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.
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.
(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.
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_forwardA 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_forward
- When 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_forwardA 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_forward
- If the speed of a proton is measured to be 2.9 × 105 m/s with a precision of 0.70% then what is the maximum precision with which its position could be measured, Ax? How does this uncertainty compare to the size of the proton?arrow_forwardIn Millikan's oil-drop experiment, one looks at a small oil drop held motionless between two plates. Take the voltage between the plates to be 2241 V and the plate separation to be 2 cm. The oil drop (of density 0.81 g/cm3) has a diameter of 4.0 ×10-6 m. Find the charge on the drop, in terms of electron units.arrow_forwardIt is possible for some fundamental particles to temporarily "violate" conservation of energy in a way consistent with the uncertainty principle by creating and quickly reabsorbing another particle. For example, a proton can emit a 7+ particle according to p→n++, where the n represents a neutron. The 7+ has a mass of 140 MeV/c². The reabsorption must occur within a time At consistent with the uncertainty principle. (a) Considering the example shown, by how much energy AE is energy conservation tem- porarily violated? (b) For how long At can the 7+ exist? (c) Assuming that the 7+ is moving at approximately speed of light, how far from the nucleus could it get in the time At? This is the approximate range of the strong nuclear force. (d) Assuming that as soon as one pion is reabsorbed another is emitted, how many pions would be recorded by a "nucleon camera" with a shutter speed of 1 us?arrow_forward
- In solid helium the spacing between atoms is about 3Å . Helium contains 2 protons and 2 neutrons, so the mass of a helium atom is 6.6×10−27 kg. What is the smallest possible energy of a helium atom in solid helium? What temperature (in Kelvin) does this energy correspond with? (Boltzmann's constant is kb=1.38×10−23 J/Karrow_forwardImagine another universe in which the value of Planck’s constant is 0.0663 J . s, but in which the physical laws and all other physical constants are the same as in our universe. In this universe, two physics students are playing catch. They are 12 m apart, and one throws a 0.25 kg ball directly toward the other with a speed of 6.0 m/s. (a) What is the uncertainty in the ball’s horizontal momentum, in a direction perpendicular to that in which it is being thrown, if the student throwing the ball knows that it is located within a cube with volume 125 cm3 at the time she throws it? (b) By what horizontal distance could the ball miss the second student?arrow_forwardWhat is the velocity of an electron with a deBroglie wavelength of 2.74 um ? Give your answer in m/s with no decimal places please.arrow_forward
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