Question

4. How far apart are a proton and electron if they exert an attractive force of 3 N on one another?

Answer 1

Answer:

$8.76\cdot 10^{-15}m$

Explanation:

The magnitude of the electrostatic force between two charges is given by the equation:

$F=k\frac{q_1 q_2}{r^2}$

where:

$k=9\cdot 10^9 Nm^{-2}C^{-2}$ is the Coulomb's constant

$q_1, q_2$ are the two charges

r is the separation between the two charges

And the force is:

- Attractive if the charges have opposite sign

- Repulsive if the charges have same sign

In this problem, we have:

F = 3 N is the force between the proton and the electron

$q_1=q_2=1.6\cdot 10^{-19}C$ is the magnitude of the charge of the proton and the electron

Therefore, solving for r, we find the separation between the two particles:

$r=\sqrt{\frac{kq_1 q_2}{F}}=\sqrt{\frac{(9\cdot 10^9)(1.6\cdot 10^{-19})^2}{3}}=8.76\cdot 10^{-15}m$