To find the ratio of electrostatic repulsion to gravitational attraction between two electrons, we need to calculate both values separately and then divide them.

1. Calculation of electrostatic repulsion:
The electrostatic force between two charged particles can be calculated using Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

The formula for the electrostatic force (F_e) between two point charges q1 and q2 separated by a distance r is given by:
F_e = (k * q1 * q2) / r^2

Where:
- k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2)
- q1 and q2 are the charges on the particles

In this case, both charges are electrons, so q1 = q2 = 1.6 x 10^-19 C.
Let's assume the distance between the electrons is d.

Therefore, the electrostatic force between the electrons is:
F_e = (k * (1.6 x 10^-19) * (1.6 x 10^-19)) / d^2

2. Calculation of gravitational attraction:
The gravitational force between two objects can be calculated using Newton's law of universal gravitation, which states that the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

The formula for the gravitational force (F_g) between two objects with masses m1 and m2 separated by a distance r is given by:
F_g = (G * m1 * m2) / r^2

Where:
- G is the gravitational constant (G = 6.67 x 10^-11 Nm^2/kg^2)
- m1 and m2 are the masses of the objects

In this case, both masses are the mass of an electron, which is 9.1 x 10^-31 kg.
Let's assume the distance between the electrons is d.

Therefore, the gravitational force between the electrons is:
F_g = (G * (9.1 x 10^-31) * (9.1 x 10^-31)) / d^2

3. Ratio of electrostatic repulsion to gravitational attraction:
To find the ratio of the electrostatic repulsion to gravitational attraction, we divide the electrostatic force (F_e) by the gravitational force (F_g):

Ratio = F_e / F_g = ((k * (1.6 x 10^-19) * (1.6 x 10^-19)) / d^2) / ((G * (9.1 x 10^-31) * (9.1 x 10^-31)) / d^2)

Simplifying the equation, we can cancel out the common terms and obtain the final answer:

Ratio = (k / G) * ((1.6 x 10^-19)^2 / (9.1 x 10^-31)^2)

Plugging in the given values for k and G, we can calculate the ratio:

Ratio = (9 x 10^9 / 6.67 x 10^-11) * ((1.6 x 10^-19)^2 / (9.1 x 10^-31)^2)

Calculating the numerical value of the ratio gives us