Problem 19.5

19.5
First of all, we want to find the charge necessary on each sphere to generate a force of 10 kN at that distance.
$F = \frac{kq^{2}}{r^{2}}$
Solving for q yields
$q = r \sqrt{\frac{F}{k}} ~=~ (1m)\sqrt{\frac{10 kN}{k}}$
$q = 1.05 \times 10^{-3} C$
Now, we can figure out how many electrons are required to produce a charge of this magnitude.
$N = (1.05 \times 10^{-3} C)(\frac{1 electron}{1.6 \times 10^{-19} C})$
$N = 6.59 \times 10^{15}$ electrons.
The whole number of electrons in each sphere is given by
$N_{tot} = (10 g)(\frac{1 mol}{107.87 g})(\frac{6.02 \times 10^{23} atoms}{1 mol})(\frac{47 electrons}{atom})$
$N_{tot} = 2.62 \times 10^{24}$ electrons.
Therefore, the fraction that were transferred is
$f = \frac{N}{N_{tot}}$
$f = \frac{6.59 \times 10^{15}}{2.62 \times 10^{24}}$
$f = 2.51 \times 10^{-9}$
or 2.51 electrons out of every billion.