Calculate the force of attraction between a \(\mathrm{K}^{+}\) and an \(\mathrm{O}^{2-}\) ion whose centers are separated by a distance of \(1.5 \mathrm{~nm}\).

Understanding the electrostatic force is essential when studying electrically charged particles such as ions. In the context of the textbook exercise, the electrostatic force refers to the invisible but measurable attraction or repulsion between two charged particles. This force is governed by Coulomb's law, which states that the magnitude of the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between the charges.

For those who might be encountering this concept for the first time, think of it like the force that holds two magnets together; only in this case, it's the charge, not magnetism, at play. The exercise demonstrates how two ions with opposing charges, specifically a potassium ion (K⁺) with a +1 charge and an oxygen ion (O²⁻) with a -2 charge, are attracted to each other. This force can be measured, as seen in the solution where the actual numerical value of the force is calculated using the provided charges and distance in Coulomb's law formula.

In real-world contexts, this electrostatic force is fundamental in areas such as chemistry where it helps explain the interactions and bonds between atoms and molecules, enabling the formation of compounds like table salt or water.

Ionic charge plays a pivotal role in the textbook exercise, and it represents the electrical charge present on an ion which is an atom or molecule that has lost or gained one or more electrons. These ions are characterized as cations (positive charge) or anions (negative charge), depending on whether they have given up or taken on electrons. In our exercise, a potassium ion is a cation with a +1 charge, and an oxygen ion is an anion with a -2 charge.

It's like a name tag that tells other particles how to interact with the ion—charges with the same sign repel each other, and charges with different signs attract. The charges of the ions are used within Coulomb's law to determine the magnitude of the electrostatic force between them. Understanding the concept of ionic charge is crucial not only in physics but also in chemistry since it underlines the reason why certain elements combine to form ionic compounds. These charges, quantified by the fundamental unit of electric charge 'e' (the charge of a single proton), are used to compute interactions on the atomic scale.

Converting nanometers to meters is an essential step in the calculation of the electrostatic force between ions. The term 'nanometer' (nm) is a unit of length in the metric system, equal to one billionth of a meter, which is represented by the prefix 'nano' meaning 10⁻⁹. In the provided example, the distance between the K⁺ and O²⁻ ion centers is 1.5 nm, which we convert to meters because the SI unit for distance in the Coulomb's law equation is meters (m).

To convert from nanometers to meters, the value in nanometers is multiplied by 10⁻⁹. Therefore, 1.5 nm becomes 1.5 x 10⁻⁹ m. This conversion is pivotal for accurately using Coulomb's law since any discrepancies in the unit of distance can drastically change the calculated force. A handy trick for these conversions is to think of a nanometer as a really tiny distance, difficult to observe with the naked eye, often used to measure wavelengths of light or the size of molecules and atomic structures.

Key Conversion:

• 1 nm = 10⁻⁹ m

Always remember to perform this conversion when dealing with microscopic distances to seamlessly bridge the gap between the scales of the atomic world and the larger world we measure in meters.