The gravitational force on the first electron is equal to its weight:
[tex]F=m_e g[/tex]
where [tex]m_e = 9.1 \cdot 10^{-31} kg[/tex] is the electron mass and [tex]g=9.81 m/s^2[/tex] is the gravitational acceleration. Substituting, we find that the gravitational force is
[tex]F=(9.1 \cdot 10^{-31} kg)(9.81 m/s^2)=8.9 \cdot 10^{-30} N[/tex]
Instead, the electric force exerted by the second electron on the first one is
[tex]F=k_e \frac{q_1 q_2}{r^2} [/tex]
where
[tex]k_e = 8.99 \cdot 10^9 N m^2 C^{-2}[/tex] is the Coulomb's constant
[tex]q_1 = q_2 = e = -1.6 \cdot 10^{-19} C[/tex] is the charge of each electron
r is the distance between them.
The problem says that the distance r is such that the electric force cancels the gravitational force, so the electric force must be equal to the gravitational force: [tex]F=8.9 \cdot 10^{-30} N[/tex]. So, if we use this value in the formula of the electric force, we can calculate the distance r between the two electrons:
[tex]r=\sqrt{k_e \frac{q_1 q_2}{F} }=\sqrt{(8.99 \cdot 10^9) \frac{(-1.6 \cdot 10^{-19} C)^2}{8.9 \cdot 10^{-30}N} }=5.1 m[/tex]
