The ratio of electrostatic force to gravitational force between two electrons can be calculated by considering the fundamental equations governing these forces. Let's break down the explanation into the following headings:

1. Electrostatic Force:
The electrostatic force between two charged particles is given by Coulomb's law. According to this law, the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

F_e = k * (q1 * q2) / r^2

Where F_e is the electrostatic force, k is the electrostatic constant (9 × 10^9 Nm^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.

2. Gravitational Force:
The gravitational force between two objects is given by Newton's law of gravitation. According to this law, the gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

F_g = G * (m1 * m2) / r^2

Where F_g is the gravitational force, G is the gravitational constant (6.67430 × 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the objects, and r is the distance between them.

3. Ratio of Forces:
To find the ratio of electrostatic force (F_e) to gravitational force (F_g) between two electrons, we need to substitute the respective values into the equations. Since the charge of an electron is -1.6 × 10^-19 C and the mass of an electron is 9.1 × 10^-31 kg, we can substitute these values into the equations:

F_e = (9 × 10^9 Nm^2/C^2) * ((-1.6 × 10^-19 C)^2) / r^2

F_g = (6.67430 × 10^-11 Nm^2/kg^2) * ((9.1 × 10^-31 kg)^2) / r^2

Now, we can calculate the ratio by dividing the electrostatic force by the gravitational force:

Ratio = F_e / F_g

By substituting the values and simplifying the equation, we can determine the numerical value of the ratio.

In conclusion, the ratio of electrostatic force to gravitational force between two electrons can be calculated by using Coulomb's law and Newton's law of gravitation. By substituting the respective values, we can determine the numerical value of the ratio.