This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values. The distance between the particles is r = 10^-13 m. The elementary charge is e = 1.6 × 10^-19 C. Coulomb's constant is k = (1)/(4_0) = 9.0 × 10^9 Nm^2/C^2. Step 2: Determine the charges of the alpha-particle and the electron. The charge of an electron is q_e = -e = -1.6 × 10^-19 C. An alpha-particle consists of two protons and two neutrons. The charge of an alpha-particle is q_ = +2e = +2 × (1.6 × 10^-19 C) = 3.2 × 10^-19 C. Step 3: Apply Coulomb's Law to find the magnitude of the electrostatic force. Coulomb's Law states that the magnitude of the electrostatic force F between two point charges q_1 and q_2 separated by a distance r is given by: F = k (|q_1 q_2|)/(r^2) Step 4: Substitute the values and calculate the force. F = (9.0 × 10^9 Nm^2/C^2) |(-1.6 × 10^-19 C) × (3.2 × 10^-19 C)|(10^-13 m)^2 F = (9.0 × 10^9) (1.6 × 10^-19) × (3.2 × 10^-19)(10^-13)^2 N F = (9.0 × 10^9) 5.12 × 10^-3810^-26 N F = (9.0 × 10^9) × (5.12 × 10^-38 × 10^26) N F = (9.0 × 10^9) × (5.12 × 10^-12) N F = 46.08 × 10^9-12 N F = 46.08 × 10^-3 N F = 4.608 × 10^-2 N The magnitude of the electrostatic force of attraction is: 4.61 × 10^-2 N