An oxygen ion O^2- is a distance r=5.0 ×10^-10 m from a H^+...

An oxygen ion $\mathrm{O}^{2-}$ is a distance $r=5.0 \times 10^{-10} \mathrm{m}$ from a $\mathrm{H}^{+}$ ion. How much energy is required to separate them completely? Treat both ions as point charges.

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Key Concepts

Coulomb's Law

Coulomb's Law describes the force between two point charges. It provides the relationship that the magnitude of the electrostatic force between charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This principle is essential for calculating the interaction between any two charged particles, independent of the specific ions involved.

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored in a system of two or more charged particles due to their positions relative to each other. In the context of point charges, this energy is given by a formula derived from Coulomb's Law and is used to determine the work required to separate the charges from a given distance to infinity. This concept is fundamental when analyzing energy changes in electrostatic systems.

Work Required to Separate Charges

The work required to separate two interacting charges is equivalent to the electrostatic potential energy they possess when separated by their initial distance. Calculating this energy involves understanding that moving the charges from a finite separation to infinite separation requires doing work against the electrostatic attraction or repulsion, highlighting the conservation of energy within the system.

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