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Chapter 42: Q 6 Conceptual Question (page 1235)
Nucleus A decays into nucleus B with a half-life of 10 s. At
t = 0 s, there are 1000 A nuclei and no B nuclei. At what time
will there be 750 B nuclei?
Therefore, at timethere will be 750 B nuclei.
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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 鈮� 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鈥檚 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 鈮� 1 - NPtunnel , where we鈥檝e 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.
What is the half-life in days of a radioactive sample with 5.0 x 1015
atoms and an activity of 5.0 x 108 Bq?
An unstable nucleus undergoes alpha decay with the release
of 5.52 MeV of energy. The combined mass of the parent and
daughter nuclei is 452 u. What was the parent nucleus?
Calculate (in ) the binding energy per nucleon for and . Which is more tightly bound?
How many half-lives must elapse until (a) 90% and (b) 99% of a radioactive sample of atoms has decayed?
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