Final answer:
Using Coulomb's Law with the given force and charges, the calculated distance between a proton and an electron is approximately 5.3 × 10^-11 meters.
Step-by-step explanation:
The question asks for the distance between a proton and an electron given the force of interaction and their charges. We can use Coulomb's Law to find this distance:
F = k * |q1*q2| / r^2
Where:
- F is the electrostatic force between the charges.
- k is Coulomb's constant (8.98755 × 10^9 N m^2/C^2).
- q1 and q2 are the magnitudes of the charges.
- r is the distance between the charges.
Given that F = 3.5 × 10^-10 N and each charge (q1 and q2) is 1.6 × 10^-19 C, we can rearrange the formula to solve for r:
r = √(k * |q1*q2| / F)
Substituting in the given values:
r = √((8.98755 × 10^9 N m^2/C^2 * (1.6 × 10^-19 C)^2) / 3.5 × 10^-10 N)
After calculating, the distance comes out to approximately 5.3 × 10^-11 meters.