Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 36, Problem 46P
To determine
The minimum energy of the system consists of five electrons in an infinite square well of width
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
One can now use integrated-circuit technology to manufacture a "box" that traps electrons in a region only a few nanometers wide. Imagine that we make an essentially one-dimensional box with a length of 3 nanometers. Suppose we put 10 electrons in such a box and allow them to settle into the lowest possible energy states consistent with the Pauli exclusion principle.
a) What will be the value of the highest energy level occupied by at least one electron?
b) What will be the electrons' total energy (ignoring their electrostatic repulsion)?
c) How would your answers to the above be different if the electrons were bosons instead of fermions?
d) What is the wavelength of the lowest energy photon that can be absorbed (the electrons in this box are fermions)?
Chapter 39, Problem 015
An electron is trapped in a one-dimensional infinite potential well that is 150 pm wide; the electron is in its ground state.
What is the probability that you can detect the electron in an interval of width dx = 5.0 pm centered at x = 56 pm? (Hint:
The interval dx is so narrow that you can take the probability density to be constant within it.)
Number
Units
Assume that an electron is confined in a one-dimensional quantum well with infinite walls, draw the wave functions for the first 3 levels, ψ1, ψ2, ψ3. Also, show the probability density functions corresponding to these three levels?
Chapter 36 Solutions
Essential University Physics (3rd Edition)
Ch. 36.1 - Prob. 36.1GICh. 36.2 - Prob. 36.2GICh. 36.3 - Prob. 36.3GICh. 36.4 - Prob. 36.4GICh. 36.5 - Prob. 36.5GICh. 36 - Prob. 1FTDCh. 36 - Prob. 2FTDCh. 36 - Prob. 3FTDCh. 36 - Prob. 4FTDCh. 36 - Prob. 5FTD
Ch. 36 - Prob. 6FTDCh. 36 - Prob. 7FTDCh. 36 - Prob. 8FTDCh. 36 - Prob. 9FTDCh. 36 - Prob. 10FTDCh. 36 - Prob. 11FTDCh. 36 - Prob. 12FTDCh. 36 - What distinguishes a Bose-Einstein condensate from...Ch. 36 - Prob. 14ECh. 36 - Prob. 15ECh. 36 - Prob. 16ECh. 36 - Prob. 17ECh. 36 - Prob. 18ECh. 36 - Prob. 19ECh. 36 - Prob. 20ECh. 36 - Prob. 21ECh. 36 - Prob. 22ECh. 36 - Prob. 23ECh. 36 - Prob. 24ECh. 36 - Prob. 25ECh. 36 - Prob. 26ECh. 36 - Prob. 27ECh. 36 - Prob. 28ECh. 36 - Prob. 29ECh. 36 - Prob. 30ECh. 36 - Prob. 31ECh. 36 - Prob. 32ECh. 36 - Prob. 33ECh. 36 - Prob. 34PCh. 36 - Prob. 35PCh. 36 - Prob. 36PCh. 36 - Prob. 37PCh. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - Prob. 41PCh. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - Prob. 45PCh. 36 - Prob. 46PCh. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - Prob. 51PCh. 36 - Prob. 52PCh. 36 - Prob. 53PCh. 36 - Prob. 54PCh. 36 - Prob. 55PCh. 36 - Prob. 56PCh. 36 - Prob. 57PCh. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - Prob. 63PCh. 36 - Prob. 64PCh. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - Prob. 68PCh. 36 - Prob. 69PCh. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Prob. 73PCh. 36 - Prob. 74PCh. 36 - Prob. 75PCh. 36 - Prob. 76PPCh. 36 - Prob. 77PPCh. 36 - Prob. 78PPCh. 36 - Prob. 79PP
Knowledge Booster
Similar questions
- A one-dimensional infinite potential well has a length of 2L. a) What are the energy eigenvalues? b) Calculate the ground state energy if ten protons are confined in the box. Assume that the protons don’t interact with each other. c) If the ten protons are replaced by ten neutral hydrogen atoms, what is the total ground state energy resulting from the confinement? Again, assume that the hydrogen atoms do not interact with each other. You can treat the mass of proton and hydrogen atom to be identical.arrow_forwardHow to write the total wave function in multi-electron systems? Write the total wave function for the helium atom.arrow_forwardThe Lennard-Jones parameters for argon are: A = 1.022 x 10-7 J m° and B = 1.579 x 10-134 J m12. Calculate the distance at which the energy will be minimum and calculate the minimum energy. Draw the energy profile also. I.arrow_forward
- A typical diameter of a nucleus is about 10-14 m. Use the infinite square-well potential to calculate the transition energy from the first excited state to the ground state for a proton confined to the nucleus. Of course, this is only a rough calculation for a proton in a nucleus.arrow_forwardConsider a one dimensional atom trap with an ideal harmonic oscillator potential with the zero-point energy of 4 eV. Assume the temperature of zero Kelvin, 8 atoms in the trap and that interactions between atoms in the trap are negligible. Calculate the total energy of atoms in the trap if 0 atoms have spin 0. O atoms have spin 1/2. 3. atoms have spin 1. atoms have spin 3/2.arrow_forwarda. For the allowed energies of a particle in a box to be large, should the box be very big or very small? Explain.b. Which is likely to have larger values for the allowed energies: an atom in a molecule, an electron in an atom, or a proton in a nucleus? Explain.arrow_forward
- The nucleus of a gold atom has a radius of 7.0 fm. Estimate the kinetic energy of a proton or neutron confined to a gold nucleus. Hint :Use HEISENBERG PRINCIPLE to find Linear Momentum of Neutron or Proton with uncertainity in position equals to radius 7.0 fm.arrow_forwardAt room temperature, the fourth excited state of a microscopic oscillator is 0. 26 eV above the ground state energy. What is the Boltzmann factor for this excited state? Boltzmann factor =arrow_forwardUse Boltzmann distribution to solve this problem.A system consists of 3, 000 particles that can only occupy two energy levels: a nondegen-erate ground state of 0.052 eV and a threefold degenerate excited state at 0.156 eV. IfT = 900 K,(a) find the number of particles at each energy level.(b) what is the total energy of the system?arrow_forward
- 7c.2. Evaluate for the total energy & at the following k-directions and evaluate at the BZ boundary. a. (1,0,0) b. (1,1,0) c. (1,1,1)arrow_forwardA particle is confined to a two-dimensional box of length L and width 2L. The energy values are E = (h²²/ 2mL²)(n+n2/4). Find the two lowest degenerate levels. C1arrow_forwardWhat is the partition function for the system shown? a. b. C. d. E₁ Eo -Eo/KT + e-E₁/kT 2e-Eo/kT +3e-ElkT 3e¯ e-Eo/2kT + e-E₁/3kT e-2Eo/kT + e-³E₁/KTarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning