How far apart are a proton and electron if they experience an electric force of 5.10N?
To determine the distance between a proton and an electron experiencing an electric force of 5.10N, we can use Coulomb's law. Coulomb's law states that the electric force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = (k * q1 * q2) / r^2
Where:
F is the electric force
k is the electrostatic constant (k ≈ 8.99 × 10^9 N·m^2/C^2)
q1 and q2 are the charges of the particles
r is the distance between the particles
In this case, we know the electric force (F = 5.10N) and the electrostatic constant (k ≈ 8.99 × 10^9 N·m^2/C^2). We need to find the distance (r) between the proton and the electron.
First, we rearrange the formula to solve for r:
r = √((k * q1 * q2) / F)
Since a proton and an electron have equal but opposite charges (1.6 × 10^-19 C and -1.6 × 10^-19 C, respectively), we plug in the values:
r = √((8.99 × 10^9 N·m^2/C^2 * (1.6 × 10^-19 C)^2) / 5.10N)
Calculating this equation, we get:
r ≈ 2.315 × 10^-10 meters
Therefore, the distance between the proton and electron would be approximately 2.315 × 10^-10 meters.