Two spherical objects are separated by a distance of 1.53 × 10-3 m. The objects are initially electrically neutral and are very small compared to the distance between them. Each object acquires the same negative charge due to the addition of electrons. As a result, each object experiences an electrostatic force that has a magnitude of 1.42 × 10-20 N. How many electrons did it take to produce the charge on one of the objects?

To determine the number of electrons that it took to produce the charge on one of the objects, we need to use the relationship between charge, electrostatic force, and the elementary charge.

Step 1: Determine the charge on one of the objects.
We know that each object acquired the same negative charge. Let's denote the charge on one of the objects as q. We can create the equation:

F = k * (q)² / r²

Here, F is the magnitude of the electrostatic force, k is Coulomb's constant (k = 8.99 × 10^9 N·m²/C²), q is the charge on one of the objects, and r is the separation distance between the objects.

Given:
F = 1.42 × 10^(-20) N
r = 1.53 × 10^(-3) m

Plugging in the values, we have:

1.42 × 10^(-20) N = (8.99 × 10^9 N·m²/C²) * (q)² / (1.53 × 10^(-3) m)²

Step 2: Solve for q.

Rearranging the equation, we have:

(q)² = (1.42 × 10^(-20) N * (1.53 × 10^(-3) m)²) / (8.99 × 10^9 N·m²/C²)

(q)² = 2.31 × 10^(-42) C²

Taking the square root of both sides, we find:

q = √(2.31 × 10^(-42) C²)

q = 4.80 × 10^(-21) C

Step 3: Calculate the number of electrons.

The charge of one electron is -1.60 × 10^(-19) C. Since each object acquired the same negative charge, the number of electrons on each object is equal to the charge on one object divided by the charge of one electron:

Number of electrons = (4.80 × 10^(-21) C) / (-1.60 × 10^(-19) C)

Number of electrons ≈ 0.3

Therefore, it took approximately 0.3 electrons to produce the charge on one of the objects.