Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 6.5, Problem 4E
To determine
Verify that the ground-state energy for an electron confined to a square well is about
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Consider a particle confined to a 1-dimensional box of length L = 6 nm.
A. What is the probability of locating the particle between x = 3 nm and x = 3.2 nm in the ground state?
B. Evaluate T where is the normalized particle in a box wave function. If the particle is an electron and the quantum number of the state it's in (n) is 3, compute the eigenvalue you get
with the formula you obtain.
(J)
C. What is the potential energy operator equal to for PIAB?
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An electron is in the ground state in a two-dimensional, square, infinite potential well with edge lengths L.We will probe for it in a square of area 400 pm2 that is centered at x=L/8 and y=L/8. The probability of detection turns out to be 4.5 * 10-8. What is edge length L?
a two-dimensional, infinite-potential well lying in an xy plane that contains an electron. We probe for the electron along a line that bisects Lx and find three points at which the detection probability is maximum. Those points are separated by 2.00 nm. Then we probe along a line that bisects Ly and find five points at which the detection probability is maximum.Those points are separated by 3.00 nm.What is the energy of the electron?
Chapter 6 Solutions
Modern Physics
Ch. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.5 - Prob. 4ECh. 6.7 - Prob. 5ECh. 6.8 - Prob. 6ECh. 6 - Prob. 1QCh. 6 - Prob. 2QCh. 6 - Prob. 3QCh. 6 - Prob. 4QCh. 6 - Prob. 5Q
Ch. 6 - Prob. 6QCh. 6 - Prob. 7QCh. 6 - Prob. 8QCh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10PCh. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 21PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Prob. 37PCh. 6 - Prob. 38P
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- Physics Consider particles of mass "m" in an infinite square well (a box) of size "L". a. Write the wave function for a situation in which the particles are in a superposition of state "s" with energies E5, E6, E8 with probabilities P(E5) =P(E6) =1/4. b. Write explicitly the integral needed to calculate in order to find the average value of the position operator < X >. No need to calculate the integrals explicitly.arrow_forwardA free electron has a kinetic energy 13.3eV and is incident on a potential energy barrier of U =32.1eV and width w =0.091nm. What is the probability for the electron to penetrate this barrier (in %)? Check the correct answer and show all workarrow_forwarda) For a particle in a one-dimensional box of length L, do the energy levels move up ordown if the box gets longer? Explain your answer clearly.b) Consider a particle in a two-dimensional box of side lengths a and b, where b = 2a.In which direction is it more expensive (in terms of energy) to add nodes? Explain youranswer clearly.c) Consider a particle in a two-dimensional box of side lengths a and b, where b = 2a.Write down the quantum numbers corresponding to the rst (lowest) 5 energy levels of thissystem. Note any degeneracies.arrow_forward
- PROBLEM 2. Calculate the probabilities of measurement of different mo- menta p for a particle with the wave function (x) = Ceka sin (gx), %3D where C is a normalization constant.arrow_forwardYour answer is partially correct. The ground-state energy of an electron trapped in a one-dimensional infinite potential well is 2.0 eV. What will this quantity be if the width of the potential well is multiplied by 6? Number 5.555 Units eVarrow_forwardFind the normalization constant B for the combination 18. As noted in Exercise 8, a linear combination of two wave functions for the same sysstem is also a valid wave function also a valid wave function functions for the same system 2TX = B sin TX +sin L. L. of the wave functions for then = 1 and n = 2 states od %3D particle in a box L wide. [A + CO]arrow_forward
- I only need help with problem 4. The answer is E = 86 meV 1. For a potential barrier with V(x) = 0 for |x| > a/2, and V(x) = 0.3 eV for |x| < a/2, 4. Consider the potential barrier discussed in problem 1. Suppose that there are two of these barriers forming a double‐barrier structure. If they are separated by 5 nm, what are the resonant energy level(s) in the well?arrow_forwardConsider a single electron confined to a one-dimensional quantum well device of length L = 0.5 nm. The quantum well device acts as a “trap” for the electron 1.What are the boundary conditions for this system? Apply them to show that ψn(x) = Asin(nπx/L), n = 1,2,3,... (check image) 2.Normalize the wave function to find the constant A. 3. Sketch ψ1, ψ2, and ψ3, as well as |ψ1|2, |ψ2|2, and |ψ3|2, and evaluate the energy levels E1, E2, and E3 in eV. 4. Suppose the particle is in the first excited state. What is the probability of finding the particle between x = L/4 and x = 3L/4? 5. Suppose, instead of one electron, we trap five electrons in the quantum well. Draw an energy-level diagram to show the electron configuration of the ground state. What is the ground state energy?arrow_forwardElectron of 5 eV is incident on a barrier of height 12 eV and 0.2 nm width. 1. Find the transmission probability of this electron. 2. How will the transmission probability get affected if the width is doubled?arrow_forward
- 6.8: A 6 eV electron is confined in an infinite 1 D potential well. The region between the potential wall is 1.00 nm long. Calculate the electrons quantum number in its current state.arrow_forwardSuppose that the electron in the Figure, having a total energy E of 5.1 eV, approaches a barrier of height Us=6.8 eV and thickness L= 750 pm. (a) What is the approximate probability that the electron will be transmitted through the barrier, to appear (and be detectable) on the other side of the barrier? Energy Us Electron Larrow_forwardAn atom with total energy 1.84 eV, in a region with no potential energy, is incident on a barrier with potential height 3.76 eV, and unknown thickness b. The probability that the atom passes through the barrier is 1.16%. If the thickness of the barrier is increased to 1.68b, what is the new probability of passing through the barrier (in %)?arrow_forward
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