Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 11, Problem 5Q
To determine
The role of Pauli’s exclusion principle in stability of molecules.
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A
+ Given that
B
7-10-
==
13) Suppose that the interaction energy between two atoms is given by E (r)
the atoms from a stable molecule with an internuclear distance of 0.3 nm and a dissociation energy
of 4 eV, calculate A and B. Also calculate the force require to break the molecule and the critical
distance between the nuclei for which this occurs.
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1) Assume that the elemental atoms are hard spheres of radius r.Calculate the maximum packing rate t obtained when this elementcrystallizes into the following structures:(a) simple cubic (sc)(b) body-centered cubic (bcc)(c) face-centered cubic (fcc)
In this problem you will model the mixing energy of a mixture in a relatively simple way, in order to relate the existence of a solubility gap to molecular behavior. Consider a mixture of A and B molecules that is ideal in every way but one: The potential energy due to the interaction of neighboring molecules depends upon whether the molecules are like or unlike. Let n be the average number of nearest neighbors of any given molecule (perhaps 6 or 8 or 10). Let μ0be the average potential energy associated with the interaction between neighboring molecules that are the same (A-A or B-B), and let μAB be the potential energy associated with the interaction of a neighboring unlike pair (A-B). There are no interactions beyond the range of the nearest neighbors; the values of μ0 and μAB are independent of the amounts of A and B; and the entropy of mixing is the same as for an ideal solution.
(a) Show that when the system is unmixed, the total potential energy due to all the…
Chapter 11 Solutions
Modern Physics
Ch. 11.2 - Compare the effective force constant for the CO...Ch. 11 - Prob. 1QCh. 11 - Prob. 2QCh. 11 - Prob. 3QCh. 11 - Prob. 4QCh. 11 - Prob. 5QCh. 11 - Prob. 7QCh. 11 - Prob. 8QCh. 11 - Prob. 9QCh. 11 - Prob. 1P
Ch. 11 - Use the data in Table 11.2 to calculate the...Ch. 11 - The CO molecule undergoes a rotational transition...Ch. 11 - Prob. 4PCh. 11 - Prob. 5PCh. 11 - Prob. 6PCh. 11 - Prob. 7PCh. 11 - The v = 0 to v = 1 vibrational transition of the...Ch. 11 - Consider the HCl molecule, which consists of a...Ch. 11 - Prob. 10PCh. 11 - Prob. 11PCh. 11 - Prob. 12PCh. 11 - Prob. 13PCh. 11 - Prob. 14PCh. 11 - Prob. 15PCh. 11 - Prob. 18P
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- i have a sample of Co2O3 with only schottky defects and dope it with Li20 9- a) What are the compensating defects that can form? b) If the compensating defect is one of the defects that is part of the intrinsic ionic defects in Co2O3, which of the defects from part a) would form? c) What is the relationship between the concentration of Li and the compensating defect from b)?arrow_forward2) An atomic nucleus can be crudely modeled as a gas of nucleons with a number density of 0.09 fm-3 (where 1 fm = 10-15m). a) Calculate the Fermi energy ɛp of this system. b) Also, calculate the Fermi temperature TF. Is it reasonable to treat the nucleus as a degenerate Fermi gas at room temperature? c) Calculate the degeneracy pressure of the nucleus. What keeps the nucleus from blowing apart due to this degeneracy pressure?arrow_forwardAs an alternative to Equation 42.1, another useful model for the potential energy of a diatomic molecule is the Morse potential U(r)=B[ea(rr0)1]2 where B, a, and r0 are parameters used to adjust the shape of the potential and its depth. (a) What is the equilibrium separation of the nuclei? (b) What is the depth of the potential well, defined as the difference in energy between the potentials minimum value and its asymptote as r approaches infinity? (c) If is the reduced mass of the system of two nuclei and assuming the potential is nearly parabolic about the well minimum, what is the vibrational frequency of the diatomic molecule in its ground state? (d) What amount of energy needs to be supplied to the ground-state molecule to separate the two nuclei to infinity?arrow_forward
- The characteristic energy for KCl is 1.4105eV . (a) Determine for the KC1 molecule, (b) Find the separation distance between the K arid Cl atoms.arrow_forward(a) In an HCl molecule, take the Cl atom to be the isotope 35Cl. The equilibrium separation of the H and Cl atoms is 0.127 46 nm. The atomic mass of the H atom is 1.007 825 u and that of the 35Cl atom is 34.968 853 u. Calculate the longest wavelength in the rotational spectrum of this molecule. (b) What If? Repeat the calculation in part (a), but take the Cl atom to be the isotope 37Cl, which has atomic mass 36.965 903 u. The equilibrium separation distance is the same as in part (a). (c) Naturally occurring chlorine contains approximately three parts of 35Cl to one part of 37Cl. Because of the two different Cl masses, each line in the microwave rotational spectrum of HCl is split into a doublet as shown in Figure P42.11. Calculate the separation in wavelength between the doublet lines for the longest wavelength.arrow_forwardIn this problem you will model the mixing energy of a mixture in a relatively simple way, in order to relate the existence of a solubility gap to molecular behavior. Consider a mixture of A and B molecules that is ideal in every way but one: The potential energy due to the interaction of neighboring molecules depends upon whether the molecules are like or unlike. Let n be the average number of nearest neighbors of any given molecule (perhaps 6 or 8 or 10). Let Uo be the average potential energy associated with the interaction between neighboring molecules that are the same (A-A or B-B), and let UAB be the potential energy associated with the interaction of a neighboring unlike pair (A-B). There are no interactions beyond the range of the nearest neighbors; the values of Uo and UAB are independent of the amounts of A and B; and the entropy of mixing is the same as for an ideal solution. Show that when the system is unmixed, the total potential energy due to all neighbor-neighbor…arrow_forward
- 3 Madelung constant of NaCl Consider the infinite series for the Madelung constant of the NaCl-type struc- ture. Its convergence depends on how the successive terms are chosen. The expression, as given below, is written such that the terms are sequential attrac- tive and repulsive interactions coming from sequential shells that purely contain cations or anions. Uc Z₁ Z2e² 4πend (6- 12 8 + √2 √3 6 24 24 + √4 √5 (1) a, Calculate the sum of this series for two, three, four, five, and six terms. For each successive shell, determine the total number of cations and anions sur- rounding the central anion. b, What can you say about the convergence of this series after 6 terms? c, Which of these successive sums is closest to the Madelung constant for the rocksalt structure of +1.7476? For which series is the total charge enclosed closest to zero? d, What can be done to achieve a more rapid convergence of this series? +arrow_forwardIn this problem you will model the mixing energy of a mixture in a relatively simple way, in order to relate the existence of a solubility gap to molecular behavior. Consider a mixture of A and B molecules that is ideal in every way but one: The potential energy due to the interaction of neighboring molecules depends upon whether the molecules are like or unlike. Let n be the average number of nearest neighbors of any given molecule (perhaps 6 or 8 or 10). Let Uo be the average potential energy associated with the interaction between neighboring molecules that are the same (A-A or B-B), and let UAB be the potential energy associated with the interaction of a neighboring unlike pair (A-B). There are no interactions beyond the range of the nearest neighbors; the values of Uo and UAB are independent of the amounts of A and B; and the entropy of mixing is the same as for an ideal solution. Find a formula for the total potential energy when the system is mixed, in terms of x, the fraction…arrow_forwardThere are three atoms: A, B, and C. The graphs of potential energy for the pairs AB and BC are shown below (the scale of the axes is the same for both graphs). Which of the following statements is correct? If there is more than one, you must select all of them. r TH U (AB) The AB bond has a smaller magnitude of binding energy than the BC bond. Breaking the AB bond releases more energy than breaking the BC bond. The reaction A + BC -> AB + C is exothermic. U (BC) None of the statements is correct. 1arrow_forward
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