A potential barrier of height V extends from x = 0 to positive x. Inside this barrier the normalized wavefunction is ψ = Ne−κx. Calculate (a) the probability that the particle is inside the barrier and (b) the average penetration depth of the particle into the barrier.

A potential barrier of height V extends from x = 0 to positive x. Inside this barrier the normalized wavefunction is ψ = Ne−κx. Calculate (a) the probability that the particle is inside the barrier and (b) the average penetration depth of the particle into the barrier.

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter7: Quantum Mechanics

Section: Chapter Questions

Problem 74P: A simple model of a radioactive nuclear decay assumes that a-particles are trapped inside a well of...

See similar textbooks

Related questions

Q: If in a box with infinite walls of size 1 nm there is an electron in the energy state n=2, find its…

A: Size of the box of infinite well = L = 1nm = 10-9m Energy state = n = 2 Particle in the box =…

Q: -A system is defined by the wavefunction: 27nx (x) = A cos for 4 (a) Determine the normalization…

Q: An electron beam having energy 2 eV incidents on a potential barrier having width 20x10 10 m and…

A: When a particle of energy E is less than a potential barrier of height U, then the transmission…

Q: ) Simple quantum systems: potential barrier Consider a uniform potential barrier of height vp = 6 eV…

A: (1) for alpha particleEquation for transmission probability;…

Q: The wave function for an electron in an infinite potential well is given as follows; TX sin L 4,(x)…

Q: Which of the following is ALWAYS FALSE for a particle encountering a potential barrier? I. The wave…

A: Option (IV.) is always false, because the wavelength of the wave function, before entering the…

Q: Is the ground-state energy of a proton trapped in a onedimensional infinite potential well greater…

A: The ground-state energy of a proton trapped in a one dimensional infinite potential well is equal to…

Q: Show that ? (x,t) = A exp [i (kx - ?t] is a solution to the time-dependent Schroedinger equation for…

Q: A particle of mass m mves in the infinite square well potential v(x)= 0. if -a/2 to a/2 infinitive…

Q: What is the ground-state energy of (a) an electron and (b) a proton if each is trapped in a…

Q: Determine the probability of finding a quantum particle (restricted to a one-dimensional box of…

Q: When low-energy electrons pass through an ionized gas, electrons of certain energies pass through…

A: Given information: The transmission coefficient will be equal to unity when the half-integral of de…

Q: For the normalized wavefunction v(x)= V2 cos(2.xx ). find the expectation value of kinetic energy

Q: Which of the following changes would increase the probability of transmission of a particle through…

Q: A particle is trapped in an infinite one-dimensional well of width L. If the particle is in its…

Q: Consider a particle in a box with edges at x = ±a . Estimate its ground state energy using…

A: We have a trial wave function, ψ=|x|λ-aλ. The energy is given by,<E>=<ψ|H|ψ><ψ|ψ>…

Q: Find the expectation value of kinetic energy E for the = 2 sin(zr) vavefunction (r)

A: Given:- The normalized wavefunction ψ(x) = 2sinπx Find:- The expectation value of kinetic energy…

Q: The eigenfunctions satisfy the condition | Vi (x)m(x)dx = &nm , &nm = 1 if n %3D %3D = m , otherwise…

Q: Consider a potential energy barrierbut whose height Ub is 6.0 eV and whose thickness L is 0.70…

A: The probability that a particle of mass m and energy E will tunnel through a potential barrier of…

Q: Consider a particle with the following wave-function: ,xL and L and A are constants. (a) What is the…

Q: Consider a particle of mass m, located in a potential energy well. one-dimensional (box) with…

A: Given data : Wave function ψn(x) = K sin(nπxL) , 0≤x≤L0 , for any other…

Q: A wave function of a particle with mass m is given by, Acosa ≤ ≤+ otherwise b(z) = {1 Find the…

A: See step 2 .

Q: Use the Schrödinger equation to calculate the energy of a 1-dimensional particle-in-a-box system in…

A: Problem 1 Wavefunction of particle in a box is given by, ψx=2LsinnπxL

Q: Consider a particle with 1-D wave-function (x) = kexp(-x²). Sketch (x),

Q: Solve the Schrodinger equation for a quantum particle of mass m trapped in a one-dimensional…

Q: A 30-eV electron is incident on a square barrier of height 40 eV.(A) What is the probability that…

A: Given Data The energy of an electron is given as E = 30 eV. The voltage of a square barrier is V =…

Q: If you have a system with two levels of energy. Prove that the probabilities of absorption and…

Q: a) Find the normalization constant A in terms of the constants a and b. b) Sketch ψ(x, 0) as a…

A: c) From the above graph we can see that the wave function is highest at x=a. That means the…

Q: Question related to Quantum Mechanics : Problem 2.38

A: (1)Time independent wave function is ψn(x,0)=∑nCnψn(x)Time dependent wave function is…

Q: The ground state energy of an electron in a one-dimensional trap with zero potential energy in the…

A: Given : Initial potential energy at the wall, E1 = 2.0 eV Let the initial width of potential well be…

Q: Suppose a particle of mass m is moving in a one-dimensional potential of a kind -20<x<2a- = (x)A-…

A: The Energy eigenvalue of a particle inside a potential well of side 'a' is given by: En =n2π2ħ22ma2…

Q: For a "particle in a box" of length, L, draw the first three wave functions and write down the…

A: Given: Length of the box is L. To show: λn = 2 L / n

Q: What is the probability of finding a particle in the last 10% of a one-dimensional box for n = 1…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: how that ? (x,t) = A cos (kx - ?t) is not a solution to the time-dependent Schroedinger equation for…

A: Given, Wave function, ψx,t = A cos kx - ωt for a free particle, U(x) = 0 We know time dependent…

Q: An electron is trapped in a one-dimensional infinite potential well that is 100 pm wide; the…

Q: if the wavefunction for a particle is : Y = Ae'(kxx-wt) Prove that the uncertainty in the particle…

A: Please see the answer below

Q: An electron is bound in a square well of width 1.50 nm and depth U0 = 6E1-IDW. If the electron is…

A: The ground state energy of a finite square well is given by E1=0.625E1-1DW Here, E1-1DW=h28mL2 Here,…

Q: Show that the oscillating probability density is linear in arbitrary wave beams that oscillates with…

A: To find the oscillates frequency is equal to the linear oscillator

Q: Can the particle in a one-dimensional box have energy degeneracy?

Q: Suppose that in a certain system a particle free to move along one dimension (with 0 ≤ x ≤ ∞) is…

Q: A particle moving in one dimension has the wave function 4(x,t) = Ael(ax-bt)] where a and b are…

Q: Find the lowest energy of an electron confined to move in a three dimensional potential box of…

Q: A one -dimensional potential box of width a. ) Show that the wavefunctrion af a particle in the 2nd…

A: A one-dimensional potential box of width a is illustrated below: The wavefunction for the nth state…

Question

100%

A potential barrier of height V extends from x = 0 to positive x. Inside this barrier the normalized wavefunction is ψ = Ne^−κx. Calculate (a) the probability that the particle is inside the barrier and (b) the average penetration depth of the particle into the barrier.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

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.

Similar questions

A particle of mass m is confined to a box of width L. If the particle is in the first excited state, what are the probabilities of finding the particle in a region of width0.020 L around the given point x: (a) x=0.25L; (b) x=040L; (c) 0.75L and (d) x=0.90L.
A simple model of a radioactive nuclear decay assumes that a-particles are trapped inside a well of nuclear potential that walls are the barriers of a finite width 2.0 fm and height 30.0 MeV. Find the tunneling probability across the potential barrier of the wall for a-particles having kinetic energy (a) 29.0 MeV and (b) 20.0 MeV. The mass of the a -particle is m=6.641027kg.
What is the ground state energy (in eV) of an a -particle confined to a one-dimensional box the size of the uranium nucleus that has a radius of approximately 15.0 fm?
A 12.0-eV electron encounters a barrier of height 15.0 eV. If the probability of the electron tunneling through the barrier is 2.5 %, find its width.
A muon, a quantum particle with a mass approximately 2(X) times that of an electron, is incident on a potential barrier of height 10.0 eV. The kinetic energy of the impacting muon is 5.5 ev and only about 0.10% of the squared amplitude of its incoming wave function filters through the barrier. What is the barrier's width?
An electron with kinetic energy 2.0 MeV encounters a potential energy barrier of height 16.0 MeV and width 2.00 nm. What is the probability that the electron emerges on the other side of the barrier?
A particle of mass m confined to a box of width L is in its first excited state 2(x). (a) Find its average position (which is the expectation value of the position). (b) Where is the particle most likely to found?
A grain of sand with mass 1.0 mg and kinetic energy 1.0 J is incident on a potential energy barrier with height 1.00000 J and width 2500 nm. How many grains of sand have to fall on this barrier before, on the average, one passes through?
Suppose a wave function is discontinuous at some point. Can this function represent a quantum state of some physical particle? Why? Why not?
A wave function of a particle with mass m is given by (x)={Acosax, 2ax+ 2a;0, otherwise where a =1.001010/m. (a) Find the normalization constant. (b) Find the probability that the particle can be found on the interval 0x0.51010m. (c) Find the particle's average position. (d) Find its average momentum. Find its average kinetic energy 0.51010mx+0.510-10m.
An electron is bound in a square well of width 1.05 nm and depth U0=6E∞, where E∞ is the ground-state energy for an infinitely deep potential well.If the electron is initially in the ground level, E1=0.625E∞ , and absorbs a photon, what maximum wavelength can the photon have and still liberate the electron from the well?
What is the independent wave function for a particle in a box x=0,L