Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 39, Problem 39P
To determine
Prove that the electron confined in an atomic nucleus would move with relativistic speed and a proton would move with non-relativistic speed in the same nucleus using uncertainty principle.
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Use the uncertainty principle to show that if an electron were confined inside an atomic nucleus of diameter
2 x 10-15 m, it would have to be moving relativistically, whereas a proton confined to the same nucleus can
be moving nonrelativistically.
(a) The lifetime of a highly unstable nucleus is 10−20 s . What is the smallest uncertainty in its decay energy? (b) Compare this with the rest energy of an electron.
Use the uncertainty principle to show that if an electron were confined inside an atomic nucleus of diameter on the order of 10-14 m, it would have to be moving relativistically, whereas a proton confined to the same nucleus can be moving nonrelativistically.
Chapter 39 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 39.1 - Prob. 39.1QQCh. 39.2 - Prob. 39.2QQCh. 39.2 - Prob. 39.3QQCh. 39.2 - Prob. 39.4QQCh. 39.3 - Prob. 39.5QQCh. 39.5 - Prob. 39.6QQCh. 39.6 - Prob. 39.7QQCh. 39 - Prob. 1PCh. 39 - Prob. 2PCh. 39 - Prob. 3P
Ch. 39 - Prob. 4PCh. 39 - Prob. 5PCh. 39 - Prob. 6PCh. 39 - Prob. 8PCh. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11PCh. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - Prob. 18PCh. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 22PCh. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 30PCh. 39 - Prob. 31PCh. 39 - Prob. 32PCh. 39 - Prob. 33PCh. 39 - Prob. 35PCh. 39 - Prob. 37PCh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40APCh. 39 - Prob. 41APCh. 39 - Prob. 43APCh. 39 - Prob. 44APCh. 39 - Prob. 45APCh. 39 - Prob. 46APCh. 39 - Prob. 47CPCh. 39 - Prob. 48CPCh. 39 - Prob. 49CPCh. 39 - Prob. 50CP
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- Show that p=h and Ef=hf are consistent with the relativistic formula E2=p2c2+m02c2 .arrow_forwardIf the uncertainty in the y -component of a proton's position is 2.0 pm, find the minimum uncertainty in the simultaneous measurement of the proton's y -component of velocity. What is the minimum uncertainty in the simultaneous measurement of the proton's x -component of velocity?arrow_forward(a) The lifetime of a highly unstable nucleus is 10-12 s. What is the smallest uncertainty (in ev) in its decay energy? ev (b) What is the ratio of this energy, AE, to the rest energy of an electron, Erest? ΔΕ Erestarrow_forward
- A nucleus emits a gamma ray of energy 1.2 MeV from a state that has a lifetime of 2.1 ns. What is the uncertainty in the energy of the gamma ray? The best gamma-ray detectors can measure gamma-ray energies to a precision of no better than a few eV. Will this uncertainty be directly measurable?arrow_forwardWhen a particle of mass 9.1 × 10^-28 g in a certain one- dimensional box goes from the n = 5 level to the n = 2 level, it emits a photon of frequency 6.0 × 10^16 /s . Find the length of the box.arrow_forwardOne proton is accelerated through a potential difference of 106 volts and another is accelerated through a potential energy of 1010 volts. For each proton, find the total energy, the momentum (actually find pc in MeV), and the wavelength.arrow_forward
- 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?arrow_forwardIn Davisson and Germer experiment, it was noted that the energy of an electron increases while entering a crystal, reducing its de-Broglie wavelength. Consider a 54 eV electron beam that is aimed at a nickel target. An electron that reaches the target increases its potential energy by 26 eV. What will be the speed and de-Broglic wavelength of clectron inside the nickel target? (b)arrow_forwardA π0 meson is an unstable particle produced in high-energy particle collisions. Its rest energy is approximately 135 MeV, and it exists for a lifetime of only 8.70 × 10-17 s before decaying into two gamma rays. Using the uncertainty principle, estimate the fractional uncertainty Δm/m in its mass determination.arrow_forward
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