Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 42, Problem 4P
(a)
To determine
The value of
(b)
To determine
The energy required to break up a diatomic molecule.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
The potential energy of two atoms in a diatomic molecule is approximated by U(r) = a/r12-b/r6, where r is the spacing between atoms and a and b are positive constants.
Suppose the distance between the two atoms is equal to the equilibrium distance found in part A. What minimum energy must be added to the molecule to dissociate it -
that is, to separate the two atoms to an infinite distance apart? This is called the dissociation energy of the molecule. Express your answer in terms of the variables a and b.
For the molecule CO, the equilibrium distance between the carbon and oxygen atoms is 1.13\times 10-10m and the dissociation energy is 1.54\times 10-18J per
molecule. Find the value of the constant a. Express your answer in joules times meter in the twelth power. Find the value of the constant b. Express your answer in joules
times meter in the sixth power.
One description of the potential energy of a diatomic molecule is given by the Lennard–Jones potential, U = (A)/(r12) - (B)/(r6)where A and B are constants and r is the separation distance between the atoms. For the H2 molecule, take A = 0.124 x 10-120 eV ⋅ m12 and B = 1.488 x 10-60 eV ⋅ m6. Find (a) the separation distance r0 at which the energy of the molecule is a minimum and (b) the energy E required to break up theH2 molecule.
The effective spring constant describing the potential energy of the HBr molecule is 410 N/m and that for the NO molecule is 1530 N/m.
(a) Calculate the minimum amplitude of vibration for the HBr molecule.
(b) Calculate the minimum amplitude of vibration for the NO molecule.
Chapter 42 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 42.1 - For each of the following atoms or molecules,...Ch. 42.2 - Prob. 42.2QQCh. 42.2 - Prob. 42.3QQCh. 42 - Prob. 1PCh. 42 - Prob. 2PCh. 42 - Prob. 3PCh. 42 - Prob. 4PCh. 42 - Prob. 5PCh. 42 - The photon frequency that would be absorbed by the...Ch. 42 - Prob. 8P
Ch. 42 - Prob. 9PCh. 42 - Prob. 10PCh. 42 - (a) In an HCl molecule, take the Cl atom to be the...Ch. 42 - Prob. 12PCh. 42 - Prob. 13PCh. 42 - Prob. 14PCh. 42 - Prob. 15PCh. 42 - Prob. 16PCh. 42 - Prob. 17PCh. 42 - Prob. 19PCh. 42 - Prob. 21PCh. 42 - Prob. 22PCh. 42 - Prob. 23PCh. 42 - Prob. 24PCh. 42 - Prob. 25PCh. 42 - Prob. 26PCh. 42 - Prob. 27PCh. 42 - Prob. 28PCh. 42 - Prob. 29PCh. 42 - Prob. 30PCh. 42 - Prob. 32PCh. 42 - Prob. 33PCh. 42 - Prob. 35PCh. 42 - Prob. 36APCh. 42 - Prob. 37APCh. 42 - Prob. 39APCh. 42 - Prob. 40APCh. 42 - As an alternative to Equation 42.1, another useful...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Consider two immiscible liquids such as water and oil. If a spherical oil molecule of radius r is taken out of the oil phase and placed in the water phase, the unfavorable energy of this transfer is proportional to the area of the solute (oil) molecule newly exposed to the solvent (water) multiplied by the interfacial energy, i, of the oil-water interface. The interfacial energy of the bulk cyclohexane-water interface is i = 50 mJ m-2, and the radius of a cyclohexane molecule is 0.28 nm. Using Boltzmann distribution, estimate the solubility of cyclohexane in water at 25 C in units of mol L-1.The concentration of water in water phase is 55.5 mol L-1.arrow_forwardV7arrow_forwardThe potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U(x) = −a/x12 − b/x6 where x is the distance between the atoms. (a) At what distance of seperation does the potential energy have a local minimum (not at x = ∞)? (b) What is the force on an atom at this separation? (c) How does the force vary with the separation distance?arrow_forward
- N 2 has a molecular weight of 28.02 g/mol a bit larger than that of a Ne atom, 20.18 g/mol. (a) At a particular temperature, Z trans= 1.90 x 10 26 for Ne in a specific container. What is the translational partition function for a N2 molecule in this container at the same temperature? (b) At 100 K, the rotational partition function for N2is found to be 17.39. What would you expect it to be at 500 K?arrow_forwardThe air is a gas mixture of oxygen, carbon dioxide, and Nitrogen. If the air can be treated as ideal gas at temperature 100 °C, what is the average kinetic energy for each of the molecule in air?(Consider Oxygen, Nitrogen, and carbon dioxide as diatomic molecule structure which consist of translational and rotational degree of freedom only. No vibration motion is considered) Boltzmann constant is kB = 1. 38 x 10 23 J/Karrow_forwardThe potential energy of a system of two atoms is given by the relation U =-A/r + B/r10 A stable molecule is formed with the release of 8 eV energy when the interatomic distance is 2.8 Å. Find A and B and the force needed to dissociate this molecule into atoms and the interatomic distance at which the dissociation occurs.arrow_forward
- The energy of the vibrational modes of a molecule are the same as those of a (quantum) harmonic oscillator with frequency w. There is a gas of nitrogen molecules in thermodynamic equilibrium for which ħw/ks-3340 K. You may approximate the vibrational partition function with the largest two terms in it. a) What fraction of the molecules are in the ground state and what fraction in the 1st excited state of their vibrational modes at a temperature of 700 K, b) At what temperature will 5% of the molecules be in the 1st excited vibrational state?arrow_forwardA molecule has states with the following energies: 0, 1ε, 2ε, 3ε, and 4ε, where ε = 1.0 x 10-20 J. Calculate the average number of molecules in the first excited state (1ε) for a collection of 1000 molecules in thermal equilibrium at T = 300 K. Note that the average number of molecules in a state is just the probability that a molecule is in the state times the number of molecules. Provide your answer as a number in normal form.arrow_forwardA molecule has states with the following energies: 0, 1ε, 2ε, 3ε, and 4ε, where ε = 1.0 x 10-20 J. Calculate the probability that a molecule is in the ground state (with zero energy) for a collection of molecules in thermal equilibrium at T = 300 K. Provide your answer as a number in normal form to 3 decimal places (in the form X.XXX). It is a good idea to keep 4 decimal places during your calculation, then round to 3 decimal places for your submitted answer. Hint: note that this molecule has a finite number of states so you must take a finite sum, do not use expressions for infinite sums. Also note that your calculations for this problem will be useful for the next two problems, so keep them.arrow_forward
- The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U(x) = −a/x¹² — b/x6 where x is the distance between the atoms. (a) At what distance of separation does the potential energy have a local minimum (x = ∞) ?arrow_forwardA room temperature gas of non interacting HF molecules are confined to a bottle with dimensions of approximately 10 cm by 1 cm by 1cm. Compute the N2/N1 Boltzmann weights for the vibrational, rotational, and translational motions of the gas. Assume a particle in a 1D box for translational (L=1 cm). Assume a particle-in-a-ring for rotations (also assume the fluorine atom is at the center of mass and that the bond length is 1 Angstrom). Assume a harmonic oscillator model for vibrations (the vibrational frequency of HF is approximately 3900 cm-1).arrow_forwardIn a certain physical system, there are two energy states available to a particle: the ground state with energy E₁ = 0 eV, and the excited state with energy E₂ = 1.5 eV. The system is in thermal equilibrium at a temperature T = 300 K. Calculate the Gibbs factor (also known as the Boltzmann factor) for the excited state . Give your answer to two decimal places.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning