Atom-ion interplay

Classical Mechanics Level 5

Charged particles such as ions can separate the charges inside of overall electrically neutral atoms, thus making an electric dipole. A dipole is characterized with a dipole moment \(p = \alpha E_{external}\), where \( \alpha\) is the polarizability of an atom, and \(E_{external}\) is the external field acting on the atom. Dipole moments can also be written as \(p = 2qd\), where \(q\) is the magnitude of the separated charge in the dipole and \(d\) is the distance of the separated charge from the center of the atom.

We can quantify the polarizability of different atoms by observing the force that acts on the passing ions. What is the ratio of the attractive force with which a polarized atom acts on a passing ion and the atom’s polarizability *in \(\frac{\mbox{N}^2}{\mbox{m C}^2}\) *?

Details and assumptions

  • The ion-atom distance is \(1 ~\mbox{m}\).
  • Charge of the ion is \(1 ~\mbox{nC}\).
  • The atom was initially polarized by the ion itself.
  • Assume the separation between the charges in the atomic dipole is much smaller than the atom-ion distance.

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