**Given Information:**
- Two electrons are placed at a distance d.
- The electrostatic force between the two electrons is equal to the sum of the weight of both electrons.

**Solution:**
To solve this problem, we need to calculate the value of d.

**Step 1:**
We know that the electrostatic force between two point charges can be calculated using Coulomb's Law:

F = (k * q₁ * q₂) / r²

Where:
F is the electrostatic force,
k is the electrostatic constant (9 x 10^9 Nm²/C²),
q₁ and q₂ are the charges of the particles, and
r is the distance between the particles.

**Step 2:**
The weight of an object can be calculated using the formula:

Weight = mass * acceleration due to gravity

For an electron, the mass (m) is 9.1 x 10^-31 kg and the acceleration due to gravity (g) is 9.8 m/s².

**Step 3:**
Given that the electrostatic force between the two electrons is equal to the sum of their weights, we can equate the formulas:

(k * q₁ * q₂) / r² = (m₁ * g) + (m₂ * g)

**Step 4:**
Since both electrons have the same charge (e = 1.6 x 10^-19 C) and mass (m = 9.1 x 10^-31 kg), we can simplify the equation:

(k * e²) / r² = (2 * m * g)

**Step 5:**
Now, we can rearrange the equation to solve for the distance (r):

r² = (k * e²) / (2 * m * g)

r = √((k * e²) / (2 * m * g))

**Step 6:**
Substituting the given values, we can calculate the value of r:

r = √((9 x 10^9 Nm²/C² * (1.6 x 10^-19 C)²) / (2 * (9.1 x 10^-31 kg) * (9.8 m/s²)))

r ≈ 2.64 x 10^-11 meters

Therefore, the value of d is approximately 2.64 x 10^-11 meters.