Physics
Physics
Problem
For an isolated ion pair A⁺ B⁻, the electrostatic potential energy is measured to be at a separation distance of 300 pm. Answer the following questions about hypothetical modifications to this ion pair. (a) Calculate the new potential energy if the separation distance is reduced to 150 pm while all charges remain unchanged. (b) Starting from the original ion pair, calculate the potential energy if instead the charge magnitude on each ion is doubled and the separation distance is left at 300 pm. (c) Relative to the original situation, by what factor does the magnitude of the potential energy change in parts (a) and (b)? Comment briefly on which variable—charge or distance—has the greater effect when altered by the same numerical factor.Intuitive explanation
The key here is understanding that electrostatic potential energy depends on the product of charges and inversely on separation distance—it's governed by Coulomb's law. When you change either the charges or the distance, the energy scales predictably: doubling the charge doubles the energy, while doubling the distance cuts the energy in half. Use the measured baseline to set up proportions for any hypothetical scenario, rather than calculating absolute energies from scratch.
Intuitive explanation
The key here is understanding that electrostatic potential energy depends on the product of charges and inversely on separation distance—it's governed by Coulomb's law. When you change either the charges or the distance, the energy scales predictably: doubling the charge doubles the energy, while doubling the distance cuts the energy in half. Use the measured baseline to set up proportions for any hypothetical scenario, rather than calculating absolute energies from scratch.