Question Detail
Question
A helium nucleus (charge +2e) and a neon nucleus (charge +10e) are separated in vacuum by 3.0 nanometers (3.0 × 10-9 m). Calculate the repulsive force between them. (Given: e = 1.60 × 10-19 C, k0 = 9.0 × 109 N·m²/C²)
Correct Answer
Option A is the correct answer.
Detailed Explanation
This is Solved Problem 24.3 on page 5. Using Coulomb's Law: FE = k0 q1q2 / r². First, calculate charges: q1 = 2e = 2(1.60 × 10-19 C) = 3.20 × 10-19 C. q2 = 10e = 10(1.60 × 10-19 C) = 1.60 × 10-18 C. Distance r = 3.0 nm = 3.0 × 10-9 m. FE = (9.0 × 109 N·m²/C²) * (3.20 × 10-19 C) * (1.60 × 10-18 C) / (3.0 × 10-9 m)². FE ≈ 5.12 × 10-10 N.
Hint
Ensure proper unit conversion (nanometers to meters) and correctly substitute the elementary charge for the nucleus charges. Remember to square the distance in the denominator.