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Chapter 42: Q.52 (page 1237)
How many half-lives must elapse until (a) 90% and (b) 99% of a radioactive sample of atoms has decayed?
Use the expression for the activity of the sample present after time t to calculate the age of the sample.
The activity of the sample present after time t is,
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The half-life of 60Co is 5.27 years. The activity of a 60Co
sample is 3.50 x 109 Bq. What is the mass of the sample?
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 graph of binding energy to estimate the total energy released if three nuclei fuse together to form a nucleus.
We’ve noted that fewer than of the known nuclei are stable (i.e., not radioactive). Because nuclei are characterized by two independent numbers, and , it is useful to show the known nuclei on a plot of neutron number versus proton number.
A radioactive tracer is made in a nuclear reactor. When it is delivered to a hospital hours later its activity is . The lowest usable level of activity is .
A. What is the tracer’s half-life?
B. For how long after delivery is the sample usable?
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