An electron and a proton are fixed at a separation distance of 1.0 nm. What is the magnitude of the electrostatic force between them?

• A. 9.0 × 10^{-9} N
• B. 1.6 × 10^{-19} N
• C. 2.3 × 10^{-10} N
• D. 8.2 × 10^{-8} N

Answer: (C)

Verified step by step guidance

1. Identify the charges involved: an electron has a charge of \(-1.6 \times 10^{-19}\) C and a proton has a charge of \(+1.6 \times 10^{-19}\) C.
2. Note the separation distance between the charges, which is given as 1.0 nm. Convert this distance to meters: \$1.0 \text{ nm} = 1.0 \times 10^{-9}$ m.
3. Recall Coulomb's law for the magnitude of the electrostatic force between two point charges: \[F = k \frac{|q_1 q_2|}{r^2}\] where \(k\) is Coulomb's constant, \$8.99 \times 10^9 \ \text{N m}^2/\text{C}^2\(, \)q_1\( and \)q_2\( are the magnitudes of the charges, and \)r$ is the separation distance.
4. Substitute the known values into Coulomb's law: \[F = (8.99 \times 10^9) \times \frac{(1.6 \times 10^{-19})^2}{(1.0 \times 10^{-9})^2}\]
5. Calculate the numerator and denominator separately, then divide and multiply by \(k\) to find the magnitude of the force. This will give you the electrostatic force in newtons.