If one of the original nitrogen-14 nuclei was converted into an atom of nitrogen-14....?

Question

Two nuclei of nitrogen-14 each have masses of 2.3 × 10−26 kg and are separated by a distance of 2.0 m. The electric charge of each nucleus is +7e.

If one of the original nitrogen-14 nuclei was converted into an atom of nitrogen-14, by the addition of 7 electrons, explain, in a few sentences, how the strength of the gravitational force and the strength of the electric force between the nitrogen-14 nucleus and the nitrogen-14 atom would change, if at all, with respect to the forces calculated in (a) and (b). (Note: you do not need to repeat the calculations from parts (a) and (b) to answer this.)

Answer 1

The electric force would disappear because the net charge on the atom is zero.  The net gravitational force would increase because of the added mass of 7 electrons to one of the masses.  However, the mass of 7 electrons compared to the mass of the whole atom is extremely small, so the change would be minute.  It can be calculated by using the gravitational attraction formula:

F = G*m1*m2/r^2.

If m is the mass of the nucleus, then the original force is F = G*m^2/r^2.  The new force is F = G*m*(m+7*me)/r^2.  The ratio is (m + 7*me)/m where me is the mass of an electron.