Textbook Question
(c) Does the potential energy of the two particles increase or decrease when the distance is increased to 1.0 nm?
Ch.5 - Thermochemistry
Chapter 5, Problem 16
Use the equations given in Problem 5.15 to calculate: (a) The electrostatic force of repulsion for two electrons separated by 75 pm. (b) The gravitational force of attraction for two electrons separated by 75 pm. (c) If allowed to move, will the electrons be repelled or attracted to one another?
Verified step by step guidance1
Step 1: Identify the relevant equations for calculating forces. For electrostatic force, use Coulomb's Law: \( F_e = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \), where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges of the electrons, and \( r \) is the separation distance. For gravitational force, use Newton's Law of Universal Gravitation: \( F_g = \frac{G \cdot m_1 \cdot m_2}{r^2} \), where \( G \) is the gravitational constant, and \( m_1 \) and \( m_2 \) are the masses of the electrons.
Step 2: Substitute the known values into Coulomb's Law. The charge of an electron \( q \) is approximately \(-1.602 \times 10^{-19} \) C, and the separation distance \( r \) is 75 pm, which needs to be converted to meters (1 pm = \( 10^{-12} \) m).
Step 3: Substitute the known values into Newton's Law of Universal Gravitation. The mass of an electron \( m \) is approximately \( 9.109 \times 10^{-31} \) kg, and use the same separation distance \( r \) as in Step 2.
Step 4: Calculate the electrostatic force \( F_e \) using the substituted values in Coulomb's Law. This will give you the magnitude of the repulsive force between the two electrons.
Step 5: Calculate the gravitational force \( F_g \) using the substituted values in Newton's Law of Universal Gravitation. Compare the magnitudes of \( F_e \) and \( F_g \) to determine whether the electrons will be repelled or attracted.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Coulomb's Law
Coulomb's Law describes the electrostatic force between two charged particles. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is essential for calculating the electrostatic force of repulsion between two electrons, which both carry a negative charge.
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01:15
Coulomb's Law Concept 2
Newton's Law of Universal Gravitation
Newton's Law of Universal Gravitation states that every mass attracts every other mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This principle is crucial for calculating the gravitational force of attraction between two electrons, despite their minuscule mass compared to the electrostatic forces at play.
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01:42Entropy of the Universe
Nature of Electric and Gravitational Forces
Electric forces can be either attractive or repulsive depending on the charges involved, while gravitational forces are always attractive. In the case of two electrons, the electrostatic force will cause them to repel each other due to their like charges, while the gravitational force, although present, is negligible in comparison. Understanding this distinction is key to predicting the behavior of the electrons when allowed to move.
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01:14Nature of Energy
Related Practice
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?
Textbook Question
A magnesium ion, Mg2+, with a charge of 3.2⨉10-19 C and an oxide ion, O2-, with a charge of -3.2⨉10-19 C, are separated by a distance of 0.35 nm. How much work would be required to increase the separation of the two ions to an infinite distance?