Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving techinque.

| 50 | Concept Questions Identical body tissues are being irradiated by two types of radiation (e.g., X-rays and protons). (a) If the absorbed doses are the same, which type of radiation, the one with the larger RBE or the smaller RBE, produces the greater biological effect on the tissue? (b) If the two types of radiation have the same RBE, which type, the one that generates the greater absorbed dose or the smaller absorbed dose, produces the greater biological effect? Provide a reason for each answer.
Problem Someone stands near a radioactive source and receives doses of the following types of radiation: rays (20 mrad, RBE = 1), electrons (30 mrad, RBE = 1), protons (5 mrad, RBE = 10), and slow neutrons (5 mrad, RBE = 2). Rank the types of radiation, highest first, as to which produces the largest biologically equivalent dose. Verify that your answers are consistent with your answers to the Concept Questions.

| 51 | Concept Question The definition of the biologically equivalent dose (Equation 32.4) uses the concept of the absorbed dose measured in a unit called the rad. The definition of the absorbed dose measured in a unit called the gray is given by Equation 32.2 as the energy absorbed divided by the mass of the absorbing material. How does one convert from the absorbed dose (in rad) to the absorbed dose (in Gy)?
Problem The biologically equivalent dose for a typical chest X-ray is 2.5 × 10−2 rem. The mass of the exposed tissue is 21 kg, and it absorbs 6.2 × 10−3 J of energy. What is the relative biological effectiveness (RBE) for the radiation on this particular type of tissue?

| 52 | Concept Questions (a) Which of the following are nucleons: protons, electrons, neutrons, -ray photons? (b) In a nuclear reaction, what is meant by the statement “The total number of nucleons is conserved”? (c) Which of the following have electric charge: protons, electrons, neutrons, -ray photons? (d) In a nuclear reaction, what is meant by the statement “The total electric charge is conserved”?
Problem For each of the nuclear reactions listed below, determine the unknown particle :

a. |
b. |
c. |
d. |

| 53 | Concept Questions During a nuclear reaction, whether it is a fission reaction or a fusion reaction, energy is released. (a) Is the total mass of the particles after the reaction greater than, equal to, or less than the total mass of the particles before the reaction? (b) How is this difference in total mass related to the energy released by the reaction?
Problem In one type of fusion reaction a proton fuses with a neutron to form a deuterium nucleus plus a -ray photon: . The masses are (1.0078 u), (1.0087 u), and (2.0141 u). The -ray photon is massless. How much energy (in MeV) is released by this reaction?

| 54 | Concept Question In Example 6 it was determined that 17.6 MeV of energy is released when the following fusion reaction occurs:

(a) Assuming that the two initial nuclei are at rest when the fusion takes place, what does the conservation of linear momentum tell you about how the momentum of the neutron is related to the momentum of the particle ? (b) Which particle has the greater speed, the neutron or the particle? (c) How is the kinetic energy KE related to the magnitude p of the momentum and the mass m of a particle? (d) Assuming that all of the energy E released in the reaction appears as kinetic energy of the neutron and the particle, how is KEn related to ? Account for each of your answers to the Concept Questions.
Problem Determine the kinetic energies of the neutron and the particle. Verify that your answers are consistent with your answers to the Concept Questions.

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