1. Understand Coulomb's Law
Coulomb's Law describes the electrostatic force between charged objects:
* F = k * (q1 * q2) / r²
* F is the force (in Newtons)
* k is Coulomb's constant (8.98755 × 10⁹ N⋅m²/C²)
* q1 and q2 are the charges of the objects (in Coulombs)
* r is the distance between the centers of the objects (in meters)
2. Identify the knowns
* F = 2.00 nN = 2.00 × 10⁻⁹ N (Force)
* q1 = q2 = -1.602 × 10⁻¹⁹ C (Charge of an electron)
* k = 8.98755 × 10⁹ N⋅m²/C² (Coulomb's constant)
3. Solve for the distance (r)
* Rearrange Coulomb's Law to solve for r:
r² = k * (q1 * q2) / F
r = √[k * (q1 * q2) / F]
* Plug in the known values:
r = √[(8.98755 × 10⁹ N⋅m²/C²) * (-1.602 × 10⁻¹⁹ C) * (-1.602 × 10⁻¹⁹ C) / (2.00 × 10⁻⁹ N)]
* Calculate the result:
r ≈ 1.01 × 10⁻⁹ m
Answer: The distance between the two electrons would be approximately 1.01 nanometers (1.01 × 10⁻⁹ m) for the repulsive force to be 2.00 nN.
