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.
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Here is the calculation for part a) using k = 9 × 10^9 N m^2/C^2. a) Calculate the magnitude of the electrostatic force between an electron and a proton. Given: • Coulomb's constant, k = 9 × 10^9 N m^2/C^2 • Elementary charge (magnitude), e = 1.602 × 10^-19 C • Charge of electron, q_e = -1.602 × 10^-19 C • Charge of proton, q_p = +1.602 × 10^-19 C • Distance, r = 1.0 × 10^-10 m (from the original problem statement) Step 1: Use Coulomb's Law to find the magnitude of the electrostatic force. F = k (|q_e q_p|)/(r^2) Step 2: Substitute the given values into the formula. F = (9 × 10^9 N m^2/C^2) |(-1.602 × 10^-19 C)(+1.602 × 10^-19 C)|(1.0 × 10^-10 m)^2 Step 3: Calculate the force. F = (9 × 10^9) (1.602 × 10^-19)^2(1.0 × 10^-10)^2 N F = (9 × 10^9) 2.566404 × 10^-381.0 × 10^-20 N F = (9 × 10^9) × (2.566404 × 10^-18) N F = 23.097636 × 10^-9 N F = 2.3097636 × 10^-8 N Rounding to three significant figures: F ≈ 2.31 × 10^-8 N That's 2 down. 3 left today — send the next one.