Answer all questions in handwriting 5) a) An electron is confined between two impenetrable walls 0.2 nm apart. Determine theenergy levels for the states n= 1, and 2.b) Find the speed of the electron in the n = 1 state.

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n is confined betwee for the states n=1.

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter29: Introduction To Quantum Physics

Section: Chapter Questions

Problem 62PE: (a) If the position of an electron in a membrane is measured to an accuracy of 1.00 m, what is the...

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63 O Figure 40-25 is an energy-level di- agram for a fictitious three-dimensional infinite potential well that contains one electron. The number of degenerate E (/8ml") 14 Triple states of the levels are indicated: "non" 12 Non means nondegenerate (which includes the ground state) and "triple" means 3 states. If we put a total of 22 electrons in the well, what multiple of h²18mL? gives the energy of the ground state of the 22-electron sys- tem? Assume that the electrostatic forces between the electrons are negligible. 11 Triple 6. Triple Triple 3. Ground Figure 40-25 Problem 63.
JC-60) SWE for 2 Particles Derive an expression for the energy of a two-particle system using the wave function given in equation 8-17 in your text. Assume particle 1 is in the n= 1 state and particle two is in the n = 2 state and that the potential is equal to zero (U = 0). %3D
2. An electron is confined to a nanowire 2 nm in length. Model this system as a 1-D particle-in-a-box, going from 0 to 2 nm. a. Compute the probability that the electron is in the range 0.95 ≤ x ≤ 1.05 nm for the states n = 1, 2, 3. b. Compute the probability that the electron is located within a distance of 0.05 nm of the left end of the wire for each of the states n = 1, 10, 100.
2. Show that the probability density for the ground-state solution of the one-dimensional Coulomb potential energy has its maximum at x = a,.
4) Suppose that an electron having a total energy E of 30 eV, as show in the figure below, approaches a barrier of height Ub = 40 eV and thickness L = 1 nm. a) What is the probability that the electron tunnels through the barrier? b) What is the probability that the electron tunnels through the barrier if the thickness L = 0.1 nm? Energy E Electron c) What is the probability that a proton with same total of energy E of 30 eV will be transmitted through the barrier of height Ub = 40 eV and thickness L = 1 nm? 0 L
Check Your Understanding What happens to the ground state energy of an electron if the dimensions of the solid increase?
(a) If the position of an electron in a membrane is measured to an accuracy of 1.00 m, what is the electron's minimum uncertainty in velocity? (b) If the electron has this velocity, what is its kinetic energy in eV? (c) What are the implications of this energy, comparing it to typical molecular binding energies?
Problem 1. Two State System Consider an atom with only two states: a ground state with energy 0, and an excited state with energy A. Determine the mean energy (e) and variance in energy (de). Sketch the mean energy versus A/k T.
4. Refer to the following one-dimensional quantum potential structure. In region 0 the potential V = 0o; in regions I and III the potential V = 0; in region II the potential V = V, = 1.0 eV. The width of region I, L, = 2.0 nm; the width of region II, AL = L, - L = 1.0 nm, or L, = 1.5 L,. There is an electron in region I. V = Vo II II X = 0 X = L, X = L2 (1) Show Schrodinger equations of the electron inside regions I, II, and III. | (2) Find initial solutions of the above equations with 6 unknown constants. (3) Find two out of six constants of the above solutions. (4) Find the next three constants of the solutions in step 2. (5) Find the allowed energy levels of the electron in region I in a unit of eV. (6) Find the last constant of the solutions in step 2. (7) Find the complete solutions for the three wave functions. (8) Find the expectation value of x at the ground state region I. (9) Calculate the transmission coefficient by using T = |Y m¥;?. III (10) Calculate the probability to…
2. Show that the probability density for the ground-state solution of the one-dimensional Coulomb potential energy has its maximum at x = =ao.
3. a) According to the spherical shell model, predict J" for the ground state and first excitation of 'Be, ¹70 and 2¹Ne. b) Explain pros and cons of the shell model based on a harmonic oscillator potential of the type: Vo = 1/2 kr².
If one of the two electrons of a H2 molecule is removed, we get a hydrogen molecular ion H+2. In the ground state of an H+2 , the two protons are separated by roughly 1.5 Å, and the electron is roughly 1 Å from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.