Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Chapter 39, Problem 2Q
To determine
To find:
Is the ground -state energy of a proton trapped in a one dimensional infinite potential well greater than, less than, or equal to that of an electron trapped in the same potential well?
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A one-dimensional simple lharmonic oscillator is subjected to a small
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A proton is confined to a one dimensional infinite potential well 100 pmwide. What is its ground-state energy?
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Chapter 39 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 39 - Prob. 1QCh. 39 - Prob. 2QCh. 39 - Prob. 3QCh. 39 - Prob. 4QCh. 39 - Prob. 5QCh. 39 - Prob. 6QCh. 39 - Prob. 7QCh. 39 - Prob. 8QCh. 39 - Prob. 9QCh. 39 - Prob. 10Q
Ch. 39 - Prob. 11QCh. 39 - Prob. 12QCh. 39 - Prob. 13QCh. 39 - Prob. 14QCh. 39 - Prob. 15QCh. 39 - Prob. 1PCh. 39 - Prob. 2PCh. 39 - Prob. 3PCh. 39 - Prob. 4PCh. 39 - Prob. 5PCh. 39 - Prob. 6PCh. 39 - Prob. 7PCh. 39 - Prob. 8PCh. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11PCh. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 14PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - Prob. 18PCh. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 21PCh. 39 - Prob. 22PCh. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 28PCh. 39 - Prob. 29PCh. 39 - Prob. 30PCh. 39 - Prob. 31PCh. 39 - Prob. 32PCh. 39 - Prob. 33PCh. 39 - Prob. 34PCh. 39 - Prob. 35PCh. 39 - Prob. 36PCh. 39 - Prob. 37PCh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46PCh. 39 - Prob. 47PCh. 39 - Prob. 48PCh. 39 - Prob. 49PCh. 39 - Prob. 50PCh. 39 - Prob. 51PCh. 39 - Prob. 52PCh. 39 - Prob. 53PCh. 39 - Prob. 54PCh. 39 - Prob. 55PCh. 39 - Prob. 56PCh. 39 - Prob. 57PCh. 39 - Prob. 58PCh. 39 - Prob. 59PCh. 39 - Prob. 60PCh. 39 - Prob. 61PCh. 39 - Prob. 62PCh. 39 - Prob. 63PCh. 39 - Prob. 64PCh. 39 - A diatomic gas molcculc consistsof two atoms of...Ch. 39 - Prob. 66PCh. 39 - Prob. 67PCh. 39 - Prob. 68PCh. 39 - Prob. 69PCh. 39 - Prob. 70PCh. 39 - An old model of a hydrogen atom has the charge e...Ch. 39 - Prob. 72PCh. 39 - Prob. 73P
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- 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…arrow_forwardA proton and an electron are trapped in identical onedimensional infinite potential wells; each particle is in its ground state. At the center of the wells, is the probability density for the proton greater than, less than, or equal to that of the electron?arrow_forwardAn electron that is trapped in a one-dimensional infinite potential well of width L is excited from the ground state to the first excited state. Does the excitation increase, decrease, or have no effect on the probability of detecting the electron in a small length of the x axis (a) at the center of the well and (b) near one of the well walls?arrow_forward
- An electron is in a three dimensional harmonic oscillator potential V (r) .A small electric field, of strength Ez , is applied in the direction. Calculate the lowest order nonzero correction to the ground state energy.arrow_forwardWhat 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 200 pm wide?arrow_forwardA particle of massm in a harmonic oscillator potential with angular frequency w is in the state (1 + {t)쭈 What is (p?) for this particle? mhw 2 O 6mħw O 3mhwarrow_forward
- A particle is confined to the one-dimensional infinite potential well of If the particle is in its ground state, what is its probability of detection between (a) x = 0 and x = 0.25L, (b) x = 0.75L and x = L, and (c) x = 0.25L and x = 0.75L?arrow_forwardThree electrons are trapped in three different one-dimensional infinite potential wells of widths (a) 50 pm, (b) 200 pm, and (c) 100 pm. Rank the electrons according to their ground-state energies, greatest first.arrow_forwardThe ground state energy of a particle of mass m in an infinite potential well is E,. It changes to E,(1+ a x 10-3), when there is a small potential bump of height and width a = L/100, as shown in the figure. The value of a is V. 50ml? to two decimal places). (up V(x) L-arrow_forward
- A particle in one-dimension is in the potental if xl If there is at least one bound state, the minimum depth of the potential is: (a) 8ml? (b) 2ml? 2h?n? (c) me? (d)- me?arrow_forwardIf you double the width of a one-dimensional infinite potential well, (a) is the energy of the ground state of the trapped electron multiplied by 4, 2, , , or some other number? (b) Are the energies of the higher energy states multiplied by this factor or by some other factor, depending on their quantum number?arrow_forwardA proton is confined to a one-dimensional infinite potential well 100 pm wide.What is its ground-state energy?arrow_forward
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