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1. The problem statement, all variables and given/known data

If the chlorine molecule at 290 K were to rotate at the angular frequency predicted by the equipartition theorem what would be the average centripetal force?

(The atmos of Cl are 2*10^-10 m apart and the mass of the chlorine atom 35.45 a.m.u)

(Correct answer is 1.6*10^-10 N)

2. Relevant equations

Kinetic energy

[tex] E_{kin} = \frac{mv^2}{2} [/tex]

Centripetal force

[tex] F_c = \frac{mv^2}{r} [/tex]

Boltzmann's constant

[tex] k_B = 1.3807*10^{-23} JK^{-1} [/tex]

3. The attempt at a solution

Hi!

I tried to solve it this way.

I think of my Chlorine molecule as two points. One stationary and the other one circulating around it.

From the equipartition theorem i get that the average energy of the molecule is

[tex] E = \frac{7k_BT}{2} [/tex]

I think that this is equal to the kinetic energy

[tex] E = \frac{7k_BT}{2} = \frac{mv^2}{2} [/tex]

so

[tex] mv^2 = 7k_BT [/tex]

Using this in the equation for the centriopetal force I get

[tex] F_c = \frac{7k_BT}{r} = 1.4014^{-10}N [/tex]

which is not the right answer and I havn't used the mass at all in the problem.

What's wrong??

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# Homework Help: Equipartition theorem and chlorine

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