Q 5 Conceptual QuestionsExpert-verified
Are the following decays possible? If not, why not?
Therefore, the decays are explained.
The following decays are given:
(a) No, the alpha particle is inserted into the incorrect nucleus.
(b) No, the original nucleus would have to lose four nucleons rather than two.
(d) No, A does not change during beta decay.
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.
Stars are powered by nuclear reactions that fuse hydrogen into helium. The fate of many stars, once most of the hydrogen is used up, is to collapse, under gravitational pull, into a neutron star. The force of gravity becomes so large that protons and electrons are fused into neutrons in the reaction p+ + e- S n + n. The entire star is then a tightly packed ball of neutrons with the density of nuclear matter. a. Suppose the sun collapses into a neutron star. What will its radius be? Give your answer in km. b. The sun’s rotation period is now 27 days. What will its rotation period be after it collapses? Rapidly rotating neutron stars emit pulses of radio waves at the rotation frequency and are known as pulsars
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