Consider an atomic nucleus to be equivalent to a onedimensional infinite potential well with L = 1.4 * 10-14 m, a typical nuclear diameter.What would be the ground-state energy of an electron if it were trapped in such a potential well? (Note: Nuclei do not contain electrons.)

Consider an atomic nucleus to be equivalent to a onedimensional infinite potential well with L = 1.4 * 10-14 m, a typical nuclear diameter.What would be the ground-state energy of an electron if it were trapped in such a potential well? (Note: Nuclei do not contain electrons.)

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter8: Quantum Mechanics In Three Dimensions

Section8.1: Particle In A Three-dimensional Box

Problem 2E

See similar textbooks

Related questions

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

Q: Calculate the energy of the nth excited state of a particle in a 1D box with hard walls at x = 0 and…

Q: A one-dimensional infinite well of length 200 pm contains an electron in its third excited state.We…

A: a) The wave function of an electron in an infinite one-dimensional potential well of length L along…

Q: A particle moving in one dimension has the wave function Y(x, t) = Aeli(ax-bt)] %3D where a and b…

Q: Show that the uncertainty in the momentum of a ground-state harmonic oscillator is (where h is…

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: Assembly consists of 8 classical systems distributed over five power strips of one cell, and their…

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: Suppose that a ground-state harmonic oscillator experiences a perturbation ax at distances 0 0 is a…

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

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

Q: An electron is trapped in a one-dimensional infinite potential well that is 170 pm wide; the…

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

Q: The ground-state energy of an electron trapped in a onedimensional infinite potential well is 2.6…

Q: answer 1. In classically behavior is forbidden regions, the wave @Oscillatory elecay or grow…

A: Solution:1. In classically forbidden regions, the wave functions behaviour is of decay or of…

Q: Calculate the threshold wave length for tungsten surface whose work function is 4.5 eV?

A: Given, Work function for the tungsten, E = 4.5 eV

Q: J. particle in an infinite potential well ait to Ax Given the wwave fonction of a L Ala-x) a/2 E x…

Q: Two adjacent energy levels of an electron in a harmonic potential well are known to be 2. and 3.64…

A: Given: Two adjacent levels of an electron Ina harmonic well are known to be 2.60eV and 3.64eV.

Q: A one-dimensional infinite potential well has a length of 2L. What are the energy eigenvalues?…

A: A one-dimensional infinite potential well has a length of 2L. The energy Eigen value of 1-d infinite…

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: 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: The ground state energy of a particle in a one-dimensional infinite potential well of width 1.5 nm…

A: Ground state energy of infinite potential well is 20eV and width is 1.5nm Ground state energy of…

Q: If the absolute value of the wave function of a proton is 2 times as large at location A than at…

Q: For a system of bosons at room temperature, compute the average occupancy of a single-particle state…

A: To determine: Average occupancy and probability of the state if the energy of the state is 1 eV…

Q: Calculate the expectation value of x2 in the state described by ψ = e -bx, where b is a ħ constant.…

Q: The energy absorbed in the transition from n=1 to n=2 for a 1-dimensional harmonic oscillator is hv.…

A: Given that: Transition from n=2 to n=1

Q: For a particle in a finite potential well, is it correct to say that each bound state of definite…

A: The bound state energy of the particle in a finite potential well is a function of the frequency as…

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

Q: A particle is confined to the 1D infinite potential well of the figure below If the particle is in…

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

A: Given: width of potential well L =273 pm =273*10-12 m

Q: The one-dimensional harmonic oscillator has a potential V(x) = ka² /2. We Henote the solutions of…

A: Please find solution to part a

Q: Consider an electron in a 2D harmonic trap with force constants kxx = 232 N/m and kyy = 517 N/m.…

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

Q: An electron, trapped in a one-dimensional infinite potential well 366 pm wide, is in its ground…

A: Width of potenial well= 366 x 10-12m mc2=5.11 x 103eV Objective- Energy needed to send electron to…

Q: Prove that assuming n = 0 for a quantum particle in an infinitely deep potential well leads to a…

A: Energy of quantum particle in a infinitely deep potential well Momentum of the particle inside the…

Q: For a particle in a 1-dimensional infinitely deep box of length L, the normalized wave function or…

A: We have to find the probability of finding the particle.

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

Q: Consider an atomic nucleus to be equivalent to a one dimensional infinite potential well with L =…

Q: An electron of mass m in a cubic box of side length (L) is perturbed in the direction and magnitude…

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

Schrödinger equation

Schrödinger equation is a prominent equation in quantum mechanics. This equation is used to predict the behavior of quantum states or quantum particles. In quantum mechanics, the particles are treated as waves. A quantity called wave function is used to represent a quantum state. The wave function completely describes the quantum system. This equation can be used to study the particles like electrons, protons and, neutrons. It is also used to study the structure of hydrogen atoms and harmonic oscillators.

Question

Consider an atomic nucleus to be equivalent to a onedimensional
infinite potential well with L = 1.4 * 10-14 m, a
typical nuclear diameter.What would be the ground-state energy
of an electron if it were trapped in such a potential well? (Note:
Nuclei do not contain electrons.)

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 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

We are going to use Heisenberg's uncertainty principle to estimate the ground- state energy of hydrogen. In our model, the electron is confined in a one- dimensional well with a length about the size of hydrogen, so that Ax = 0.0529 nm. Estimate Ap, and then assume that the ground-state energy is roughly Ap2/2me. (Give your answer in Joules or electron-volts.)
Consider an atomic nucleus to be equivalent to a one dimensional infinite potential well with L = 1.4 x1014 m, a typical nuclear diameter .What would be the ground-state energy of an electron if it were trapped in such a potential well? (Note: Nuclei do not contain electrons.)
An electron is confined to move in the xy plane in a rectangle whose dimensions are Lx and Ly. That is, the electron is trapped in a two dimensional potential well having lengths of Lx and Ly. In this situation, the allowed energies of the electron depend on the quant numbers Nx and Ny, the allowed energies are given by E = H^2/8Me ( Nx^2/ Lx^2 + Ny^2/Ly^2) i) assuming Lx and Ly =L. Find the energies of the lowest for all energy levels of the electron ii) construct an energy level diagram for the electron and determine the energy difference between the second exited state and the ground state?
A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator are 5e-21 J apart. Use k = 1.4e-23 J/K. When the nanoparticle's energy is in the range 5(5e-21) J to 9(5e-21) J, what is the approximate heat capacity per atom?
An electron in a one-dimensional infinite potential well of length L has ground-state energy E1.The length is changed to L' so that the new ground-state energy is E'1 = 0.500E1 .What is the ratio L'/L?
An electron bounces elastically in 1D between two infinite potential walls separated by a distance L. The electron is in its lowest possible energy state. (a) What is the energy of this state? (b) The separation between the walls is slowly (a.k.a. 'adiabatically') increased to 2L. That the process occurs slowly means that the electron slowly adapts to continue to occupy the ground state of this new well of width 2L. What is the change in energy that the electron experiences? (c) With the walls again at a distance of L, imagine now that the separation is abruptly increased from L to 2L. This means that, at the moment when the change is made, the wavefunction is unchanged for a L. Write a (normalized) expression for 1(x) at this very moment, and draw it for the interval x = [0, 2L]. What is the expectation value of the energy for this ₁(a)? I'm calling it 1(a) not (x) to make it clear that it represents the ground state. (d) Show that the above 1(r) is no longer a solution for the…
An electron is trapped in a one-dimensional infinite potential well that is 200 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width öx = 5.0 pm centered at x = 100 pm? (Hint: The interval öx is so narrow that you can take the probability density to be constant within it.) Number i Units
1.3 The effective potential of a particle is given by: Veff(r) = 2mr? + V(r). Find the effective force corresponding to this effective potential. 1.4 A hydrogen atom has an electron radial eigenfunction given by: u0,1(r) : (ezan, Obtain the probability density of this eigenfunction. 10
What is the ground-state energy of (a) an electron and (b) a proton if each is trapped in a one-dimensional infinite potential well that is 273 pm wide? (a) Number 8.083824566 Units eV (b) Number 4.401408127 Units eV
An electron is trapped in a one-dimensional infinite potential well that is 430 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width &x = 5.0 pm centered at x = 260 pm? (Hint: The interval Sx is so narrow that you can take the probability density to be constant within it.) Number i Units
Impurities in solids can be sometimes described by a particle-in-a-box model. Suppose He is substituted for Xe, and assume a particle-in-a-cubic-box model, the length of whose sides is equal to the atomic diameter of Xe (≈ 2.62 Å). Compute the lowest excitation energy for the He atom’s motion. (This is the energy difference between the ground state and the first excited state.)
An electron is trapped in a one-dimensional infinite potential well that is 460 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width δx = 5.0 pm centered at x = 300 pm? (Hint: The interval δx is so narrow that you can take the probability density to be constant within it.)