The Coulomb's law expresses the force between two charged particles as:
Fe = k * (q1 * q2) / r^2
where k is Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between them.
The gravitational force between two particles is given by:
Fg = G * m1 * m2 / r^2
where G is the gravitational constant, m1 and m2 are the masses of the particles, and r is the distance between them.
For two electrons, the charges q1 and q2 are equal and have a magnitude of 1.602 x 10^-19 C, and their masses m1 and m2 are also equal and have a value of 9.109 x 10^-31 kg.
Using the values of Coulomb's constant (k = 8.987 x 10^9 N.m^2/C^2) and gravitational constant (G = 6.674 x 10^-11 N.m^2/kg^2), we can calculate the ratio of the Coulomb electric force to the gravitational force between two electrons in vacuum as:
Fe/Fg = [k * (q1 * q2) / r^2] / [G * m1 * m2 / r^2]
Fe/Fg = k * (q1 * q2) / (G * m1 * m2)
Fe/Fg = (8.987 x 10^9 N.m^2/C^2) * (1.602 x 10^-19 C)^2 / [(6.674 x 10^-11 N.m^2/kg^2) * (9.109 x 10^-31 kg)^2]
Fe/Fg = 2.396 x 10^42
Therefore, the ratio of the Coulomb electric force to the gravitational force between two electrons in vacuum is approximately 2.396 x 10^42.