:
A

`m=(70xx10^(-3))/(2xx6.02xx10^(23))=5.81xx10^(-26)kg` and
`r=(2.0xx10^(-10)m,M.I=2(mr^(2))=2mr^(2)`
`I=2(5.81xx10^(-26))(10^(-10))^(2)`
`therefore K_(R)=(1)/(2)Iomega^(2)=2.32xx10^(21)J`
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