College Physics: A Strategic Approach (4th Edition)
4th Edition
ISBN: 9780134609034
Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher: PEARSON
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Chapter 28, Problem 57P
To determine
The smallest range in the velocity of proton.
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The nucleus of a typical atom is 5.0 fm (1 fm = 10-15 m) in diameter. A very simple model of the nucleus is a onedimensional box in which protons are confined. Estimate the energy of a proton in the nucleus by finding the first three allowed energies of a proton in a 5.0-fm-long box.
The speed of a proton is measured to within an uncertainty of 1 × 103m/s. Calculate the length of the smallest region of space in which the electron can be confined.
Chapter 28 Solutions
College Physics: A Strategic Approach (4th Edition)
Ch. 28 - Prob. 1CQCh. 28 - Prob. 2CQCh. 28 - Prob. 3CQCh. 28 - Prob. 4CQCh. 28 - Prob. 5CQCh. 28 - Prob. 6CQCh. 28 - Prob. 7CQCh. 28 - Prob. 8CQCh. 28 - Prob. 9CQCh. 28 - Prob. 10CQ
Ch. 28 - Prob. 11CQCh. 28 - Prob. 12CQCh. 28 - Prob. 13CQCh. 28 - Prob. 14CQCh. 28 - Prob. 15CQCh. 28 - Prob. 16CQCh. 28 - Prob. 17CQCh. 28 - Prob. 18CQCh. 28 - Prob. 19CQCh. 28 - Prob. 20CQCh. 28 - Prob. 21CQCh. 28 - Prob. 22CQCh. 28 - Prob. 23CQCh. 28 - Prob. 24CQCh. 28 - Prob. 25CQCh. 28 - Prob. 26CQCh. 28 - Prob. 27CQCh. 28 - Prob. 28MCQCh. 28 - Prob. 29MCQCh. 28 - Prob. 30MCQCh. 28 - Prob. 31MCQCh. 28 - Prob. 32MCQCh. 28 - Prob. 33MCQCh. 28 - Prob. 34MCQCh. 28 - Prob. 35MCQCh. 28 - Prob. 36MCQCh. 28 - Prob. 37MCQCh. 28 - Prob. 38MCQCh. 28 - Prob. 1PCh. 28 - Prob. 2PCh. 28 - Prob. 3PCh. 28 - Prob. 4PCh. 28 - Prob. 5PCh. 28 - Prob. 6PCh. 28 - Prob. 7PCh. 28 - Prob. 8PCh. 28 - Prob. 9PCh. 28 - Prob. 10PCh. 28 - Prob. 11PCh. 28 - Prob. 12PCh. 28 - Prob. 13PCh. 28 - Prob. 14PCh. 28 - Prob. 15PCh. 28 - Prob. 16PCh. 28 - Prob. 17PCh. 28 - Prob. 18PCh. 28 - Prob. 19PCh. 28 - Prob. 20PCh. 28 - Prob. 21PCh. 28 - Prob. 22PCh. 28 - Prob. 23PCh. 28 - Prob. 24PCh. 28 - Prob. 25PCh. 28 - Prob. 26PCh. 28 - Prob. 27PCh. 28 - Prob. 28PCh. 28 - Prob. 29PCh. 28 - Prob. 30PCh. 28 - Prob. 31PCh. 28 - Prob. 32PCh. 28 - Prob. 33PCh. 28 - Prob. 34PCh. 28 - Prob. 35PCh. 28 - Prob. 36PCh. 28 - Prob. 37PCh. 28 - Prob. 38PCh. 28 - Prob. 39PCh. 28 - Prob. 40PCh. 28 - Prob. 41PCh. 28 - Prob. 42PCh. 28 - Prob. 43PCh. 28 - Prob. 44PCh. 28 - Prob. 45PCh. 28 - Prob. 46PCh. 28 - Prob. 47PCh. 28 - Prob. 48PCh. 28 - Prob. 49PCh. 28 - Prob. 50PCh. 28 - Prob. 51PCh. 28 - Prob. 52PCh. 28 - Prob. 53PCh. 28 - Prob. 54PCh. 28 - Prob. 55PCh. 28 - Prob. 56PCh. 28 - Prob. 57PCh. 28 - Prob. 58GPCh. 28 - Prob. 59GPCh. 28 - Prob. 60GPCh. 28 - Prob. 61GPCh. 28 - Prob. 62GPCh. 28 - Prob. 63GPCh. 28 - Prob. 64GPCh. 28 - Prob. 65GPCh. 28 - Prob. 66GPCh. 28 - Prob. 67GPCh. 28 - Prob. 68GPCh. 28 - Prob. 69GPCh. 28 - Prob. 70GPCh. 28 - Prob. 71GPCh. 28 - Prob. 72GPCh. 28 - Prob. 73GPCh. 28 - Prob. 74GPCh. 28 - Prob. 75GPCh. 28 - Prob. 76GPCh. 28 - Prob. 77GPCh. 28 - Prob. 78GPCh. 28 - Prob. 79MSPPCh. 28 - Prob. 80MSPPCh. 28 - Prob. 81MSPPCh. 28 - Prob. 82MSPPCh. 28 - Prob. 83MSPPCh. 28 - Prob. 84MSPPCh. 28 - Prob. 85MSPPCh. 28 - Prob. 86MSPPCh. 28 - Prob. 87MSPPCh. 28 - Prob. 88MSPPCh. 28 - Prob. 89MSPPCh. 28 - Prob. 90MSPPCh. 28 - Prob. 91MSPPCh. 28 - Prob. 92MSPP
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- 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_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_forwardThe speed of an electron is measured to within an uncertainty of 2.0 × 104 m/s. What is the size of the smallest region of space in which the electron can be confined?arrow_forward
- Q:-3(a)-An electron moves in the x direction with a speed of 2.8 x 106 m/s. We can measure its speed to a precision of 2 %. With what precision can we simultaneously measure its x coordinate? (b)- Repeat the calculations of the previous example in the case of a pitched baseball (m = 0.135 kg) moving at a speed of (44.5 ms). Again assume that its speed can be measured to a precision of 2%arrow_forwardA nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator are 5e-21 J apart. Use k = 1.4e-23 J/K. When the nanoparticle's energy is in the range 5(5e-21) J to 9(5e-21) J, what is the approximate heat capacity per atom?arrow_forwardProblem 2: Line XY was measured by four parties a, b, c, d. Each party has two measurements as follows: Trial B 91.21 91.27 D 91.20 91.18 91.26 A 1 2 91.25 91.19 91.22 Find the precision of each party and find out which has the highest precision. b. What is the most probable length of XY? a.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_forwardIn an electron microscope, the nonrelativistic electron beam is formed by a setup similar to the electron gun used in the Davisson– Germer experiment. The electrons have negligible kinetic energy before they are accelerated. What accelerating voltage is needed to produce electrons with wavelength 10 pm = 0.010 nm (roughly 50,000 times smaller than typical visible-light wavelengths)?arrow_forwardThe "radius of the hydrogen atom" is often taken to be on the order of about 10-10m. If a measurement is made to determine the location of the electron for hydrogen in its ground state, what is the probability of finding the electron within 10-10m of the nucleus?arrow_forward
- Please Asaparrow_forwardIf 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_forwardAn electron is trapped within a sphere whose diameter is 5.40×10−155.40×10−15 m (about the size of the nucleus of a medium sized atom). What is the minimum uncertainty in the electron's momentum?arrow_forward
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