FUNDAMENTALS OF PHYSICS (LLF)+WILEYPLUS
11th Edition
ISBN: 9781119459132
Author: Halliday
Publisher: WILEY
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Chapter 38, Problem 69P
To determine
To show:
a) The uncertainty in the momentum component is equal to the component itself,
b) Are the measured momentum of 0, 0.5p, 2p, and 12p surprising?
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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 radii of atomic nuclei are of the order of 5.0 * 10-15 m. (a) Estimate the minimum uncertainty in the momentum of a proton if it is confined within a nucleus. (b) Take this uncertainty in momentum to be an estimate of the mag- nitude of the momentum. Use the relativistic relationship between energy and momentum, Eq. (37.39), to obtain an estimate of the ki- netic energy of a proton confined within a nucleus. (c) For a proton to remain bound within a nucleus, what must the magnitude of the (negative) potential energy for a proton be within the nucleus? Give your answer in eV and in MeV. Compare to the potential energy for an electron in a hydrogen atom, which has a magnitude of a few tens of eV. (This shows why the interaction that binds the nucleus together is called the “strong nuclear force.”)
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Chapter 38 Solutions
FUNDAMENTALS OF PHYSICS (LLF)+WILEYPLUS
Ch. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Prob. 5QCh. 38 - Prob. 6QCh. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10Q
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- If the speed of an electron is measured to within an uncertainty of 2.0×10 4 m/s, what wouldbe the size of the smallest region of space in which the electron can be confined? me = 9.11×10 -31kg.arrow_forward(a) Calculate the minimum uncertainty in momentum (expressed in MeV/?) for a proton confined to a nucleus of diameter 5.0 fm. (1 fm = 1 * 10-15 m). (b) A proton (rest mass 938.3 MeV/?2) in a nucleus of radius 6.0 fm has a kinetic energy of 5.6 MeV. If the proton were represented by a de Broglie wave, how many wavelengths could fit across the diameter of that nucleus? (1 fm = 1 * 10-15 m). (c) Electrons (rest mass 0.51 MeV/?2) moving with a speed of 1.60 × 105 m/s are described by a wave packet of width 2.65 nm. What range of values will most likely result from a measurement of the speed of the electrons? Please use:ℎ? 1240 eVnmℏ? 197 eVnmarrow_forward(a) The uncertainty in the y-component of a proton’s position is 2.0 * 10^-12 m. What is the minimum uncertainty in a simultaneous measurement of the y-component of the proton’s velocity? (b) The uncertainty in the z-component of an electron’s velocity is 0.250 m>s. What is the minimum uncertainty in a simultaneous measurement of the z-coordinate of the electron?arrow_forward
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