Textbook Question
(a) What is the electrostatic potential energy (in joules) between two electrons that are separated by 62 pm?
Ch.5 - Thermochemistry
Chapter 5, Problem 14c
(c) Does the potential energy of the two particles increase or decrease when the distance is increased to 1.0 nm?
Verified step by step guidance1
Identify the relationship between potential energy and distance for two particles. Typically, potential energy (U) is inversely proportional to the distance (r) between two charged particles, as described by Coulomb's Law: $U = k \frac{q_1 q_2}{r}$, where $k$ is Coulomb's constant, and $q_1$ and $q_2$ are the charges of the particles.
Understand that as the distance (r) increases, the denominator in the equation $U = k \frac{q_1 q_2}{r}$ becomes larger, which means the overall value of U decreases if the charges are of the same sign (both positive or both negative).
Consider the nature of the charges: If the charges are opposite (one positive and one negative), the potential energy is negative, and increasing the distance makes the potential energy less negative, which is effectively an increase in potential energy.
Apply this understanding to the given problem: As the distance between the two particles increases to 1.0 nm, determine whether the charges are like or unlike to decide if the potential energy increases or decreases.
Conclude based on the type of charges: If the charges are like, the potential energy decreases with increased distance. If the charges are unlike, the potential energy increases with increased distance.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Potential Energy in Physics
Potential energy is the energy stored in an object due to its position in a force field, such as gravitational or electrostatic fields. In the context of particles, the potential energy between two charged particles is influenced by their distance; as they move further apart, the potential energy typically changes based on the nature of their charges.
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Kinetic & Potential Energy
Coulomb's Law
Coulomb's Law describes the electrostatic interaction between charged particles. It states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This relationship implies that as the distance increases, the potential energy associated with the interaction changes, depending on whether the charges are like or unlike.
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Work and Energy Relationship
The relationship between work and energy is fundamental in physics, where work done on a system can change its energy state. When two particles are separated, work is done against the electrostatic force, which can either increase or decrease the potential energy depending on the nature of the forces involved. Understanding this relationship helps in predicting how energy changes as particles move apart.
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Related Practice
Textbook Question
(b) What is the change in potential energy if the distance separating the two electrons is increased to 1.0 nm?
Textbook Question
(a) The electrostatic force (not energy) of attraction between two oppositely charged objects is given by the equation F = k (Q1Q2/d2) where k = 8.99⨉109N-m2/C2, Q1 and Q2 are the charges of the two objects in Coulombs, and d is the distance separating the two objects in meters. What is the electrostatic force of attraction (in Newtons) between an electron and a proton that are separated by 1⨉102 pm?
Textbook Question
A sodium ion, Na+, with a charge of 1.6⨉10-19 C and a chloride ion, Cl - , with charge of -1.6⨉10-19 C, are separated by a distance of 0.50 nm. How much work would be required to increase the separation of the two ions to an infinite distance?