Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 42, Problem 4P
(a)
To determine
The value of
(b)
To determine
The energy required to break up a diatomic molecule.
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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. Find, in terms of A and B, (a) the value r0 at which the energy is a minimum and (b) the energy E required to break up a diatomic molecule.
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.
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...
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- (a): Calculate Miller's indices in the hexagonal structure of its intersections. ai = 1, ar--1/2, as = 1,c= o and draw it. (b): the potential energy of a diatomic molecule is given by U = A B . 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. m2 and B = 1.488 x 10 eV.m. Find the separation distance at which the energy of the molecule is a minimum. Q3: Calculate the dhai of tetragonal using the concepts of reciprocal latticearrow_forwardQ3: The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x) = - 읆 옮 , where a and b are constant and x is the distance between the atoms. If the dissociation energy of the molecule is (U(x= ∞) -U at equilibrium), D is (a) b²/6a (b) b²/2a (c) b²/12a (d) b²/4aarrow_forwardN 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_forward
- The 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_forwardThe 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_forward
- A 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_forwardGlasses are materials that are disordered – and not crystalline – at low temperatures. Here is a simple model. Consider a system with energy E, the number of accessible microstates is given by a Gaussian function: Ω(E) = Ω0 e −(E−E¯) 2/(2∆2 ) , where Ω0 and E¯ and ∆ are positive constants. E¯ is the average energy. In this problem, we consider only the states whose energy E is below E¯. 1. Show that the entropy is an inverted parabola: S(E) = S0 − α (E − E¯) Find S0 and α. Write your answers in terms Ω0, ∆, and other universal constants. 2. An entropy catastrophy happens when S = 0, which occurs at energy E0. (i) Find E0. (ii) What is the number of accessible states for energy below E0? 3. The glass transition temperature Tg is the temperature of entropy catastrophy. Compute Tg. 4. Find the energy E as a function of T. 5. Without any calculation, explain why E → E¯ as T → +∞. Hint: consider the Boltzmann distributionarrow_forward
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