According to Coulomb's law, which pair of charged particles has the lowest potential energy? a. a particle with a 1- charge separated by 150 pm from a particle with a 2+ charge b. a particle with a 1- charge separated by 150 pm from a particle with a 1+ charge c. a particle with a 1- charge separated by 100 pm from a particle with a 3+ charge

Verified step by step guidance

1. Understand Coulomb's Law: Coulomb's law states that the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The potential energy (PE) associated with two charges is given by the formula PE = k * (q1 * q2) / r, where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.
2. Identify the charges and distances in each option: a) q1 = -1, q2 = +2, r = 150 pm; b) q1 = -1, q2 = +1, r = 150 pm; c) q1 = -1, q2 = +3, r = 100 pm.
3. Convert distances from picometers to meters for calculation: 1 pm = 1e-12 meters.
4. Calculate the potential energy for each pair using the formula: Substitute the values of q1, q2, and r into the formula PE = k * (q1 * q2) / r for each option.
5. Compare the calculated potential energies: The pair with the lowest potential energy will be the one with the highest magnitude of the product of charges (q1 * q2) and the shortest distance (r).

Key Concepts

Coulomb's Law

Coulomb's Law describes the electrostatic interaction between charged particles. It states that the potential energy (U) between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the distance between them. Mathematically, it is expressed as U = k * (q1 * q2) / r, where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance separating them.

Potential Energy of Charged Particles

The potential energy of charged particles is influenced by their charges and the distance separating them. Opposite charges (positive and negative) attract each other, resulting in lower potential energy, while like charges repel, leading to higher potential energy. Thus, the configuration of charges and their separation distance is crucial in determining the stability and energy of the system.

Comparison of Charge Magnitudes

When comparing pairs of charged particles, the magnitude of the charges plays a significant role in determining potential energy. A larger charge will exert a stronger force, affecting the potential energy more significantly than a smaller charge. Therefore, in scenarios where distances are constant, the combination of charge magnitudes is essential for identifying which pair has the lowest potential energy.