) Simple quantum systems: potential barrier Consider a uniform potential barrier of height vp = 6 eV and width L = 900 pm. Assume that the wavefunction inside the barrier continuously decays and smoothly connects the region on the left and on the right as illustrated below. Incoming Outgoing amplitude amplitude The wavefunction inside the barrier is a solution of the time-independent Schrödinger equa- tion 2m Əg² + uo♥(z) = E♥{z) where vp is the barrier height. Assume that the particle is travelling from the left to the right (from negative to positive on the -axis) and inside the barrier it keeps traveling to the right. A) In the radioactive decay an a-particle (¿He²+) with de Broglie wavelength of A = 0.8 nm impacts the barrier. Assume that the barrier is very high and wide (from the perspective of the particle that is impacting the barrier from the left) and that the particle inside the barrier is described by a wavefunction V(x) = Ae™a", where a and A are constants. What is the probability the a-particle will tunnel through the barrier? B) If an electron with de Broglie A = 0.8 nm impacts the barrier. Provide quantitative reasoning for the questions below: • You cannot assume that the that the barrier is very high and wide in this case, why? • Use the appropriate expression for the transmission probability and demonstrate whether the electron will have a higher probability of transmission than the a- particle?
) Simple quantum systems: potential barrier Consider a uniform potential barrier of height vp = 6 eV and width L = 900 pm. Assume that the wavefunction inside the barrier continuously decays and smoothly connects the region on the left and on the right as illustrated below. Incoming Outgoing amplitude amplitude The wavefunction inside the barrier is a solution of the time-independent Schrödinger equa- tion 2m Əg² + uo♥(z) = E♥{z) where vp is the barrier height. Assume that the particle is travelling from the left to the right (from negative to positive on the -axis) and inside the barrier it keeps traveling to the right. A) In the radioactive decay an a-particle (¿He²+) with de Broglie wavelength of A = 0.8 nm impacts the barrier. Assume that the barrier is very high and wide (from the perspective of the particle that is impacting the barrier from the left) and that the particle inside the barrier is described by a wavefunction V(x) = Ae™a", where a and A are constants. What is the probability the a-particle will tunnel through the barrier? B) If an electron with de Broglie A = 0.8 nm impacts the barrier. Provide quantitative reasoning for the questions below: • You cannot assume that the that the barrier is very high and wide in this case, why? • Use the appropriate expression for the transmission probability and demonstrate whether the electron will have a higher probability of transmission than the a- particle?
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)...
Related questions
Question
Hi I will appreciate your help with this problem
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
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.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON