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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 withb 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` ?
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Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Moment of inertia,
`I = 2 (mr^2) = 2mr^2`
Here, `m = (70 xx 10^-3)/(2 xx 6.02 xx 10^23)`
= `5.81 xx 10^-26 kg`
and `r = (2.0 xx 10 ^-10)/2`
`1.0 xx 10^-10 m`
`:. I = 2 (5.81 xx 10^-26) ( 1.0 xx 10^-10)^2`
`= 1.16 xx 10^-45 kg - m^2`
`:. K_R = 1/2 I omega^2`
`= 1/2 xx (1.16 xx 10^-45) xx (2.0 xx 10^12)^2`
`= 2.32 xx 10^-21 J`.
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