University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 41, Problem 41.42P
(a)
To determine
The quantum numbers
(b)
To determine
The side lengths of
(c)
To determine
The quantum numbers, energies and degeneracy for the next higher energy state.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
An electron is in a three-dimensional box. The x- and z-sides of the box have the same length, but the y-side has a different length. The two lowest energy levels are 2.24 eV and 3.47 eV, and the degeneracy of each of these levels (including the degeneracy due to the electron spin) is two. (a) What are the nX, nY, and nZ quantum numbers for each of these two levels? (b) What are the lengths LX, LY, and LZ for each side of the box? (c) What are the energy, the quantum numbers, and the degeneracy (including the spin degeneracy) for the next higher energy state?
Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (?),(n), the angular momentum quantum number (?),(?), the magnetic quantum number (??),(m?), and the spin quantum number (?s)(ms) have strict rules which govern the possible values.
Identify all allowable combinations of quantum numbers for an electron.
A. ?=4,n=4, ?=1,?=1, ??=2,m?=2, ?s=−1/2ms
B.?=3,n=3, ?=−1,?=−1, ??=1,m?=1, ?s=−1/2ms
C.?=5,n=5, ?=2,?=2, ??=2,m?=2, ?s=+1/2ms
D.?=3,n=3, ?=3,?=3, ??=1,m?=1, ?s=−1/2ms
E.?=2,n=2, ?=1,?=1, ??=1,m?=1, ?s=0ms
F. ?=3,n=3, ?=1,?=1, ??=1,m?=1, ?s=+1/2
An electron is in a three-dimensional box. The xx- and zz-sides of the box have the same length, but the yy-side has a different length. The two lowest energy levels are 2.18 eVeV and 3.47 eVeV, and the degeneracy of each of these levels (including the degeneracy due to the electron spin) is two.
What is the length LY for side of the box?
What are the lengths LXLX, LZLZ for sides of the box?
What is the energy for the next higher energy state?
What are the quantum numbers for the next higher energy state?
What is the degeneracy (including the spin degeneracy) for the next higher energy state?
Chapter 41 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 41.1 - Prob. 41.1TYUCh. 41.2 - Prob. 41.2TYUCh. 41.3 - Prob. 41.3TYUCh. 41.4 - In this section we assumed that the magnetic field...Ch. 41.5 - In which of the following situations is the...Ch. 41.6 - Prob. 41.6TYUCh. 41.7 - Prob. 41.7TYUCh. 41.8 - Prob. 41.8TYUCh. 41 - Prob. 41.1DQCh. 41 - Prob. 41.2DQ
Ch. 41 - Prob. 41.3DQCh. 41 - Prob. 41.4DQCh. 41 - Prob. 41.5DQCh. 41 - Prob. 41.6DQCh. 41 - Prob. 41.7DQCh. 41 - In the ground state of the helium atom one...Ch. 41 - Prob. 41.9DQCh. 41 - Prob. 41.10DQCh. 41 - Prob. 41.11DQCh. 41 - Prob. 41.12DQCh. 41 - Prob. 41.13DQCh. 41 - Prob. 41.14DQCh. 41 - Prob. 41.15DQCh. 41 - Prob. 41.16DQCh. 41 - Prob. 41.17DQCh. 41 - Prob. 41.18DQCh. 41 - Prob. 41.19DQCh. 41 - Prob. 41.20DQCh. 41 - Prob. 41.21DQCh. 41 - Prob. 41.22DQCh. 41 - Prob. 41.23DQCh. 41 - Prob. 41.1ECh. 41 - Prob. 41.2ECh. 41 - Prob. 41.3ECh. 41 - Prob. 41.4ECh. 41 - Prob. 41.5ECh. 41 - Prob. 41.6ECh. 41 - Prob. 41.7ECh. 41 - Prob. 41.8ECh. 41 - Prob. 41.9ECh. 41 - Prob. 41.10ECh. 41 - Prob. 41.11ECh. 41 - Prob. 41.12ECh. 41 - Prob. 41.13ECh. 41 - Prob. 41.14ECh. 41 - Prob. 41.15ECh. 41 - Prob. 41.16ECh. 41 - Prob. 41.17ECh. 41 - Prob. 41.18ECh. 41 - A hydrogen atom in a 3p state is placed in a...Ch. 41 - Prob. 41.20ECh. 41 - Prob. 41.21ECh. 41 - Prob. 41.22ECh. 41 - Prob. 41.23ECh. 41 - Prob. 41.24ECh. 41 - Prob. 41.25ECh. 41 - Prob. 41.26ECh. 41 - Prob. 41.27ECh. 41 - Prob. 41.28ECh. 41 - Prob. 41.29ECh. 41 - (a) Write out the ground-state electron...Ch. 41 - Prob. 41.31ECh. 41 - Prob. 41.32ECh. 41 - Prob. 41.33ECh. 41 - Prob. 41.34ECh. 41 - Prob. 41.35ECh. 41 - Prob. 41.36ECh. 41 - Prob. 41.37ECh. 41 - Prob. 41.38ECh. 41 - Prob. 41.39PCh. 41 - Prob. 41.40PCh. 41 - Prob. 41.41PCh. 41 - Prob. 41.42PCh. 41 - Prob. 41.43PCh. 41 - Prob. 41.44PCh. 41 - Prob. 41.45PCh. 41 - Prob. 41.46PCh. 41 - Prob. 41.47PCh. 41 - Prob. 41.48PCh. 41 - Prob. 41.49PCh. 41 - Prob. 41.50PCh. 41 - Prob. 41.51PCh. 41 - Prob. 41.52PCh. 41 - Prob. 41.53PCh. 41 - Prob. 41.54PCh. 41 - Prob. 41.55PCh. 41 - Prob. 41.56PCh. 41 - Prob. 41.57PCh. 41 - Effective Magnetic Field. An electron in a...Ch. 41 - Prob. 41.59PCh. 41 - Prob. 41.60PCh. 41 - Prob. 41.61PCh. 41 - Prob. 41.62PCh. 41 - Prob. 41.63PCh. 41 - Prob. 41.64PCh. 41 - Prob. 41.65PCh. 41 - Prob. 41.66PCh. 41 - Prob. 41.67PCh. 41 - Prob. 41.68CPCh. 41 - Prob. 41.69CPCh. 41 - Prob. 41.70PPCh. 41 - Prob. 41.71PPCh. 41 - Prob. 41.72PPCh. 41 - Prob. 41.73PP
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
- An electron is in a three-dimensional box with side lengths LX = 0.600 nm and LY = LZ = 2LX. What are the quantum numbers nX, nY, and nZ and the energies, in eV, for the four lowest energy levels? What is the degeneracy of each (including the degeneracy due to spin)?arrow_forwardThe electronic structure of one-dimensional chain of sodium (Na) atoms can be approximately described by the particle-in-a-box model. The energy of each state can be calculated using n²h? En = 5,n = 1,2,3, ... 8mL2 where L is the length of the 1D chain. Assuming L = ao(N – 1), where N is the number of Na atoms and ao = 0.360 nm is the internuclear distance. a) Determine the energy gap between the highest occupied energy level and the lowest unoccupied energy level as a function of N. Assume that N is an even number that is large enougharrow_forwardA rectangular corral of widths Lx= L and Ly = 2L containsseven electrons. What multiple of h2/8mL2 gives the energy of theground state of this system? Assume that the electrons do not inter-act with one another, and do not neglect spin.arrow_forward
- A rectangular corral of widths Lx =L and Ly =2L contains seven electrons. What multiple of h2/8mL2 gives the energy of the ground state of this system? Assume that theelectrons do not interact with one another, and do not neglect spin.arrow_forward= = Imagine that we have a box that emits electrons in a definite but unknown spin state y). If we send electrons from this box through an SGz device, we find that 20% are determined to have Sz +ħ and 80% to have S₂ -ħ. If we send electrons from this box through an SGx device, we find that 90% are determined to have Sx +ħ and 10% to have Sx Determine the state vector for electrons emerging from the box. You may assume that the vector components are real. -1/ħ. = -arrow_forwardFor a helium atom in its ground state, what are quantum numbers (n,L, mL and nL ) for the (a) spin-up electron and (b) spindown electron?arrow_forward
- An Atom has zero orbital angular momentum ad a spin quantum number 1/2. It is found to be in the |↑z> state. A measurement is performed on the value of its angular momentum in a direction at an angle Θ (theta) to the z-axis. Show that the probability of its angular momentum being parallel to this new axis is cos2(Θ/2).arrow_forwardAn electron is in an infinite square well of width 2.0 nm. What is the wavelength of the emitted photon in nanometers as the electron transitions from the n=8 to the n=4 state? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19J). Please give your answer with no decimal places.arrow_forwardThe quantum mechanical model of the hydrogen atom requires that if the principal quantum number is 6, there will be how many different permitted orbital quantum number(s)?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax