Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
error_outline
This textbook solution is under construction.
Students have asked these similar questions
A neutron is confined in a deuterium nucleus (deu-
teron) of diameter 3.1 X 10-15 m. Use the energy-
level calculation of a one-dimensional box to calcu-
late the neutron's minimum kinetic energy. What is
the neutron's minimum kinetic energy according to
the uncertainty principle?
A proton is confined in a uranium nucleus of diameter 7.2 x 10-15 m. Use the energy-level
calculation of a one-dimensional box that has length equal to the nuclear diameter to calculate the
proton's minimum kinetic energy. What is the proton's minimum kinetic energy according to the
uncertainty principle?
A neutron is confined in a deuterium nucleus (deuteron) of diameter 3.1 x 10-15 m. Use the energylevel calculation of a one-dimensional box to calculate the neutron’s minimum kinetic energy. What is the neutron’s minimum kinetic energy according to the uncertainty principle?
Knowledge Booster
Similar questions
- A gas of helium atoms at 273 K is in a cubical container with 25.0 cm on a side. (a) What is the minimum uncertainty in momentum components of helium atoms? (b) What is the minimum uncertainty in velocity components? (c) Find the ratio of the uncertainties in (b) to the mean speed of an atom in each direction.arrow_forwardP17.5 Another important uncertainty principle is encountered in time-dependent systems. It relates the lifetime of a state At with the measured spread in the photon energy AE associated with the decay of this state to a stationary state of the system. "Derive" the relation AE At ≥ h/2 in the following steps. a. Starting from E = p/2m and AE = (dE/dpx)^px, Vx Apx. show that AE = b. Using vx = Ax/At, show that AE At = ApxAx ≥ h/2. c. Estimate the width of a spectral line originating from the decay of a state of lifetime 1.0 × 10s and 1.0 × 10-¹¹ s in inverse seconds and inverse centimeters.arrow_forwardA sodium gas is contained in a cubical container (T=250 K) with one side measuring 25.0 m. a.) What is the minimum uncertainty in momentum components of the sodium atoms? b.) What is the minimum uncertainty in velocity components? c.) Find the ratio of uncertainties in your answer in letter b, to the mean speed of an atom in each direction.arrow_forward
- An effective treatment for some cancerous tumors involves irradiation with "fast" neutrons. The neutrons from one treatment source have an average velocity of 3.5×107 m/s. If the velocities of individual neutrons are known to within 2.0% of this value, what is the uncertainty in the position of one of them? answer in marrow_forwardWhat constraints does the uncertainty principle place on our knowledge of the world? To get a sense of scale, we’ll look at the uncertainty in speed for a confined electron and for a confined dust particle.a. What range of velocities might an electron have if confined toa 0.30-nm-wide region, about the size of an atom?b. A 1.0@mm@diameter dust particle (m ≈ 10-15 kg) is confined within a 5-μm-long box. Can we know with certainty if the particle is at rest? If not, within what range is its velocity likely to be found?arrow_forwardThe decay energy of a short-lived nuclear excited state has an uncertainty of 2.1 eV due to its short lifetime. What is the smallest lifetime (in s) it can have? ____sarrow_forward
- A particle is created in a shower of particle decays. Its velocity is measured to a precision of 50 micrometers/second and its mass is inferred to be (exactly) 6.64×10−27 kg. What is the minimum uncertainty in our knowledge of the particle’s position? Explain.arrow_forwardAn electron is located on a pinpoint having a diameter of 6.11 µm. What is the minimum uncertainty in the speed of the electron?arrow_forwardSuppose Fuzzy, a quantum-mechanical duck, lives in a world in which h = 2 J s. Fuzzy has a mass of 1.90 kg and is initially known to be within a pond 1.00 m wide. (a) What is the minimum uncertainty in the duck's speed? m/s (b) Assuming this uncertainty in speed to prevail for 4.90 s, determine the uncertainty in Fuzzy's position after this time. marrow_forward
- 1. Consider an electron confined in a region of nuclear dimensions (about 5 fm). Find its minimum possible kinetic energy in MeV. Treat this problem as one-dimensional, and use the relativistic relation between E and p. Give your answer to 2 significant figures. (The large value you will find is a strong argument against the presence of electrons inside nuclei, since no known mechanism could contain an electron with this much energy.)arrow_forward1) If you can measure the position of a particle with a precision of gx-1(2n), where λ is the DsBroglic wavelength of the particle, then: a) What is the minimum uncertainty for gp, in terms of the particle's momentum p? b) Would you be surprised if you measured the momentum to be zero? c) Would you be surprised if you measured the momentum to be 2p? d) What is the minimum value gx, in terms of so that g-p?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning