Chapter 42: Q 33 Exercise (page 1237)
The doctors planning a radiation therapy treatment have determined that a 100 g tumour needs to receive 0.20 J of gamma
radiation. What is the dose in grays?
Hence, the dose in grays is 2 grays.
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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 ≈ 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.
The technique known as potassium-argon dating is used to date old lava flows. The potassium isotope 40 K has a 1.28-billionyear half-life and is naturally present at very low levels. 40 K decays by two routes: 89% undergo beta-minus decay into 40 Ca while 11% undergo electron capture to become 40 Ar. Argon is a gas, and there is no argon in flowing lava because the gas escapes. Once the lava solidifies, any argon produced in the decay of 40 K is trapped inside and cannot escape. A geologist brings you a piece of solidified lava in which you find the 40 Ar/ 40 K ratio to be 0.013. What is the age of the rock?
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?
Use the graph of binding energy to estimate the total energy released if three 4 He nuclei fuse together to form a 12 C nucleus
What is the energy (in MeV) released in the alpha decay of
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