Hello!! I need help on this problem very urgently. Would appreciate step-by-step

Question

Hello!!

I need help on this problem very urgently. Would appreciate step-by-step answer.

An electron and a neutral carbon atom of polarizability alpha are at a distance r apart (r is much greater than the diameter d of the atom). Due to polarization of the atom by the electron, there is a force F between the electron and the carbon atom. If we change r to 2.6r, what will be the ratio of F'/F where F' is the new force between the two? Hint: To find the r-dependence of the force, first find the induced polarization (dipole moment) of the atom as a function of r. Then find the force exerted by this induced dipole on the electron.

Explanation / Answer

F will be proportional to 1/r2

F=k/r2

F' =k/(2.6r)2

F'/F=1/2.62 =25/169 =0.148

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