To find the ratio of the attractive force with which a polarized atom acts on a passing ion and the atom's polarizability, we need to determine the attractive force and the polarizability.
First, let's calculate the attractive force between the polarized atom and the passing ion. The attractive force is given by Coulomb's Law:
F = k * (q1 * q2) / r^2,
where F is the force, k is the electrostatic constant (9 × 10^9 N2m^2/C2), q1 and q2 are the charges, and r is the distance between the charges.
In this case, the charge of the ion is given as 1 nC (1 × 10^-9 C) and the ion-atom distance is 1 m. Since the atom was initially polarized by the ion itself, we assume an equal and opposite charge separated by a distance much smaller than the atom-ion distance.
Thus, the force acting on the ion due to the polarized atom is:
F = k * ((1 × 10^-9 C) * (-1 × 10^-9 C)) / (1 m)^2
= -9 N
The negative sign indicates that the force is attractive.
Now, let's determine the atom's polarizability. The dipole moment of the atom is given by:
p = 2 * q * d,
where p is the dipole moment, 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.
Since the atom was initially polarized by the ion itself, we can assume that the separated charge is the same as the ion's charge (1 nC) and the distance is negligible compared to the atom-ion distance.
So, the dipole moment is:
p = 2 * (1 × 10^-9 C) * 0
= 0
The polarizability, α, is defined as the proportionality constant between the dipole moment and the external field acting on the atom:
p = α * Eexternal.
Since the atom is initially polarized by the ion itself, we can consider the external field to be the electric field created by the ion.
Therefore, α is:
α = p / Eexternal
= 0 / (k * q / r^2)
= 0.
Now, we can calculate the ratio of the attractive force to the atom's polarizability:
Ratio = F / α
= (-9 N) / 0.
However, division by zero is undefined. In this case, the ratio is undefined, indicating that the force between the polarized atom and the passing ion is infinite relative to the atom's polarizability.