Consider a one-dimensional square potential well with a width of L and depth Vo. A electron is confined within this potential well. a) Calculate the energy levels of the electron in terms of L and Vo. b) Determine the wavelength of the electron associated with its lowest energy state (n=1). c) If the potential well has the width of L=5nm and Vo=10eV, calculate the energy of the electron in its lowest energy state.

Consider a one-dimensional square potential well with a width of L and depth Vo. A electron is confined within this potential well. a) Calculate the energy levels of the electron in terms of L and Vo. b) Determine the wavelength of the electron associated with its lowest energy state (n=1). c) If the potential well has the width of L=5nm and Vo=10eV, calculate the energy of the electron in its lowest energy state.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A quantum simple harmonic oscillator consists of an electron bound by a restoring force proportional to its position relative to a certain equilibrium point. The proportionality constant is 8.11 N/m. What is the longest wavelength of light that can excite the oscillator? ps:- answer is not 443.68
An electron is confined to a one-dimensional region in which its ground-state (n = 1) energy is 1.45 eV. (a) What is the length L of the region? nm(b) What energy input is required to promote the electron to its first excited state? eV
3. Particle in a 2D Box. A quantum mechanical particle is confined in side a square 2D box, with side length L. Inside the box V=0 and outside the box V=infinity. Let the wave function to be (x,y). (a) write down the Schrodinger equation of (x,y). (b) Use the separation of variable method solve (x,y) (let the quantum numbers to be nx and ny.) (c) What is the energy for the state (nx, ny)? (d) What is the probability density p(x,y) for the state nx=3 and ny=3? Sketch this p(x,y) in a square.
Assume an electron moves in one dimensional infinite potential box its width L= 6nm, theni) Draw the energy level diagram and determine the value of this energy for the three first energy states.ii) Plot and explain the wave function for n= 1, 2, 3 states.iii) Sketch and explain the probability distribution of the electron for n=2 and n=3 states.iv) Mark on the figure the probability of finding the electron between x= L/3 and 2L/3 for n= 3 state.
E8A.12 At what radius does the probability density of an electron in the H atom fall to 50 per cent of its maximum value? E8A.13 At what radius in the H atom does the radial distribution function
Consider a particle in a 2-D box having Lx = 10 nm and Ly = 10 nm. a) Make a surface plot of all the wave functions for the first and second energy levels. b) What is the degeneracy of the second energy level? Compare and contrast the wave functions of the second energy level. c) How does the number of nodes in the x-coordinate change as n increases? How does the number of nodes in the y-coordinate change as n, increases? d) Explain whether or not those same states would be degenerate if Lx = 10 nm and Ly = 15 nm.
View Policies Current Attempt in Progress Suppose that the electron in the figure, having a total energy E of 4.9 eV, approaches a barrier of height Up = 6.9 eV and thickness L = 700 pm. What percentage change in the transmission coefficient T occurs for a 0.5% change in (a) the barrier height, (b) the barrier thickness, and (c) the kinetic energy of the incident electron? Energy E Elcciron L. (a) Number i Units (b) Number i Units (c) Number i Units MacBook Pro
The electron moves in an infinitely deep. potential well with a width of l=0.15 nm. a) Calculate the minimum (i.e. ground state) speed of the electron. V₁=? b) Calculate the reaction force that the electron causes when it moves back and forth and collides with the other wall of the well adiabatically (thermally insulated). F=? c) Calculate the frequency of the electron's back and forth motion. f=?
Subjects;