Cancer cells are more vulnerable to x and gamma radiation than are healthy cells. In the past, the standard source for radiation therapy was radioactive 60Co, which decays, with a half-life of 5.27 y, into an excited nuclear state of 60Ni. That nickel isotope then immediately emits two gamma-ray photons, each with an approximate energy of 1.2 MeV. How many radioactive 60Co nuclei are present in a 7000 Ci source of the type used in hospitals?

31. Cancer cells are more vulnerable to x and gamma radiation than are healthy cells. In the past, the standard source for radiation therapy was radioactive 60Co, which decays, with a half-life of 5.27 y, into an excited nuclear state of 60Ni. That nickel isotope then immediately emits two gamma-ray photons, each with an approximate energy of 1.2 MeV. How many radioactive 60Co nuclei are present in a 7000 Ci source of the type used in hospitals? (Energetic particles from linear accelerators are now used in radiation therapy.) ______units
32. The half-life of a radioactive isotope is 120 d. How many days would it take for the decay rate of a sample of this isotope to fall to 0.58 of its initial rate? (______units)
33. A radioactive nuclide has a half-life of 24.1 y. What fraction of an initially pure sample of this nuclide will remain undecayed at the end of 78.8 y? _____
34. A certain radioactive nuclide decays with a disintegration constant of 0.0143 h-1. (a) Calculate the half-life (in terms of hours) of this nuclide. What fraction of a sample will remain at the end of (b) 4.64 half-lives and (c) 7.69 days?
a. ______units
b. ______
c. ______
35. Plutonium isotope 239Pu decays by alpha decay with a half-life of 24100 y. How many milligrams of helium are produced by an initially pure 13.5 g sample of 239Pu at the end of 19610 y? (Consider only the helium produced directly by the plutonium and not by any by-products of the decay process.) _____units
36. The cesium isotope 137Cs is present in the fallout from aboveground detonations of nuclear bombs. Because it decays with a slow (30.2 y) half-life into 137Ba, releasing considerable energy in the process, it is of environmental concern. The atomic masses of the Cs and Ba are 136.9071 and 136.9058 u, respectively; calculate the total energy released in such a decay. (_____MeV)
37. The isotope 238U decays to 206Pb with a half-life of 4.47 x 109 y. Although the decay occurs in many individual steps, the first step has by far the longest half-life; therefore, one can often consider the decay to go directly to lead. That is, 238U → 206Pb + various decay products A rock is found to contain 4.17 mg of 238U and 2.760 mg of 206Pb. Assume that the rock contained no lead at formation, so all the lead now present arose from the decay of uranium. How many atoms of (a) 238U and (b) 206Pb does the rock now contain? (c) How many atoms of 238U did the rock contain at formation? (d) What is the age of the rock?
a. _______
b. _______
c. _______
d. _______years
38. A radiation detector records 77 x 102 counts in 1.0 min. Assuming that the detector records all decays, what is the activity of the radiation source in (a) becquerels and (b) nanocuries?
a. _______units
b. _______units
39. A 83 kg person receives a whole-body radiation dose of 2.3 x 10-4 Gy, delivered by alpha particles for which the RBE factor is 12. Calculate (a) the absorbed energy (in terms of mJ) and (b) the dose equivalent.
a. _____MJ
b. _____units
40. During the Cold War, the Premier of the Soviet Union threatened the United States with 4.0 megaton 239Pu warheads. (Each would have yielded the equivalent of an explosion of 4.0 megatons of TNT, where 1 megaton of TNT releases 2.6 × 1028 MeV.) If the plutonium that actually fissioned had been 9.61% of the total mass of the plutonium in such a warhead, what was that total mass? (______kg)