University Physics Volume 3
17th Edition
ISBN: 9781938168185
Author: William Moebs, Jeff Sanny
Publisher: OpenStax
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Textbook Question
Chapter 8, Problem 50P
What is the magnitude of the spin momentum of an electron? (Express you answer in terms of h.)
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Physics
When we use the notation |k,m,n> in angular momentum, for the case of spin we write, for example |k,1/2,1/2>. In that case, what is the meaning of the k?
Angular momentum and Spin. An electron in an H-atom has orbital angular momentum
magnitude and z-component given by
L² = 1(1+1)ħ²,
L₂ = m₂h,
1 = 0,1,2,..., n-1
m₁ = 0, +1, +2, ..., ±l
3
1
S² = s(s+1)h²=h², S₂ = m₂h = + = h
+/-ħ
4
Consider an excited electron (n > 1) on an H-atom.
What is the minimum angle 0min that the S can have with the z-axis?
Clue: the angle a vector with magnitude V from the z-axis can be computed from
cos 0 = V²/V
Consider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit. Each electron has orbital angular momentum U (that is, the orbit is the smallest-radius Bohr orbit), and the two electrons are always on opposite sides of the nucleus. Ignore the effects of spin. What is the total kinetic energy of the electrons?
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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- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax