Question

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

Answer 1

`8.76\cdot 10^(-15)m`

Step-by-step explanation:

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

`F=k(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{(kq_1 q_2)/(F)}=\sqrt{((9\cdot 10^9)(1.6\cdot 10^(-19))^2)/(3)}=8.76\cdot 10^(-15)m`