Answered: A 30-eV electron is incident on a…

A 30-eV electron is incident on a square barrier of height 40 eV.(A) What is the probability that the electron tunnels through the barrier if its width is 1.0 nm?

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 70P: A 6.0-eV electron impacts on a barrier with height 11.0 eV. Find the probability of the electron to...

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: Consider an electron of energy 1 eV that encounters a potential barrier of width 0.1nm and energy…

Q: Electron of 5 eV is incident on a barrier of height 12 eV and 0.2 nm width. 1. Find the transmission…

A: Given, Energy of electron = 5 [eV] = E Barrier height energy= 12 [eV] = U Barrier width= 0.2×10-9…

Q: What is the smallest box in which you can confine an electron if you want to know for certain that…

A: According to the uncertainty principle, ∆x∆p=h2π We know that, ∆x∆p≥h4π

Q: A particle is confined to the one-dimensional infinite potential well of If the particle is in its…

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

Q: Calculate the probability of finding the particle in the box region between 1/4 L and 3/4 L

Q: An electron is trapped in a one-dimensional infinite potential well in a state with quantum number n…

Q: If p=-iħ d/dx is the linear momentum operator. What is its eigenvalue if it is affected on a…

A: if any operator operates on wave function, than the result should be some constant multiplied by…

Q: For a particle in cubic box, what is the degeneracy of the energy level 81 times the ground state…

A: The general expression of the particle’s energy (Enx,ny,nz) in a cubic box of side a is given as,…

Q: A proton is confined to a one dimensional infinite potential well 100 pm wide. What is its…

A: Ground state energy one dimensional infinite potential well E1=h28mpL2=6.626×10-34 J·s281.672×10-27…

Q: An electron is trapped in a finite potential well that is deep enough to allow the electron to exist…

Q: An electron, trapped in a one-dimensional infinite potential well 250 pm wide, is in its ground…

A: The expression for the required energy is,

Q: An electron is trapped in a one-dimensional infinite potential well. Show that the energy difference…

Q: equation for the particle in a one-dimensional box, the quantization of energy levels results when…

A: Schrodinger wave equation for the particle in a one dimensional box is : δ2ψδx+8π2mh2E-vψ=0

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

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: Calculate the uncertainty in momentum for a proton confined to a nucleus of radius 5.0 fm.

A: Using Heisenberg's uncertainty principle, ∆x∆p≥h4π∆p≥h4π∆x

Q: A stream of electrons is of energy E is incident on a potential barrier of height U and thickness d.…

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: If the function is a normalization then the formula Y ¥dt gives the probability that the particle…

Q: Given a quantum particle trapped in aninfinite 1 D potential well of length, L the ratio of energy…

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: What is the probability that the electron tunnels through the barrier? (Use 9.11 10-31 kg for the…

A: Given data: The kinetic energy is: E = 3.10 eV The width of barrier is: L = 0.230 nm The mass of an…

Q: Suppose that an electron trapped in a one- dimensional infinite well of width 250 pm is excited from…

A: The energy of a particle in a one-dimensional infinite well is given by,

Q: Calculate the transmission probability for quantum-mechanical tunneling in each of the following…

A: The expression for the transmission probability, The expression for the constant value,

Q: Q. Aparticle is moving in one-dimension that characterized by the state Iw) with wave function y-Ae…

A: Given:- A particle is moving in one -dimension that is characterized by the state ψ with the wave…

Q: An electron having total energy E = 4.50 eV approaches a rectangular energy barrier with U = 5.00 eV…

A: (a) To determine the transmission coefficient, first, it needs to determine the constant α by the…

Q: Consider an infinite potential well with the width a. What happens to the ground state wavelength if…

Q: An electron is trapped in a one-dimensional infinite potential well that is 470 pm wide; the…

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: .In the 1-D problem shown below, a 5-MeV alpha particle is approaching a square potential barrier. a…

A: Quantum Tunneling

Q: What must be the width of a one-dimensional infinite potential well if an electron trapped in it in…

A: Given: mass of electron, m = 9.1 x 10-31 kg state, n = 3 Energy of electron, E = 4.7 eV = 4.7 x…

Q: A 100 g arrow travels with a speed of 30 ms-l over a distance of 50 m. If the initial size of the…

Q: An electron is trapped in a one-dimensional infinite well of width 250 pm and is in its ground…

Q: Given a quantum particle trapped in an infinite 1D potentialwell of length L wave-function is A ex…

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

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: A photon passes through a horizontal slit of width 5 × 10-6 m. What uncertainty in the vertical…

A: Given: The width of the slit is ∆r=5×10-6 m. The expression to calculate the minimum uncertainty…

Q: If the position of an electron in a membrane is measured to an accuracy of 1.00 μm , what is the…

A: Given data *The uncertainity in position is ∆x=1.00 μm=1.00×10-6 m *The value of the Planck's…

Q: An electron and a proton, each initially at rest, are accelerated across the same voltage. Assuming…

A: Heisenberg's uncertainty principle states that it is impossible to measure the position and momentum…

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…

Concept explainers

Connection formulae for WKB approximation

In quantum mechanics, Schrödinger’s equation for certain systems with varying parameters cannot be solved directly. In such a case, an approximation method is used to obtain the approximate solution. WKB method is a special technique used to obtain the approximate solution for Schrödinger’s time-independent equation. In general, the WKB method is used to solve linear differential equations with varying coefficients. This method is called semiclassical approximation in quantum mechanics.

Question

A 30-eV electron is incident on a square barrier of height 40 eV.
(A) What is the probability that the electron tunnels through the barrier if its width is 1.0 nm?

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Connection Formulae for WKB approximation

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 6.0-eV electron impacts on a barrier with height 11.0 eV. Find the probability of the electron to tunnel through the barrier if the barrier width is (a) 0.80 nm and (b) 0.40 nm.
When an electron and a proton of the same kinetic energy encounter a barrier of the same height and width, which one of them will tunnel through the barrier more easily? Why?
A 2.0 eV electron encounters a barrier 5.0 eV high. What is the probability that it will tunnel through the barrier if the barrier width is (a) 1.00 nm and (b) 0.50 nm?
A stream of electrons is of energy E is incident on a potential barrier of height U and thickness d. Even though U >> E, 5% of the electrons tunnel through the barrier. If the thickness of the barrier decrease to 0.12 d, what percentage of the electrons will tunnel through?
An electron with total energy En approaches a barrier of height Ub and thickness L . Calculate the transmission coefficient T. Where the energy En= 25.5 eV, Ub=34.005 eV the width L=75 pm is given .
Suppose 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 L
An electron of energy 1 eV got trapped inside the surface of a metal. If the potential barrier is 4.0 eV and width of the barrier is 2 Angstrom, the probability of its transmission is, * O 0.01 0.09 0.5 0.085
An electron with total energy E = 5.0 eV approaches a rectangular potential energy barrier with U0 = 6.0 eV. What should the width L of the potential barrier be so that the probability of the electron crossing it is one in a million?
Two copper nanowires are insulated by a copper oxide nano-layer that provides a 10.0-eV potential barrier. Estimate the tunneling probability between the nanowires by 7.00-eV electrons through a 5.00-nm thick oxide layer. What if the thickness of the layer were reduced to just 1.00 nm? (Hint: the rest mass of the electron (m) = 511 keV/c2, ℏ = 0.1973 keVnm/c)
A particle with mass 2.5 × 10^(-27) kg and energy 4.0 eV approaches a potential barrier with a height of 2.5 eV and a width of 1.0 nm. Calculate the probability of the particle tunneling through the barrier.
In a particular semiconductor device, electrons that are accelerated through a potential of 5 V attempt to tunnel through a barrier of width 0.8 nm and height 10 V. What fraction of the electrons are able to tunnel through the barrier if the potential is zero outside the barrier?
(a) An electron with initial kinetic energy 32 eV encounters a square barrier with height 41 eV and width 0.25 nm. What is the probability that the electron will tunnel through the barrier? (b) A proton with the same kinetic energy encounters the same barrier. What is the probability that the proton will tunnel through the barrier?