How many rubber bands are needed to cause an object with half the mass to accelerate six times as quickly?

an ion is a charged atom or molecule. it is charged because the number of electrons do not equal the number of protons in the atom or molecule. an atom can acquire a positive charge or a negative charge depending on whether the number of electrons in an atom is greater or less then the number of protons in the atom.

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.