Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 4, Problem 52P
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In Rutherford scattering we noted that angular momentum is conserved. The angular momentum of the incident αparticle relative to the target nucleus is mv0b where m is the mass, v0 is the initial velocity of the αparticle, and b is the impact parameter. Start with L = r x p and show that angular momentum is conserved, and the magnitude is given by mv0b along the entire path of theα particle while it is scattered by the Coulomb force from a gold nucleus.
ts) We can approximate the 232Th nucleus as a one-dimensional infinite square well
with length L equal to the nuclear radius R = R₁A¹/3, where Ro = 1.2 fm and A is the atomic
mass number.
(a) What is the length of this infinite square well? What is the ground state energy of a
proton (which has mass m₂ = 938.3 MeV/c²) in this infinite square well?
(b) 232Th has 90 protons and 142 neutrons. Assume that all these protons and neutrons
trapped in the infinite square well. How many energy levels of this infinite square well
contain protons? How many energy levels contain neutrons?
Because a nucleon is confined to a nucleus, we can take the uncertainty in its position to be approximately the nuclear radius r. Use the uncertainty principle to determine the uncertainty p in the linear momentum of the nucleon. Using the approximation p =p and the fact that the nucleon is nonrelativistic, calculate the kinetic energy of the nucleon in a nucleus with A = 100.
Chapter 4 Solutions
Modern Physics for Scientists and Engineers
Ch. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10Q
Ch. 4 - Prob. 11QCh. 4 - Prob. 12QCh. 4 - Prob. 13QCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - What fraction of 5-MeV α particles will be...Ch. 4 - Prob. 9PCh. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - Prob. 14PCh. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Prob. 17PCh. 4 - Prob. 18PCh. 4 - Prob. 19PCh. 4 - Prob. 20PCh. 4 - Prob. 21PCh. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 24PCh. 4 - Prob. 25PCh. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Prob. 43PCh. 4 - Prob. 44PCh. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Prob. 56PCh. 4 - Prob. 57PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61P
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- (a) Show that if you assume the average nucleus is spherical with a radius r=r0A1/3, and with a mass at A u, then its density is independent at A. (b) Calculate that density in u/fm3 and kg/m3, and compare your results with those found in Example 31.1 for 56Fe.arrow_forward(a) Calculate the radius of 58Ni, one of the most tightly bound stable nuclei. (b) What is the ratio of the radius of 58Ni to that at 258Ha, one of the largest nuclei ever made? Note that the radius of the largest nucleus is still much smaller than ?le size of an atom.arrow_forward(a) Calculate the energy released in the a decay of 238U. (b) What fraction of the mass at a single 238U is destroyed in the decay? The mass of 234Th is 234.043593 u. (c) Although the fractional mass loss is laws for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?arrow_forward
- Compute the Coulomb repulsion energy between two nuclei of 238U.arrow_forwardWrite the mathematical expression for the radial probability function. The radial probability function for any orbital is zero at the nucleus, it also approaches zero at long distance from the nucleus. Explain why.arrow_forwardA nucleus with even-even nucleons in the ground state is subjected to alpha decay. Calculate the allowed values of total angular momentum ??, parity ?? and hence allowed states of ???? of the daughter nucleusarrow_forward
- a) The pion π0 is a force carrier for the nuclear force. Assuming that this force is descibed by a Yukawa potential, estimate the range of the force from the mass of π0 , which is mπ0 = 135 MeV/c2 b) Sketch a diagram indicating the s-process path from 102Ru to 109Ag. Specify the type ofeach process (i.e. neutron capture, electron capture, beta decays) in the path. c) Consider the five isotopes of Pd with mass number from 104 to 108. For each of these determine whether in stellar nucleosynthesis it can produced via the s-process, the r-process or both. Explain your reasoning.arrow_forwardIn a Geiger-Marsden experiment, calculate the distance of closest approach to the nucleus of Z = 80, when an α-particle of 8 MeV energy impinges on it before it comes momentarily to rest and reverses its direction. How will the distance of closest approach be affected when the kinetic energy of the α-particle is doubled?arrow_forwardStarting from the Clasius-Clapeyron equation, Lo + constant kBT log p and assuming the latent heat of evaporation per gram of water to be constant, and equal to L= 2260 J/g , find the boiling temperature of water in degrees Celcius at a pressure of 50.0 atm. Each oxygen atom has 8 protons and 8 neutrons in its nucleus. The boiling temperature of water at a pressure of 50.0 atm is around 250 °C. How do you account for the difference? R = 8.31 //(mol · K) , m,-1.67x1027 kg , NA=6.02x1023 mol-1arrow_forward
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