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Chapter 42: Q.54 (page 1237)

The fact that A cancels means that all nuclei have this density. It is a staggeringly large density, roughly 1014 times larger than the density of familiar liquids and solids. One early objection to Rutherford’s model of a nuclear atom was that matter simply couldn’t have a density this high. Although we have no direct experience with such matter, nuclear matter really is this dense .

Short Answer

Expert verified

The Ratio of calcium atoms to barium atoms after 2.5 weeks is 0.37.

Step by step solution

01

N=N0e-λκ Nuclei Density :

01

Ca-47atoms:

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Most popular questions from this chapter

Radioactive isotopes often occur together in mixtures. Suppose a 100gsample contains 131Ba, with a half-life of 12days, and 47Ca, with a half-life of localid="1650485393662" 4.5days. If there are initially twice as many calcium atoms as there are barium atoms, what will be the ratio of calcium atoms to barium atoms localid="1650485404787" 2.5weeks later?

Particle accelerators fire protons at target nuclei so that investigators can study the nuclear reactions that occur. In one experiment, the proton needs to have 20 MeV of kinetic energy as it impacts a 207 Pb nucleus. With what initial kinetic energy (in MeV) must the proton be fired toward the lead target? Assume the nucleus stays at rest

Alpha decay occurs when an alpha particle tunnels through the Coulomb barrier. FIGURE CP42.63 shows a simple one-dimensional model of the potential-energy well of an alpha particle in a nucleus with A ≈ 235. The 15 fm width of this one-dimensional potential-energy well is the diameter of the nucleus. Further, to keep the model simple, the Coulomb barrier has been modeled as a 20-fm-wide, 30-MeV-high rectangular potential-energy barrier. The goal of this problem is to calculate the half-life of an alpha particle in the energy level E = 5.0 MeV. a. What is the kinetic energy of the alpha particle while inside the nucleus? What is its kinetic energy after it escapes from the nucleus? b. Consider the alpha particle within the nucleus to be a point particle bouncing back and forth with the kinetic energy you found in part a. What is the particle’s collision rate, the number of times per second it collides with a wall of the potential? c. What is the tunneling probability Ptunnel ? d. Ptunnel is the probability that on any one collision with a wall the alpha particle tunnels through instead of reflecting. The probability of not tunneling is 1 - Ptunnel. Hence the probability that the alpha particle is still inside the nucleus after N collisions is 11 - Ptunnel 2N ≈ 1 - NPtunnel , where we’ve used the binomial approximation because Ptunnel V 1. The half-life is the time at which half the nuclei have not yet decayed. Use this to determine (in years) the half-life of the nucleus.

Use the potential-energy diagram in Figure 42.8to estimate the ratio of the gravitational potential energy to the nuclear potential energy for two neutrons separated by 1.0fm.

a. What is the smallest value of Afor which there are two stable nuclei? What are they?

b. For which values ofAless than this are there no stable nuclei?
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