(a) What is the electrostatic potential energy (in joules) betwee...

Question

(a) What is the electrostatic potential energy (in joules) between an electron and a proton that are separated by 230 pm? (b) What is the change in potential energy if the distance separating the electron and proton is increased to 1.0 nm? (c) Does the potential energy of the two particles increase or decrease when the distance is increased to 1.0 nm?

Accepted Answer

Step 1: Understand the concept of electrostatic potential energy, which is given by the formula: $U = \frac{k \cdot q_1 \cdot q_2}{r}$, where $k$ is Coulomb's constant ($8.99 	imes 10^9 	ext{ N m}^2/	ext{C}^2$), $q_1$ and $q_2$ are the charges of the particles, and $r$ is the separation distance between the charges.. Step 2: Identify the charges involved. For an electron, $q_1 = -1.602 	imes 10^{-19}$ C, and for a proton, $q_2 = 1.602 	imes 10^{-19}$ C. The separation distance $r$ for part (a) is 230 pm, which needs to be converted to meters (1 pm = $10^{-12}$ m).. Step 3: Calculate the electrostatic potential energy for part (a) using the formula from Step 1 with the given values for $q_1$, $q_2$, and $r$.. Step 4: For part (b), calculate the potential energy again using the new separation distance of 1.0 nm (1 nm = $10^{-9}$ m) and the same charges.. Step 5: Compare the potential energies calculated in parts (a) and (b) to determine the change in potential energy and whether it increases or decreases when the distance is increased to 1.0 nm.

Key Concepts

Electrostatic Potential Energy

Coulomb's Law

Distance and Potential Energy Relationship