University Physics Volume 3
17th Edition
ISBN: 9781938168185
Author: William Moebs, Jeff Sanny
Publisher: OpenStax
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Textbook Question
Chapter 8, Problem 12CQ
What is Pauli's exclusion principle? Explain the importance of this principle for the understanding of atomic structure and molecular bonding.
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4. Liner ionic crystal. Consider a line of 2N ions of alternating charge ±q with a
repulsive potential energy A/R" between nearest neighbors. (a) Show that at the
equilibrium separation
(CGS)
(b) Let the crystal be compressed so that R. → R. (1-8). Show that the work done
in a compressing a unit length of the crystal has the leading term C8²/2, where
2
(n-1)q² In 2
(CGS)
C =
U(R):
=
2Nq² In 2 (₁-1).
Ro
n
Ro
To obtain the results in SI, replace q² by q²/4л. Note: We should not expect to
obtain this result from the expression for U(R), but we must use the complete
expression for U(R).
You are preparing to compete in the Physics Olympics. Your instructor is coaching you by providing you with challenging problems of the type you might see on an Olympics exam. He comes up with the following problem and gives you 15 minutes to solve it: Imagine a perfectly rigid HCl molecule that does not stretch as it rotates. The equilibrium separation of its ions is 0.127 5 nm. There are two isotopes for chlorine on the sample, Cl-35 and Cl-37. This results in double peaks in the molecular spectrum as shown. (a) Find an expression for the difference in the frequency between the peaks to the right of the gap as a function of the masses of the two chlorine isotopes and the quantum number J. (b) Estimate the difference in frequency numerically for J = 0, without consulting tables. Quick! Get to work!
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.
Chapter 8 Solutions
University Physics Volume 3
Ch. 8 - Check Your Understanding Can the magnitude of...Ch. 8 - Check Your Understanding If the Stem-Gerlach...Ch. 8 - Check Your Understanding X-rays are produced by...Ch. 8 - Identify the physical significance of each of the...Ch. 8 - Describe the ground state of hydrogen in terms of...Ch. 8 - Distinguish between Bohr’s and Schiödinger’s model...Ch. 8 - Explain why spectral lines of the hydrogen atom...Ch. 8 - A hydrogen atom is placed in a magnetic field....Ch. 8 - On what factors does the orbital magnetic dipole...Ch. 8 - Explain how a hydrogen atom in the ground state (l...
Ch. 8 - Compare orbital angular momentum with spin angular...Ch. 8 - List all the possible values of s and msfor an...Ch. 8 - Are the angular momentum vectors L necessarily S...Ch. 8 - What is spin-orbit coupling?Ch. 8 - What is Pauli's exclusion principle? Explain the...Ch. 8 - Compare the electron configurations of the...Ch. 8 - Compare the electron configurations of the...Ch. 8 - Atomic and molecular spectra are discrete. What...Ch. 8 - Discuss the process of the absorption of light by...Ch. 8 - NGC1763 is an emission nebula in the Large...Ch. 8 - Why are X-rays emitted only for electron...Ch. 8 - How do the allowed orbits for electrons in atoms...Ch. 8 - Distinguish between coherent and monochromatic...Ch. 8 - Why is a metastable state necessary for the...Ch. 8 - How does light from an incandescent light bulb...Ch. 8 - How is a Blu-Ray player able to read more...Ch. 8 - What are the similarities and differences between...Ch. 8 - The wave function is evaluated at rectangular...Ch. 8 - If an atom has an election in the n = 5 state with...Ch. 8 - What are the possible values of m for an electron...Ch. 8 - What, if any, constraints does a value of m = 1...Ch. 8 - What are the possible values of m for an electron...Ch. 8 - (a) How many angles can L make with the z-axis for...Ch. 8 - The force on an electron is “negative the gradient...Ch. 8 - What is the total number of states with orbital...Ch. 8 - The wave function is evaluated at spherical...Ch. 8 - Coulomb's force law states that the force between...Ch. 8 - Write an expression for the total number of states...Ch. 8 - Consider hydrogen in the ground state, 100 . (a)...Ch. 8 - What is the probability that the is electron of a...Ch. 8 - How many polar angles are possible for an electron...Ch. 8 - What is the maximum number of orbital angular...Ch. 8 - What is the maximum number of orbital angular...Ch. 8 - Find die magnitude of the orbital magnetic dipole...Ch. 8 - A current of I = 2A flows through a square-shaped...Ch. 8 - Estimate the ratio of the electron magnetic moment...Ch. 8 - Find die magnitude of the orbital magnetic dipole...Ch. 8 - For a 3d electron in an external magnetic field of...Ch. 8 - An electron in a hydrogen atom is in the n = 5, l...Ch. 8 - Find the minimum torque magnitude that acts on...Ch. 8 - An election in a hydrogen atom is in 3p state....Ch. 8 - Show that U=B . (Hint: An infinitesimal amount of...Ch. 8 - What is the magnitude of the spin momentum of an...Ch. 8 - What are the possible polar orientations of the...Ch. 8 - For n = 1, write all the possible sets of quantum...Ch. 8 - A hydrogen atom is placed in an external uniform...Ch. 8 - If the magnetic field in the preceding problem is...Ch. 8 - If the magnetic moment in the preceding problem is...Ch. 8 - For n = 2, write all the possible sets of quantum...Ch. 8 - (a) How many electrons can be in the n = 4 shell?...Ch. 8 - (a) What is the minimum value of l for a subshell...Ch. 8 - Unreasonable result. Which of die following...Ch. 8 - Write the electron configuration for potassium.Ch. 8 - Write the election configuration for iron.Ch. 8 - The valence election of potassium is excited to a...Ch. 8 - (a) If one subshell of an atom has nine electrons...Ch. 8 - Write the electron configuration for magnesium.Ch. 8 - Write the electron configuration for carbon.Ch. 8 - The magnitudes of the resultant spins of the...Ch. 8 - What is the minimum frequency of a photon required...Ch. 8 - The ion Li2+ makes ail atomic transition from ail...Ch. 8 - The red light emitted by a ruby laser has a...Ch. 8 - The yellow light from a sodium-vapor street lamp...Ch. 8 - Estimate the frequency of the KaX-ray from cesium.Ch. 8 - Estimate the frequency of the K X-ray from cesium.Ch. 8 - X-rays are produced by striking a target with a...Ch. 8 - For the preceding problem, what happens to the...Ch. 8 - Suppose the experiment in the preceding problem is...Ch. 8 - An X-ray tube accelerates an electron with an...Ch. 8 - A color television tube generates some X-rays when...Ch. 8 - An X-ray tube has an applied voltage of 100 kV....Ch. 8 - The maximum characteristic X-ray photon energy...Ch. 8 - What are the approximate energies of the K and...Ch. 8 - Compare the X-ray photon wavelengths for copper...Ch. 8 - The approximate energies of the K and K X-rays for...Ch. 8 - A carbon dioxide laser used in surgery emits...Ch. 8 - An excimer laser used for vision correction emits...Ch. 8 - For a hydrogen atom in an excited state with...Ch. 8 - What is the probability that the Is electron of...Ch. 8 - Sketch the potential energy function of an...Ch. 8 - Find the value of l, the orbital angular momentum...Ch. 8 - Show that the maximum number of orbital angular...Ch. 8 - What is the magnitude of an electron magnetic...Ch. 8 - What is the maximum number of electron states n =...Ch. 8 - A ground-state hydrogen atom is placed in a...Ch. 8 - Show that the maximum number of electron states...Ch. 8 - The valence election of chlorine is excited to a...Ch. 8 - Which of the following notations are allowed (that...Ch. 8 - The ion Be3+ makes an atomic transition from an n...Ch. 8 - The maximum characteristic X-ray photon energy...Ch. 8 - Derive an expression for the ratio of X-ray photon...Ch. 8 - Compare the X-ray photon wavelengths for copper...Ch. 8 - (a) What voltage must be applied to an X-ray tube...Ch. 8 - A student in a physics laboratory observes a...
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- 2. / Consider the rotational energy level with quantum number J=2. a. How many degenerate states comprise that energy level? How are the populations of the degenerate states related to one another? How are their energies related to one another? b. Write the J=2 term in the partition function in two ways: (1) Enumerating every state individually, and (2) combining them into a single term for the J=2 energy level.arrow_forwardWhich of the (110) type directions lie in the (112) plane? OA. [110] and [110] OB. [101] and [101] OC. [011] and and [101] OD.[110] and [110] OE. [110] and [101] QUESTION 30 The lattice constant of the unit cell of a-iron (has a bcc structure) is 0.287 nm. The number of atoms/mm2 (atoms per unit area) for the (111) plane is: OA. 9.86 X 10° atoms/mm² OB. 48.56 X 10° atoms/mm² OC. 0.96 X 10¹3 atoms/mm² OD. 22.11 X 10¹3 atoms/mm² 2 poarrow_forward2. Next nearest neighbor interactions. Consider a monatomic lattice. The potential energy of the crystal system, modeled as a linear chain of atoms is UpE. = 1/(2a)E, where n runs over all the atoms in the chain and r, is the net displacement of the n'th atom. (a) Show that if the atom is interacting with p atoms on either side instead of one (as we discussed in class), the the force acting on the n'th atom is given by, F, = -E,(un – Un+p); where a, represents the force constant between atoms numbered n and n + p. (b) Let's now consider an atom interacting with four neighboring atoms, two on each side (i.e., p= 2). If a and m have the usual meanings, show that the dispersion relation is given by, 4a w² = () sin" () (1 + 4cos" (). ga ga (c) Plot this dispersion relation, comparing it with the dispersion involving only nearest neighbor interactions. Label your axes and edges of the Brillouin zone appropriately.arrow_forward
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