Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron).

• 4π∈₀F
• 4π∈₀F / 2
• √(4π∈₀F / d²)
• √(4π∈₀F / e²)

To determine the number of electrons missing from each ion, we can start by using Coulomb's law, which states that the force of repulsion (F) between two charges is given by:

Understanding the Relationship

The formula is:

F = (1 / (4π∈₀)) * (q₁ * q₂) / d²

In this case, both ions have the same charge (q), so we can rewrite the equation as:

F = (1 / (4π∈₀)) * (q²) / d²

Finding the Charge of Each Ion

From the equation, we can express the charge (q) in terms of the force (F) and distance (d):

q² = 4π∈₀F * d²

Taking the square root gives:

q = √(4π∈₀F * d²)

Calculating the Number of Missing Electrons

The charge of a single electron (e) is approximately 1.6 x 10^-19 coulombs. The number of missing electrons (n) from each ion can be calculated using:

n = q / e

Substituting our expression for q:

n = √(4π∈₀F * d²) / e

Final Expression

Thus, the number of electrons missing from each ion is:

n = √(4π∈₀F / e²) * d

This formula allows you to find out how many electrons are absent based on the force of repulsion and the distance between the ions.