Here's how to determine the ratio of gravitational force to electrostatic force between two electrons:

1. Formulas:

* Gravitational Force: F_g = G * (m₁ * m₂) / r²

* G = Gravitational constant (6.674 × 10^-11 N m²/kg²)

* m₁, m₂ = Masses of the objects

* r = Distance between the objects

* Electrostatic Force: F_e = k * (q₁ * q₂) / r²

* k = Coulomb's constant (8.98755 × 10⁹ N m²/C²)

* q₁, q₂ = Charges of the objects

* r = Distance between the objects

2. Properties of Electrons:

* Mass: m_e = 9.109 × 10^-31 kg

* Charge: q_e = -1.602 × 10^-19 C

3. Ratio Calculation:

* Divide the gravitational force formula by the electrostatic force formula:

F_g / F_e = [G * (m_e * m_e) / r²] / [k * (q_e * q_e) / r²]

* Simplify:

F_g / F_e = (G * m_e²) / (k * q_e²)

* Substitute the values:

F_g / F_e = (6.674 × 10^-11 N m²/kg² * (9.109 × 10^-31 kg)²) / (8.98755 × 10⁹ N m²/C² * (-1.602 × 10^-19 C)²)

* Calculate the result:

F_g / F_e ≈ 2.4 × 10^-43

Conclusion:

The ratio of gravitational force to electrostatic force between two electrons is approximately 2.4 × 10^-43. This means that the electrostatic force between two electrons is incredibly stronger than the gravitational force.

Important Note: The gravitational force between two electrons is extremely weak. For practical purposes, it is almost always negligible compared to the electrostatic force.