Answered: What is the smallest box in which you…

What is the smallest box in which you can confine an electron if you want to know for certain that the uncertainty in the electron’s speed is no more than 20 m/s?

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 49P: An electron confined to a box has the ground state energy of 2.5 eV. What is the width of the box?

See similar textbooks

Related questions

Q: If the electron is positioned in the region of width 10-12 m then calculate the time constant of the…

A: Given values: Width of the region, ∆x=10-12 m Plank's constant, h=6.626×10-34 J·s Mass of electron,…

Q: What minimum frequency of light is needed to ejectelectrons from a metal whose work function is 4.8…

A: work function, W = 4.8 x10-19 J

Q: As an electron in a one-dimensional box of length 0.600 nm jumps between two energy levels, a photon…

A: Given: The length of box is 0.600 nm. The energy of 8.36 eV.

Q: Electrons are accelerated from rest through an 8000 V potential difference. By what factor would…

A: Given: The potential difference in the first case is 8000 V. The potential difference in the second…

Q: Through what potential difference must an electron be accelerated from rest to have a de Broglie…

A: given that, de-Broglie wavelength is 500 nm, then velocity of electron λ=hmvv=hmλ=6.626×10-34…

Q: The wave function for a quantum particle confined to moving in a one-dimensional box located between…

A: The wave function for a quantum particle confined to moving in a one-dimensional box located between…

Q: An electron is moving with a speed of 5 x 10^6 m/s (± 2 x 10^-2 m/s). Using thisinformation,…

Q: A 1.0 kg ball has a position uncertainty of 0.20 m. What is its minimum momentum uncertainty?…

A: The mass of the ball is m = 1.0 kg. The position uncertainty of the ball is ∆x=0.20 m Assume the…

Q: If an electron's position can be measured to a precision of 3.0 × 10¬8 m, how precisely can its…

Q: Determine the probability of an electron in the region of x = 0.490L and 0.510L in a box of length L…

A: It is given that an electron lies in a certain region.

Q: An electron has a velocity of 610.03 m/s, +/- 0.001 m/s. What is the smallest uncertainty (+/-…

A: Given that, Velocity = 610.03 m/s Accuracy = ±0.001 m/s

Q: A proton is moving with a speed of v = 1.20 x 10° m/s. What is its de Broglie wavelength (in m)?…

Q: An electron is confined to a rigid box that is 1.20nm long. If the electron is in the third excited…

A: The wavelength for the third state (n=4) can be calculated as,

Q: An electron is confined to a region of space of length 0.19 nm— comparable in size to an atom. What…

A: E1=n2h28mL2E1=126.626×10-34 Js289.11×10-31 kg0.19×10-9 m2E1=1.7×10-18 J The first allowed energy is,…

Q: You are able to determine an electron's location within an uncertainty of 430 nm. What is the…

A: This question is based on Heisenberg's Uncertainty principle. The Heisenberg's Uncertainty principle…

Q: An electron in a one-dimensional box has ground-state energy 2.00 eV. What is the wavelength of the…

A: Given: The energy of electron in-ground energy state = 2 eV

Q: An electron confined in a one-dimensional box emits a 200 nm photon in a quantum jump from n = 2 to…

A: The energy of nth state of a particle confined to a one-dimensional box of length L is given by;…

Q: A proton confined in a one-dimensional box emits a 2.0 MeV gamma-ray photon in a quantum jump from n…

Q: What do you understand by the wave-particle duality? Estimate the de Broglie wavelength of an…

Q: An electron confined in a one-dimensional box is observed, at different times, to have energies of…

A: It is a basic problem where quantum mechanics starts to show its nature. It has a particle existing…

Q: An ultrashort pulse has a duration of 8.00 fs and produces light at a wavelength of 557 nm. What are…

A: We know the uncertainty relation between position and momentum given by ∆E.∆t >_ h/4π For minimum…

Q: An electron is trapped in a one-dimensional infinite well of the width 1angstrom. (i) calculate…

A: Given data: The width of the one dimensional well, L=1 Å . (i) The energy of the electron in the…

Q: The electrons in a beam are moving at 18 m/s. (melectron = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s)…

A: Speed of electron, v=18 m/s Mass of electron, m=9.11 × 10-31 kg

Q: A laser produces light of wavelength 255 nm in an ultrashort pulse. What is the minimum duration of…

Q: Suppose the visible light of wavelength i=500 nm position of an is used to determine the electron to…

Q: What is the length of a box in which the minimum energy of an electron is 1.5 x 10-18 J?

A: The energy of a particle in the box is given by, En=n2h28mL2

Q: Two adjacent allowed energies of an electron in a one-dimensional box are 2.0 eV and 4.5 eV. What is…

Q: What is the work function for the metal (in eV), if the maximum wavelength of light to produce…

Q: What is the de Broglie wavelength of a red blood cell with a mass of 1.00 x 10-11 g that is moving…

A: The expression for find wavelength is λ=hmv

Q: In a conductor of size 20 mm x 10 mmx 10 mm, the wavelength of the slowest moving free electron is

A: According to question--- Given data--- size of conductor = 20mm×10mm×10mm. We have to find--…

Q: The general solution of the Schrodinger equation for a particle confined in an infinite square-well…

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: An electron is accelerated from rest through a potential difference of 100 V. What is the de…

A: Given: An electron is accelerated through a potential difference , V = 100 V To determine: The…

Q: An electron is accelerated from rest through a potential difference so that its de Broglie…

A: Given that the de broglie wavelength and We have to determine the value of potential difference.

Q: What is the independent wave function for a particle in a box x=0,L

Q: An elementary particle has a very short lifetime, 1.34 x 101 s. What is the minimum uncertainty with…

Q: An electron is confined between two perfectly reflecting walls separated by the distance 10 x…

A: We have ∆x=10*10-11m. We need to find the lowest energy of the electron using 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: If an electron's position can be measured to a precision of 3.0 × 10¯ m, how precisely can its speed…

A: Given: The precision in the electron's position is 3x10-8 m.

Q: What is the de Broglie wavelength for an electron with speed (a) v = 0.480c and (b) v = 0.960c?

A: Given that: A) Speed of electron, v = 0.480 c B) When, Speed of electron, v = 0.480 c

Q: for the electron Find the momentum of the crystal for the electron if you know that its wavelength…

Question

What is the smallest box in which you can confine an electron if you want to know for certain that the uncertainty in the electron’s speed is no more than 20 m/s?

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

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

Is it possible that when we measure the energy of a quantum particle in a box, the measurement may return a smaller value than the ground state energy? What is the highest value of the energy that we can measure for this particle?
An electron confined to a box has the ground state energy of 2.5 eV. What is the width of the box?
A quantum mechanical oscillator vibrates at a frequency of 250.0 THz. What is the minimum energy of radiation it can emit?
What is the ground state energy (in eV) of a proton confined to a one-dimensional box the size of the uranium nucleus that has a radius of approximately 15.0 fm?
An electron confined to a box of width 0.15 nm by infinite potential energy barriers emits a photon when it makes a transition from the first excited state to the ground state. Find the wavelength of the emitted photon.
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?
If an electron is moving at 2m/s with an uncertainty of 10%, what is the minimum uncertainty in the electron’s position?
An electron confined in a one-dimensional box emits a 200 nm photon in a quantum jump from n = 2 to n = 1. What is the length of the box?
assume that an electron is moving along the x-axis and that you measure its speed to be 20.5*10^6m/s, which can be known with of precision of 0.50%. what is the minimum uncertainty (as allowed by the uncertainty principle in quantum theory )with which you can simultaneously measure the position of the electron along the x-axis?
The positional uncertainty of an electron is 0.020 nm. What is the momentum's least uncertainty, ∆p (b) What is an electron's kinetic energy when its momentum equals this uncertainty (∆p = p)?
An electron has been accelerated by a potential difference of 100 V. If its position is known to have an uncertainty of 1 nm, what is the percent uncertainty (Δp/p×100) of the electron
Two adjacent allowed energies of an electron in a one-dimensional box are 2.0 eV and 4.5 eV. What is the length of the box?